ROMERO C. 2010
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Examining the possible effect of forest area, abundance of snakes and snake species richness on the abundance of short-toed eagle, in Spain. Ciro Patricio Romero March, 2010 Course Title: Geo-Information Science and Earth Observation for Environmental Modeling and Management Level: Master of Science (M.Sc.) Course Duration: September 2008 March 2010 Consortium partners: University of Southampton (UK) Lund University (Sweden) University of Warsaw (Poland) University of Twente (The Netherlands) 2010-23 GEM thesis number: Disclaimer This document describes work undertaken as part of a programme of study at the Faculty of Geo-information Science and Earth Observation of the University of Twente. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the university. Abstract It is a well known fact that short-toed eagle preys on snakes and nests on trees. However, it is unknown how forest area, abundances of different snake species and snake species richness affect the abundance of short-toed eagle. Therefore, path analysis, a method that estimates direct and indirect effects using multiple regression equations, was used to identify and measure the presumed causal relationships that have support on the observed data. The presumed causal relationships were established based on knowledge about natural history, functional hypothesis, professional experience and expert’s intuition. Data about abundance of snakes and short-toed eagles are un-existent. Therefore, relative abundances of snakes and short-toed eagles, estimated based on occurrence data, were used as indirect estimations of abundance. The results revealed that the relative abundances of Malpolon monspesulanus, Rhinechis scalaris, Hemorrhois hippocrepis and Natrix natrix may not have a significant direct effect on the relative abundance of short-toed eagle. Besides, snake species richness does not seem to influence directly the relative abundance of the eagle. Apparently, snake species richness may affect directly only the relative total abundance of snakes, which it seems to affect, directly, the relative abundance of the eagle. Moreover, forest area also seems to affect, directly, the relative abundance of short-toed eagle. Path analysis does not prove or disprove causality. Thereby, a replication of the present research, using data from other countries, could increase the level of certainty that the direct and indirect effects identified and measure in the present thesis may represent causal relationships. Besides, new theories should be tested. Key words: Short-toed eagle, Circaetus gallicus, snake species richness, snakes, forests, kernel density, path analysis. i ii Resumen Es un hecho conocido que el águila culebrera se alimenta de culebras y anida en árboles. Sin embargo, no se conoce como el área de bosques, abundancias de diferentes especies de culebras y la riqueza de especies de culebras afecta la abundancia del águila culebrera. Por lo tanto, un método que estima efectos directos e indirectos usando ecuaciones de regresión múltiple, fue usado para identificar y medir las posibles relaciones causales que tiene soporte en los datos observados. Las posibles relaciones causales fueron establecidas en base a conocimiento de historia natural, hipótesis funcionales, experiencia profesional e intuición de expertos. No existen datos acerca de la abundancia de culebras y águilas culebreras. En consecuencia, abundancias relativas de culebras y águilas culebreras, estimadas en base a observaciones, fueron usadas como mediciones indirectas de abundancia. Los resultados revelaron que las abundancias relativas de Malpolon monspesulanus, Rhinechis scalaris, Hemorrhois hippocrepis y Natrix natrix posiblemente no tienen un efecto directo significativo sobre la abundancia relativa del águila culebrera. Además, la riqueza de especies de culebras no parece influenciar directamente la abundancia del águila. Aparentemente, la abundancia de especies de culebras podría afectar directamente solo la abundancia relativa total de culebras, la cual parece afectar directamente la abundancia relativa del águila. Además, el área de bosques también parece afectar directamente la abundancia relativa del águila culebrera. Análisis de trayectoria no prueba ni niega causalidad. Por lo tanto, una replica del la presente investigación, usando datos de otros países, podría incrementar el nivel de certidumbre de que los efectos directos e indirectos identificados y medidos en la presente tesis pueden representar relaciones causales. Además, nuevas teorías deberían ser evaluadas. Palabras clave: Águila culebrera, Circaetus gallicus, riqueza de especies de culebras, culebras, bosques, kernel, análisis de trayectoria. iii Acknowledgements “Search through me, O God, and know my heart. Examine me, and know my disquieting thoughts, and see whether is in me any painful way, and lead in the way of time indefinite” (Psalms 139: 23-24). “ … , and the appointed time … to give reward to … those fearing your name, the small and the great…” (Revelation 11:18). As worshiper of the creator of the heavens and the Earth, and all the wonderful things that human beings enjoy on Earth, I thank him for the merciful way he protects me and my family: “For this is what Jehovah of armies has said … for he that is touching you is touching my eyeball” (Zechariah 2: 7). My sincere gratitude to the Erasmus Mundus Programme for helping skilled professionals, from developing countries, to continue their academic studies in Europe. My gratitude to the University of Southampton, Lund University, University of Warsaw, and University of Twente for all the knowledge acquired during this Master course. My special thanks to the anonymous members of the selection committee, for having offered to me a place in the course, and to Andre Kooiman, for the efficient way he coordinated it. iv Table of contents 1. Introduction: ………………………………………………………………………………….. 1 1.1. Autoecology of short-toed eagle in Spain:……………………………… 2 1.2. Snake species of Spain:……………………………………………………….. 3 1.3. Research problem: ……………………………………………………………… 3 1.4. Research objectives:……………………………………………………………. 6 1.4.1. General objective: ……………………………………………………… 6 1.4.2. Specific objectives: ……………………………………………………. 6 1.5. Research questions:…………………………………………………………….. 6 1.6. Research hypothesis:…………………………………………………………… 7 1.6.1. Hypothesis 1……………………………………………………………… 7 1.6.2. Hypothesis 2……………………………………………………………… 7 1.6.3. Hypothesis 3……………………………………………………………… 7 1.6.4. Hypothesis 4……………………………………………………………… 7 1.6.5. Hypothesis 5……………………………………………………………… 7 1.7. Research outputs: ……………………………………………………………….. 8 2. Materials and methods: …………………………………………………………………… 9 2.1. Study area: ………………………………………………………………………… 9 2.2. Data description: ………………………………………………………………… 9 2.3. Software requirements: ……………………………………………………… 10 2.4. Field work: ………………………………………………………………………. 10 2.5. Research workflow: ………………………………………………………….. 10 2.6. Occurrence density estimation:…………………………………………… 11 2.7. Estimation of snake species richness: ………………………………….. 13 2.8. Estimation of forest area: …………………………………………………… 13 2.9. Path analysis method: ……………………………………………………….. 13 2.9.1. Data analysis: ………………………………………………………….. 13 2.9.1.1. Linearity transformations:……………………………………. 14 2.9.1.2. Outlier detection: ……………………………………………….. 14 2.9.1.3. Spatial autocorrelation test:………………………………….. 14 2.9.1.4. Normality Assessment: ……………………………………….. 15 2.9.1.5. Multicollinearity assessment:……………………………….. 16 2.9.2. Selection of the method to estimate model parameters:…. 17 2.9.3. Construction of models to be tested: …………………………… 18 v 2.9.4. Estimation of model parameters:………………………………… 22 2.9.5. Model-trimming approach: ……………………………………….. 22 2.9.6. Model comparison:…………………………………………………… 24 2.9.6.1. Incremental fit index:…………………………………………. 24 2.9.6.2. Noncentrality parameter:…………………………………….. 24 2.9.6.3. Expected cross validation index:………………………….. 25 2.9.6.4. Akaike’s information criterion: ……………………………. 25 2.9.7. Validation procedure:……………………………………………….. 25 3. Results: ……………………………………………………………………………………….. 27 3.1. Data analysis: ………………………………………………………………….. 27 3.2. Path analysis: ………………………………………………………………….. 27 3.2.1. Models A:……………………………………………………………….. 28 3.2.2. Models B: ……………………………………………………………….. 34 3.2.3. Model C:…………………………………………………………………. 40 3.2.4. Comparison between models 8A and 8B: ……………………. 41 3.2.5. Evaluation of “Additional model”:…………………………….. 42 3.2.6. Direct and indirect effects of model 8A: ……………………… 43 4. Discussion: ………………………………………………………………………………….. 47 4.1. Effect of snake species richness on the relative abundance of short-toed eagle: …………………………………………………………………………… 47 4.2. Effect of the relative abundances of M. monspesulanus, R. scalaris, H. hippocrepis and N. natrix on the relative abundance of shorttoed eagle: …………………………………………………………………………………… 49 4.3. Effect of forest area on the relative abundance of short-toed eagle:……….. ……………………………………………………………………………… 50 4.4. Data limitations:……………………………………………………………….. 51 5. Conclusions and recommendations: ………………………………………………… 53 6. References: ………………………………………………………………………………….. 55 7. Appendices:…………………………………………………………………………………. 65 vi List of figures Figure 1 1: Short-toed eagle on flight. ……………… …………………………2 Figure 1 2: Short-toed eagle eating. ……………………………………………………. 2 Figure 1 3: Influence diagram of the possible direct and indirect effects of forest area, relative abundance of snakes and snake species richness on the relative abundance of short-toed eagle. …………………………………………………. 5 Figure 2 1: Kernel density interpolation (Fischer et al. 2001). ……………… 12 Figure 2 2: Kernel density estimation (Fischer et al. 2001)………………….. 12 Figure 2 3: Path diagram of model A………………………………………………… 20 Figure 2 4: Path diagram of model B………………………………………………… 20 Figure 2 5: Path diagram of model C………………………………………………… 21 Figure 2 6: Path diagram of “Additional model”. ……………………………….. 21 Figure 2 7: Model-trimming approach (adapted from Derek and Rao, 2000)………………………………………………………………………………………………. 23 Figure 3 1: Model 1A……………………………………………………………………… 28 Figure 3 2: Model 2A……………………………………………………………………… 29 Figure 3 3: Model 3A……………………………………………………………………… 29 Figure 3 4: Model 4A……………………………………………………………………… 30 Figure 3 5: Model 5A……………………………………………………………………… 31 Figure 3 6: Model 6A……………………………………………………………………… 31 Figure 3 7: Model 7A……………………………………………………………………… 32 Figure 3 8: Model 8A……………………………………………………………………… 33 Figure 3 9: Model 1B……………………………………………………………………… 35 Figure 3 10: Model 2B……………………………………………………………………. 35 Figure 3 11: Model 3B……………………………………………………………………. 36 Figure 3 12: Model 4B……………………………………………………………………. 36 Figure 3 13: Model 5B……………………………………………………………………. 37 Figure 3 14: Model 6B……………………………………………………………………. 38 Figure 3 15: Model 7B……………………………………………………………………. 38 Figure 3 16: Model 8B……………………………………………………………………. 39 Figure 3 17: Model 1C……………………………………………………………………. 41 Figure 3 18: Initial “Additional model”…………………………………………….. 42 Figure 3 19: Final “Additional model” ……………………………………………… 43 Figure 3 20: Schematic diagram of model 8A ……………………………………. 46 vii List of tables TABLE 1 1: Snake species of Spain…………………………………………………… 3 TABLE 2 1: Software used in the present thesis. ……………………………….. 10 TABLE 3 1: Evaluation of model 8A compared to a new model that excludes the proposed effect 12. ………………………………………………………… 34 TABLE 3 2: Evaluation of model 8B compared to a new model that excludes the proposed effect 12. ………………………………………………………… 40 TABLE 3 3: Goodness of fit of models 8A and 8B…………………………….. 41 TABLE 3 4: Standardized direct effects of model 8A…………………………. 44 TABLE 3 5: Confidence intervals of standardized direct effects (confidence level = 99%) of model 8A, estimated using bootstrap method. ………………. 44 TABLE 3 6: Confidence intervals of standardized indirect effects (confidence level = 99%) of model 8A, estimated using bootstrap method, in running procedure. …………………………………………………………………………… 44 TABLE 3 7: Confidence intervals of standardized indirect effects (confidence level = 99%) of model 8A, estimated using bootstrap method, in validation procedure…………………………………………………………………………. 45 viii Glossary Autoecology: “The part of ecology that deals with individual species and their reactions to environmental factors” (Unesco-Unep 1983). Chi-square: “A measure of the discrepancy existing between the observed and expected variance-covariance matrices” (Gnanadesikan, 1997). Coefficient of determination: “Is the percentage of variance in one variable that is accounted for by the variance in the other variable” (Salkind, 2004). Correlation coefficient: “Reflects the amount of variability that is shared between two variables and what they have in common” (Salkind, 2004). Covariance: “Is a measure of how much two variables change together” (Gravetter and Wallnau, 2009). Critical ratio (CR): “Is computed dividing the regression weight by its standard error. It indicates how many standard errors above or below zero the regression weight is” (Arbuckle, 2007). Foraging: “Is a cyclical activity in which a behavioural acts lead to the final consumption of each unit of food” (Fox et al. 2001). Goodness of fit of a model: “A measure of the agreement between observed and expected variance-covariance matrices. The expected variancecovariance matrix is determined by a theoretical model” (Cramer and Howitt, 2004). Home range: “Is defined as the area an individual animal uses during its normal activities, such as obtaining food, gaining access to mates, and raising young” (Martin and Handasyde, 1999). Interespecific competition: “Is an interaction in which species inhibit each other such that increased abundance of one species leads to lower growth rates of the other species. Interespecific competition is a major force determining species abundances” (May and McLean, 2007). Kernel density estimation: “Is a non-parametric technique for density estimation in which a known density function (the kernel) is averaged across the observed data points to create a smooth approximation” (Fotheringham et al. 2000). Kurtosis: “The sharpness of a peak on a curve of a probability density function” (Cramer and Howitt, 2004). ix Model: “A model can be defined as a representation of reality that attempts to explain the behaviour of some aspect of it” (Miller and Starr, 1969). Multicollinearity: “is a high level of correlation within the set of explanatory variables… that affects the independence of explanatory variables, and the precision of regression coefficient estimates, as well” (Cramer and Howitt, 2004). Natural history: “Is the science which treats of the earth an all natural objects upon its surface and within its crust” (Tenney, 1866). Outlier: “Is an observation that deviates so much from other observations as to arose suspicion that it was generated by a different mechanism” (Cramer and Howitt, 2004). Path analysis: “An analysis in which three or more variables are ordered by the researcher in terms of their presumed causal relationships” (Cramer and Howitt, 2004). Path coefficient: “Path coefficients represent the direct effects of one variable on another in the path model” (Cramer and Howitt, 2004). “Path coefficients are standardized regression coefficients” (Bryman and Cramer, 2003). Path diagram: “Shows the presumed causal relationships between three or more variables… The causal relationships between the variables are shown on the diagrams by arrows” (Cramer and Howitt, 2004). Path model: “Refers to a causal model in which the relationships between the variables have been represented by magnitudes of effects along paths connecting the variables in the model” (Cramer and Howitt, 2004). Regression coefficient: “Is the coefficient or any regressor in a regression equation” (Cramer and Howitt, 2004). Regurgitated pellet: “All indigestible materials are compacted in the stomach, of many birds of prey, into a pellet, which is regurgitated”(Peeters and Peeters, 1997). Significance level: “The significance level α of the test of a statistical hypothesis Ho is the probability of rejecting Ho when it is true” (Cramer and Howitt, 2004) In path analysis the significance level (P) indicates the probability that the critical ratio is different from zero (Arbuckle, 2007). Skewness: “A form of asymmetry in an unimodal frequency d distribution. The distribution is positively skewed more that 50% of elements lie bellow x the mean, and negatively skewed when more than 50% of elements lie above the mean” (Cramer and Howitt, 2004). Spatial autocorrelation: “Describes how an attribute is distributed over space – to what extent the value of the attribute in one zone depends on the values of the attribute in neighbouring zones”(Fotheringham et al. 2000). Species richness: “Is the diversity of species within an ecological community” (Dyke, 2008). Squared multiple correlation: “Measures the proportion of the observed total variability in an specific response that is accounted for by its regression on the remaining responses, and hence provides a measure of common or shared variance” (Gnanadesikan, 1997). Standard error of a parameter: “Measures how sensitive the estimate of the parameter is to changes in a few observations in the sample” (Schroeder et al. 1986). Structural Equation Modelling: “Is a confirmatory, multivariate technique that looks at causal relationships between variables in a diagrammatic form” (Foster et al. 2006). Variance: “Is the average squared distance from the mean” (Gravetter and Wallnau, 2009). Variance-covariance matrix: “Is made up of variance terms on the diagonal and covariance terms on the off-diagonal” (Schumacker and Lomax, 1996). xi xii 1. Introduction: Short-toed eagle (Circaetus gallicus) has a wide distribution in southern and central Europe (Martinûa and Katzirûb, 1999). However, since the 19th century its populations have been declining in several European regions. There is not a unique explanation about the possible causes of its decline (Gil and Pleguezuelos, 2001). Nowadays it is considered a rare species in many European countries (Barbaro et al. 2003, Birdlife International, 2004, Sacchia et al. 2004, Valevski, 2008, Berezovikov et al. 2009). The low reproductive rate and high diet specialization make short-toed eagle vulnerable to extinction (Morbioli, 2001). Considering that snakes are the main preys of short-toed eagle, any change in the populations of snakes could affect the population of the eagle. In Europe, many snake species have specialized requirements of habitat and food, which make them vulnerable (Filippi and Luiselli, 1999, O’shea, 2005, Edgar and Bird, 2005, Santos et al. 2008). Several snake species are threatened by extinction (Ujvari et al. 2002, Edgar and Bird, 2005, O’shea, 2005, Santos et al. 2008), and 19 to 27 snake species require active management for their conservation, mainly as a consequence of land use change (Greene, 2000, Santos et al. 2008). Climate change could worsen that situation (O’shea, 2005, Santos et al. 2008). In Spain, snake species are not only threatened by land use change, but also by excessive use of pesticides and introduction of exotic species (Marquez and Lizana, 2007). As a consequence, in the last decade, several snake species have experienced a retreat in their distribution (Mañosa, 2003, Marquez and Lizana, 2007, Pleguezuelos et al. 2007, Santos et al. 2008). The decrease in the population of snakes is not the only factor that could affect the abundance of short-toed eagle. Considering that short-toed eagle nests on forests, (Sanchez-Zapata and Calvo, 1999) changes in forest area could also affect its population. Europe has experienced a long and continuous process of deforestation (Goudie, 2006). During the last century many European countries have made considerable efforts to stop it (Palo and Vanhanen, 2000). However, deforestation is still one of the main environmental problems of many European countries (Schnabel, 2001), included Spain (Geeson et al. 2002, Borzel, 2003). 1 1.1. Autoecology of short-toed eagle in Spain: Short-toed eagle is a temporal inhabitant of Spain, where it breeds. In winter it migrates, through the Straight of Gibraltar, to the savannah, in the south of the Sahara desert (Bildstein, 2006, Agostini and Mellone, 2008). During migration it displays a passive flight taking advantage of thermals (Agostini et al. 2002). When it comes back to Spain, since March to April, it tends to occupy the same territories (Ontiveros, 2005), mainly areas with patches of forests where it nests (SanchezZapata and Calvo, 1999). Around May and June the female incubates, for 40 days, a unique egg. Sixty to eighty days later the small eagle leaves the nest. It reaches the adulthood after 4 years. It can live 17 years in freedom. (Cramp and Simmons, 1980, Darawshi, 2007). Short-toed eagle has short toes and a pointed heel (Breuil et al. 1998), which explains its specialized diet (Breuil et al. 1998, Morbioli, 2001). At least 80% of its diet is composed by snakes, reason why it is called Snake-eagle (Bernard, 2003, Malafosse, 2009). The rest of its diet is composed by small birds, rodents, squirrels, insects and hedgehogs (Forschler, 2000, Malafosse, 2009). There is scientific evidence that short-toed eagle has some immunity to snake poison (Darawshi, 2007). On top of that, the assemblage of feathers provides it an extra protection. The eagle localizes its preys from air (Ontiveros, 2005). Small preys are eaten on flight. Big snakes are killed and eaten on the floor (Breuil et al. 1998). Figure 1 1: Short-toed eagle on flight. Figure 1 2: Short-toed eagle eating. Image source: / 2 1.2. Snake species of Spain: Spain has 13 snake species. Ten of them pertain to the family Colubridae, and three to the family Viperidae (See TABLE 1-1) (Galan, 2004, Ontiveros, 2005, Pleguezuelos, 2005, Brito, 2006, Martinez-Freira, 2009). TABLE 1 1: Snake species of Spain. Family Scientific name Hemorrhois hippocrepis Hierophis viridiflavus Coronella austriaca Coronella girondica Macroprotodon brevis Zamenis longissimus Rhinechis scalaris Malpolon monspesulanus Natrix maura Natrix natrix Vipera aspis Vipera latastei Vipera seoanei Colubridae Viperidae Pictures of the 13 snake species are included in Appendix 7.3. 1.3. Research problem: The distribution of specialist feeders is expected to coincide with the distribution of their preys (Newton, 1998). However, it is not clear how snake species richness and abundances of different snake species affect the abundance of short-toed eagle (Moreno-Rueda and Pizarro, 2007). Moreno-Rueda and Pizarro (2007) found that snake species richness had a contribution predicting the probability of occurrence of short-toed eagle, in south-eastern Spain. The authors mentioned two possible explanations for this result. Firstly, it could be that each short-toed eagle specializes on different preys; thereby, more snake species would attract more individuals (See figure 1-3, arrow 1). Secondly, snake species richness could be directly related to the total abundance of snakes (Moreno-Rueda and Pizarro, 2007), which could have an 3 effect on the abundance of the eagle (Vlachos and Papageorgiou, 1994, Ontiveros, 2005, Moreno-Rueda and Pizarro, 2007) (See figure 1-3, arrows 2 and 3). Gil and Plaguezuelos (2001) found that in south-eastern Spain the snake species Malpolon monspesulanus, Rhinechis scalaris, and Hemorrhois hippocrepis constituted the main preys of short-toed eagle (See Figure 1-3, arrows 4, 5 and 6). However, in other areas a different snake species is reported to be its main prey. It is reported that in Dadia forest (north-eastern Greece), the snake Natrix natrix is the favourite prey of short-toed eagle (Bakaloudis et al. 1998). In Landes de Gascogne forests (south-western France), the main prey of short-toed eagle is N. natrix (Barbaro et al. 2003). Also, in eastern Slovakia, N. natrix is reported to be one of the main preys of short-toed eagle (Danko et al. 2007). Therefore, it is possible that N. natrix is an important prey of short-toed eagle in Spain (See figure 1-3, arrow 7). It is also possible that the combination of the abundance of the ‘main preys’ together affect the abundance of the eagle. M. monspesulanus is an ophidiophagous snake, which indicates that it preys on other snakes (Pleguezuelos, 2009, Feriche, 2004, Santos et al. 2008). Pianka (2000) thinks that when a predator preys on dominant species, it reduces the competition allowing the presence of more species. Thereby, it is likely that the abundance of M. monspesulanus affects snake species richness (See Figure 1-3, arrow 8), which as stated before, could affect the abundance of the eagle. The abundance of snakes is not the only factor that could affect the abundance of short-toed eagle. The eagle needs forests for nesting. In consequence, forest area could also affect the abundance of the short-toed eagle (Sanchez-Zapata and Calvo, 1999) (See Figure 1-3, arrow 12). Moreover, forests could be important for snakes as well. Many snake species depend directly on forests either as refuge or source of food (Galan, 2004, Pleguezuelos, 2005, Brito, 2006, Martinez-Freira, 2009). Thereby, forest area could have a direct effect on snake species richness and total abundance of snakes (See Figure 1-3, arrows 10 and 11), which could affect, as mentioned before, the abundance of short-toed eagle. Data about the abundance of snake species and short-toed eagles in Spain are unexistent. Thereby, relative abundances based on occurrence data were used. The most appropriate way to represent the possible influence of forest area, relative abundance of snakes and snake species richness on the relative abundance of shorttoed eagle is through an influence diagram (See Figure 1-3). This diagram is meant to understand the broad structure of a system (Pidd, 1996). 4 Figure 1 3: Influence diagram of the possible direct and indirect effects of forest area, relative abundance of snakes and snake species richness on the relative abundance of short-toed eagle. Legend: + Positive correlation. In order to examine how forest area, relative abundance of snakes and snake species richness affect the relative abundance of short-toed eagles it is necessary to incorporate all the possible effects into a formal and well-structured explanatory model (Pidd, 1996). Explanatory models are based on theory, and their function is to understand underlying mechanisms and processes (DeVries et al. 1998, Skitmore and Marson, 1999, Lucertini et al. 2004). The prior knowledge incorporated into explanatory models enhances their stability and the interpretability of results (Leeuw, 1986, Skitmore and Marson, 1999). Path analysis is a very useful explanatory method to model presumed causal relationships among independent and dependent variables. On top of that, it allows some variables to be dependent making it possible to identify and measure not only possible direct effects but also possible indirect effects (Keane, 1993, Raykov and Marcoulides, 2000). Therefore, path analysis can contribute to analyze the way in which forest area, relative abundance of snakes and snake species richness could affect the relative abundance of short-toed eagle. In path analysis, the influence diagram of Figure 1-3 is called path diagram. 5 1.4. Research objectives: 1.4.1. General objective: Examine the possible influence of forest area, relative abundance of snakes and snake species richness on the relative abundance of short-toed eagle (See Figure 13). 1.4.2. Specific objectives: • Examine the possibility that snake species richness affect, directly or indirectly, the relative abundance of short-toed eagle. • Examine the possibility that the relative total abundance of snakes affect, directly or indirectly, the relative abundance of short-toed eagle. • Examine the possibility that the relative abundance of the ‘main preys’ of short-toed eagle (Malpolon monspesulanus, Rhinechis scalaris, and Hemorrhois hippocrepis) affect the relative abundance of short-toed eagle. • Examine the possibility that the relative abundance of Natrix natrix affect, directly, the relative abundance of short-toed eagle. • Examine the possibility that forest area affect, directly or indirectly, the relative abundance of short-toed eagle. 1.5. Research questions: • Has snake species richness any direct or indirect effect on the relative abundance of short-toed eagle? • Has the relative total abundance of snakes any direct or indirect effect on the relative abundance of short-toed eagle? • Has the relative abundance of the ‘main preys’ of short-toed eagle (Malpolon monspesulanus, Rhinechis scalaris, and Hemorrhois hippocrepis) any direct or indirect effect on the relative abundance of short toed eagle? 6 • Has the relative abundance of Natrix natrix a direct effect on the relative abundance of short-toed eagle? • Has forest area any direct or indirect effect on the relative abundance of short-toed eagle? 1.6. 1.6.1. Research hypothesis: Hypothesis 1. H0 = Snake species richness has not any direct or indirect effect on the relative abundance of short-toed eagle. 1.6.2. Hypothesis 2. H0 = The relative total abundance of snakes has not any direct or indirect effect on the relative abundance of short-toed eagle. 1.6.3. Hypothesis 3. H0 = The relative abundances of the ‘main preys’ of short-toed eagle (Malpolon monspesulanus, Rhinechis scalaris, and Hemorrhois hippocrepis) have no effect on the relative abundance of short-toed eagle. 1.6.4. Hypothesis 4. H0= The relative abundance of Natrix natrix has no direct effect on the relative abundance of short-toed eagle. 1.6.5. Hypothesis 5. H0= Forest area has not any direct or indirect effect on the relative abundance of short-toed eagle. 7 1.7. Research outputs: • Discussion about the conflicts or agreements between the theories used to develop the hypothesis, and the results. • Ecological interpretation of the proposed effects that, according to the results, could affect significantly the relative abundance of short-toed eagle. • Recommendations of specific studies that should be carried out to increase the existent knowledge about the factors that affect the abundance of short toed eagle. 8 2. Materials and methods: 2.1. Study area: The study area was Spain. The country has a total area of 499,542 km2 (Dobson, 2006). Spain was selected due to the apparent stable population of short-toed eagle in that country (Gil and Pleguezuelos, 2001, Sacchia et al. 2004), and the large and recent occurrence data of short-toed eagles and snakes that the Spanish Ministry of Environment has collected (Inventario Nacional de Biodiversidad 2007, PerezMellado and Cortazar, 2007). The mentioned occurrence data and the spatial information of Spanish forests available in Corine 2000 (Corine Land Cover 2009) could contribute to analyze the possible influence of forest area, relative abundance of snakes and snake species richness on the relative abundance of short-toed eagle. 2.2. Data description: In the first trimester of 2000, the Ministry of Environment of Spain (MMA) began collecting occurrence data from recent provincial inventories and biodiversity projects, in order to create the inventory of reptiles of Spain. However, for 3711 cells (10 x 10 km) of the country there was no data. By April of 2002 the MMA had finished sampling the mentioned cells (Perez-Mellado and Cortazar, 2007). Besides, with the purpose of creating an inventory of breeding birds of the country, occurrence data of short-toed eagles, for the whole country, were collected during 5 years of field work organized by MMA, from 1998 to 2002. All habitats of each cell (10 x 10 km) were sampled. Breeding season was taken into account to decide the dates when each cell had to be visited (Inventario Nacional de biodiversidad 2007). The occurrence data for short-toed eagle and the 13 snake species present in Spain are accessible online on the website of the Global Biodiversity Information Facility Network: http://data.gbif.org, with an accuracy of 7,000m. Spatial information of Spanish forests is available, in raster format, in Corine 2000. This product was generated by the European Environment Agency using satellite data, aerial photography, topographic maps, medium-scale thematic maps and statistical information of land cover. The spatial resolution of the product is 100 x 100m. Corine Land Cover 2000 and a detailed description of the methodology used 9 to generate the product are accessible on the website of the European Environment Agency: http://dataservice.eea.europa.eu (Corine land cover 2009). 2.3. Software requirements: Several software packages were used for the preparation and analysis of the data: TABLE 2 1: Software used in the present thesis. Software Description ArcGIS Desktop: GIS software SPSS Statistical software Amos (Student version) Software for path analysis Excel Calculation sheets 2.4. Field work: Path diagrams are constructed based on the available knowledge about natural history, functional hypothesis, professional experience and expert’s intuition (Carrascal, 2001). Thereby, the main activity during fieldwork was to discuss the proposed effects of Figure 1-3 with experts in short-toed eagle and herpetologists, in order to incorporate new possible effects based on their professional experience and intuition. Besides, it was fundamental to get a rapid view of the habitats in which short-toed eagle forages and nests, before starting the modelling work. 2.5. Research workflow: Path analysis is a powerful tool to analyze presumed causal relationships. However, as all statistical methods, its power depends on the fulfilment of assumptions. Therefore, a sequence of steps was necessary to be certain that the data fitted the conditions of the method. Firstly, the occurrence data were transformed, using kernel density estimator, into relative abundances, forest area was calculated based on Corine 2000, and snake species richness was created adding up snake species presences. Secondly, a linearity test was performed for each pair of variables involved in proposed direct effects and, when necessary, transformations were done. Thirdly, the possible presence of outliers was analyzed. Fourthly, a spatial 10 autocorrelation index was computed and tested for significance. Fifthly, a normality assessment was carried out to check the distribution of the data. Sixthly, a multicollinearity test was carried out. Finally, the possible direct and indirect effects were incorporated into a model, which was tested and assessed. 2.6. Occurrence density estimation: Kernel density estimator was used to estimate the relative abundances of snakes and short-toed eagles. The relative abundances of snakes and short-toed eagles were created using occurrence data, under the assumption that as the abundance of a species increases, the amount of occurrences of that species increases as well. The relative abundance (%) of the thirteen snake species, estimated using kernel density, are presented in Appendix 7.4. The relative total abundance of snakes was created summing up the relative abundances of the thirteen snake species of Spain. A spatial resolution of 10 x 10km was used as output for all density estimations. Occurrence data do not reveal the fact that the intensity of occurrence of any species varies gradually in the borders of its distribution (Bowman and Azzalini, 1997). In other words, they do not reflect the true distribution of a population (Cerrito, 2007). Kernel density estimator is a non-parametric method with powerful capabilities to estimate the true probable distribution, even with noisy data (Fischer et al. 2001, Elith et al. 2006). Kernel density estimator is widely used to estimate the relative abundance of a species using occurrence data (Schenone et al. 2004, Tellmann et al. 2008, Mendes et al. 2009). Kernel density estimator fits a curved surface around each known location, to interpolate its whole neighbourhood, established by the bandwidth. Thereby, the interpolated values are lower than the center cell, and decrease with the distance. Each time a kernel if fitted, it moves until the whole study area has been interpolated (See Figure 2-1). The new value of each location is estimated summing up all the kernel surfaces that overlay it (See Figure 2-2) (Silverman, 1986, Fischer et al. 2001, Cerrito, 2007). The way in which kernel density (f) is estimated is described below: 1 n  x − xi  f(x) =  ∑ K nh i =1  h  Where, h is the bandwidth and K is the kernel function (Gaussian). 11 Figure 2 1: Kernel density interpolation (Fischer et al. 2001). Figure 2 2: Kernel density estimation (Fischer et al. 2001). As stated above, the bandwidth is a scaling factor that determines the size of the neighbourhood that influences each site; thereby, controlling the smoothness of the density estimate (Gerard and Schucany, 1998, Fischer et al, 2001, Kostaki, 2004). Least squares cross-validation was used to estimate the optimum bandwidth. The method uses a process of cross-validation to minimize the integrated squared error, which is the difference between the estimated and true density functions (Wand and Jones, 2000). The true density function is unknown; thereby, an approximation is used (Silverman, 1986). 12 2.7. Estimation of snake species richness: The occurrence data of each snake species was reclassified to represent presence or absence in each cell (10 x 10km). Snake species richness was estimated adding up the presences of all snake species. 2.8. Estimation of forest area: Forest area was computed counting all the cells 100 x 100m of the class forests of Corine 2000, contained inside each cell 10 x 10km of the country. 2.9. Path analysis method: Path analysis is a special case of Structural Equation Modelling designed to examine presumed causal relationships among a set of three or more variables (Asher, 1983, Goob, 2001, Oliveira et al. 2002, Cramer and Howitt, 2004). The method assumes a linear relationship between variables (Asher, 1983, Goob, 2001, Oliveira et al. 2002). Contrary to regression, which treats all explanatory variables as independent, path analysis allows some explanatory variables to be dependent, making possible to estimate direct and indirect effects (Keane, 1993). Path analysis estimates standardized direct effects, called path coefficients (standardized regression coefficients), using multiple regression equations (Byrne, 2001, Bryman and Cramer, 2003, Khsrowpour, 2002). Indirect effects are estimated based on multiplications of direct effects, according to the path of the indirect effect (Asher, 1983). Path analysis does not prove causality, but highlights the presumed causal relationships that are not contradicted by the data (Wadsworth, 1993, Grace and Pugesek, 1998, Oliveira et al. 2002). 2.9.1. Data analysis: In path analysis, knowledge about the characteristics of the data is critical to estimate unbiased model parameters. Consequently, several steps were needed: 13 2.9.1.1. Linearity transformations: Considering that path analysis assumes linear relationships between variables, linearity was tested plotting the dependent and independent variables. When the points did not seem to be distributed around a straight line it was considered as an indication of potential non-linearity in the data (Jordan, 1992, Schumacker and Lomax, 1996, Quinn and Keough, 2002). A linearization process was carried out using the method ‘Ladder of transformations’ proposed by Tukey (1977). This method includes 8 different transformations: y3, y2, y1, Sqrt y, log y, y-1, y-2 and y-3. Pearson correlation coefficients were estimated to select the transformation that better linearized the data (Salkind, 2004). Transformations do not alter the relations between the variables; they only change the scale of the variables (Stamatis, 2001, Quinn and Keough, 2002). 2.9.1.2. Outlier detection: The possible presence of outliers was analyzed inspecting normal probability plots. The main idea of looking at normal probability plots was to detect values that could not be logically explained (Kuniavsky, 2003, Meyers et al. 2006). Outliers have to be eliminated to avoid bias in the estimations (Schumacker and Lomax, 1996). 2.9.1.3. Spatial autocorrelation test: The presence of spatial autocorrelation is one of the characteristics of the datasets that could cause bias in the estimation of model parameters (Singer and Willett, 2003). The method most commonly used to evaluate spatial autocorrelation is Moran’s I (Orland, 1988, Shekhar and Xion, 2008). The method compares the values of a variable at each location with values of the same variable at other locations. In general terms, Moran’s I is the ratio: similarity of pairs over total variation: I= NΣiΣj Wi, j(Xi X)(Xj X) (ΣiΣj Wi, j) Σi(Xi X) 2 14 Where, N is the number of cases, X is the mean value of variable X at locations i and j, and Wi,j is the weight applied to the comparison between the values at i and j, which is inversely proportional to the distance between the two locations (Shekhar and Xion, 2008). In order to test the significance of the spatial autocorrelation, a Z score was estimated: ZI = Where, 2.9.1.4. E [I ] = −1 (n − 1) and I − E[I ] V [I ] [ ] [ ] V [I ] = E I 2 − E I 2 Normality Assessment: Several approaches were taken to evaluate normality in the data. Normal probability plots were created (Morris, 1993, Mendenhall and Beaver, 1994, Thode Jr., 2002, Norman and Streiner, 2002, Marques de Sa, 2007). Shapiro-Wilks test was used to check if the residuals are normally distributed. Shapiro-Wilks test evaluates if the sample comes from a normally distributed population (Norman and Streiner, 2002). The way Shapiro-Wilks test is computed is presented below: N  ∑ ai (x n −i +1 − xi )  i =1  W= N _ 2   ∑  xi − x   i =1  2 Where, coefficient ai is fixed for a given sample size and is calculated based on analytical expressions. W value was tested for significance. 15 However, with large sample sizes, powerful tests as Shapiro-Wilks test tend to reject the assumption of normality even when the deviation from normality is minor. Therefore, skewness and kurtosis were also used to evaluate the distribution of the data, and particularly to estimate the degree of non-normality in the data sets (Hancock and Mueller, 2006). A deviation from normality is considered extreme when skewness is higher than 2 and kurtosis is higher than 7 (Pugesek et al. 2003, Hancock and Mueller, 2006). Skewness measures the symmetry of the distribution curve, and kurtosis its peakedness (Kerr et al. 2002):  ∑ z4 Kurtosis =   n  Skewness =  −3    ∑ z3     n    Where, z is the distance, measured in standard deviations, from each observation to the mean. 2.9.1.5. Multicollinearity assessment: Multicollinearity tests prevent the user from including in the model variables that are interdependent. Multicollinearity could cause errors in the estimation of the model parameters, and increase the standard errors of the estimates (Huan et al. 2002, Grewal et al. 2004). Variance inflation factor (VIF) was used to test multicollinearity. VIF estimates the strength of the linear relationship between two explanatory variables: VIF = 1 1− R2 Where, R2 is the coefficient of determination for the regression of one of the independent variables on all the other independent variables (Grewal et al. 2004). By rule of thumb, VIF values higher than 10 are considered unacceptable levels of collinearity (Forthofer et al. 2006). The problem of multicollinearity may be 16 compensated through a large sample size (Grewal et al. 2004). However, considering that the problems with multicollinearity are difficult to mitigate, unacceptable levels of collinearity were excluded from the analysis using the following procedure: The variable with highest collinearity was eliminated and VIF was computed again. Then, that variable was restored and the variable with second highest collinearity was eliminated and VIF computed again. Finally, that variable was restored and the variable with third highest collinearity was eliminated and VIF estimated again. The main purpose of this cyclic process was to know what sets of variables could be included in a model in order to avoid unacceptable levels of collinearity. 2.9.2. Selection of the method to estimate model parameters: There are several methods to estimate model parameters. The selection of the method is critical to compute unbiased estimates. Maximum Likelihood (ML) and Generalized Least-Squares (GLS) are the most common methods. Asymptotically Distribution-free (ADF) is rarely used (Singer and Willett, 2003). ADF gets more accurate estimates than ML or GLS only when the sample sizes are larger than 5000, the models are very simple and the distribution of the data is extremely deviated from normality. ML give accurate estimates only when the data are normally and independently distributed (Hoyle, 1995, Marcoulides, 2000). GLS yields unbiased estimates when autocorrelation is present in the data (Berry and Feldman, 1985, Barreto and Howman, 2006). GLS estimates a variance-covariance matrix based on observations that are not meant to be spatially independent (Dormann et al. 2007, Rahbek, 2007). This method minimizes a weighted function of the squared residuals giving low weight to the residuals associated to observations with large disturbances as a consequence of autocorrelation (Kennedy, 1992). In other words, when autocorrelated residuals are present in the datasets, the minimization of the weighted sum of squared residuals carried out by GLS allows computing unbiased estimates (Kennedy, 1992, ElShaarawi and Piegorsch, 2002, Singer and Willett, 2003, Ismail, 2005). The weighted sum of squared residuals is: N ∑ i =1 ( yf − yi ) σ 2i 17 2 Where, yf is the regression estimate, yi is the actual observation, and uncertainty of each observation (yi). σ 2 is the As stated above GLS aims to find a regression line with the lowest weighted sum of squared residuals. Then, N ∑ (a1 + a 2 x1 − yi )2 σ 2i i =1 Where, a1 is the intercept, and a2 is the slope. However, the weighted sum of squared residuals is created assigning to each residual a weight inversely proportional to its size (Kennedy, 1992). Although GLS assumes that the data is normally distributed, when the distribution of the data is not extremely deviated from normality GLS still gives accurate estimates. Extreme kurtosis is more probable to pose problems to GLS that extreme skewness (Cutance and Ecob, 1987, Raycov and Marcoulides, 2000, Byrne, 2001, Pugesek et al. 2003, Hardy and Bryman, 2004). Consequently, considering that the data was significantly autocorrelated and kurtosis was not extreme, GLS method was selected to estimate model parameters (Hoyle, 1995, Pugesek et al. 2003, Rao et al. 2008). 2.9.3. Construction of models to be tested: As a consequence of multicollinearity, it was not possible to evaluate the proposed effects included in the influence diagram of Figure 1-3 using a unique model. Instead four different models, called A, B, C, and “Additional model” were constructed: The high correlation between relative total abundance of snakes and relative abundance of Malpolon monspesulanus (r = 0.787), and between relative abundance of Rhinechis scalaris and the relative abundance of M. monspesulanus (r = 0.938) caused unacceptable levels of collinearity. The high correlation between relative abundance of R. scalaris and relative abundance of M. monspesulanus was also detected by Gil and Pleguezuelos (2001) in South-eastern Spain. They think that the correlation is caused by preference for similar habitats. 18 As a consequence of the collinearity problems explained above, it was not possible to include the proposed effect of the relative abundance of M. monspesulanus on the relative abundance of short-toed eagle (See Figure 1-3, arrow 4) and the proposed effect of the relative total abundance of snakes on the relative abundance of shorttoed eagle (See Figure 1-3, arrow 3) together in the same model. In order to evaluate both proposed effects, models A and B were needed. Model A excludes the proposed effect of the relative abundance of M. monspesulanus on the relative abundance of short-toed eagle (See Figure 2-3), and model B excludes the proposed effect of the relative total abundance of snakes on the relative abundance of shorttoed eagle (See Figure 2-4). In other words, models A and B include the same variables. Models A and B just differ in the proposed effect that was dropped to avoid unacceptable levels of collinearity. The specification of models A and B copes with unacceptable levels of collinearity avoiding the presence of proposed effects 3 and 4 together in the same model. However, it is possible that the best fitting model is actually a combination of final models A and B. Therefore, it is necessary to construct a model that includes proposed effects 3 and 4 together. This model, called “additional model” copes with unacceptable levels of collinearity excluding from the analysis the proposed effect 5, which is the effect of the relative abundance of R. scalaris on the relative abundance of short-toed eagle (See Figure 2-6). The only purpose of Model C is to evaluate if the sum of the relative abundances of the ‘main preys’ of short-toed eagle has a significant effect on the relative abundance of short-toed eagle (See Figure 2-5). 19 Figure 2 3: Path diagram of model A Figure 2 4: Path diagram of model B 20 Figure 2 5: Path diagram of model C. Figure 2 6: Path diagram of “Additional model”. 21 2.9.4. Estimation of model parameters: Before running path analysis, to remove the effect of using different units, dependent and independent variables were standardized to a mean of zero and standard deviation of 1 (Wadsworth, 1993, Oliveira et al. 2002). Then, path coefficients for all proposed effects were estimated using Generalized Least-Squares (GLS). In order to estimate confidence intervals of path coefficients, a bootstrap method was used with 2000 bootstrap samples. Bootstrapping is a statistical method to derive robust standard errors and confidence intervals of path coefficients. The method performs a successive analysis of random samples with replacement from the full sample (Byrne, 2001, Arbuckle, 2007). Other parameters estimated by path analysis were: squared multiple correlations and Chi-square. The squared multiple correlation (R2) measures the variability of the dependent variable that is accounted for by its explanatory variables (Oliveira et al. 2002). R2 = Ryx1x2 = r 2 yx1 + r 2 yx 2 − 2ryx1 ryx rx1x 2 1 − r 2 x1x 2 Chi-square (x2) measures how much the implied (reproduced) and sample (observed) variance-covariance matrices of the path model differ. The difference between both matrices is stored as residual matrix. As the residual values of the residual matrix increase decreases the goodness of fit of the model (Schumacker and Lomax, 1996, Raycov and Marcoulides, 2000, Goob, 2001). x2 = I − S Where, I is the implied or estimated variance-covariance matrix, and S is the sample or observed variance-covariance matrix. 2.9.5. Model-trimming approach: After running path analysis not all the proposed effects were significant. Therefore, it was necessary to eliminate insignificant effects using a model-trimming approach: The model was re-specified eliminating the proposed effect with lowest path 22 coefficient; then, the model was run to estimate again the path coefficients. This procedure was repeated until all the remaining effects had a significant contribution in the model (See Figure 2-7). In other words, the mentioned cyclic procedure was stopped only when Chi-square and the four indices of fit indicated that having eliminated a proposed effect worsened the fit of the model. Besides, a decline of the squared multiple correlation after having eliminated a proposed effect was also an indication that the proposed effect could have a contribution in the model. Eliminating insignificant effects, one by one, using a systematic approach, balances type I and II errors (Byrne, 2001, Khsrowpour, 2002). Figure 2 7: Model-trimming approach (adapted from Derek and Rao, 2000). 23 2.9.6. Model comparison: The comparison between the models A and B with best fit was carried out subtracting the Chi-square of the first model from the Chi-square of the second model, and this value was tested for significance (Albright and Park, 2008). Besides, four indices of fit were used to contribute in the evaluation of the models: Incremental fit index (NCP), Expected cross validation index (ECVI), Incremental fit index (IFI) and Akaike’s information criterion (AIC) (Schumacker and Lomax, 1996, Byrne, 2001). The purpose of using several indices of fit was to increase the level of certainty when selecting the best model. The mentioned indices of fit are described below: 2.9.6.1. Incremental fit index: Incremental fit index (IFI) measures how much better the model fits the data compared to the baseline model. The baseline model is called independence model or null model. In the baseline model all path coefficients are zero. The index ranges from 0 to 1. Zero means that the fit of the proposed model equals the baseline model, and 1 indicates a perfect fit (Bollen, 1986, Schumacker and Lomax, 1996, Byrne, 2001, Loehlin, 2004). IFI = (x (x 2 2 n ull null − x 2 mod el − df mod el ) ) Where, x2 is Chi-square. 2.9.6.2. Noncentrality parameter: Noncentrality parameter (NCP) measures the discrepancy between the hypothesized model and the true model (Byrne, 2001). In other words, it estimates the extent to which the proposed model fails to fit the observed data. The lower the NCP index the better the fit of the model (Schumacker and Lomax, 1996, Raycov and Marcoulides, 2000, Byrne, 2001). ( NCP = max 0, x 2 − df 24 ) Where, x2 is Chi-square and df are degrees of freedom, which are calculated subtracting the number of parameters to be estimated from the total number of sample moments (sample variances and covariances). 2.9.6.3. Expected cross validation index: Expected cross validation index (ECVI) calculates the discrepancy between the fitted and expected covariance matrices (Browne and Cudeck, 1993, Byrne, 2001). ECVI evaluates if a model is likely to cross-validate across sub-samples of the same size. Simple models with good fit are more likely to cross-validate than more complex models. The lower the ECVI index the better the fit of the model (Schumacker and Lomax, 1996, Raycov and Marcoulides, 2000, Loehlin, 2004). x 2 mod el q +2 ECVI = (n − 1) (n − 1) Where, x2 is Chi-square and q is the number of parameters to be estimated. 2.9.6.4. Akaike’s information criterion: Akaike’s information criterion (AIC) compares the fit of the proposed model with the fit of the original covariance matrix. It addresses the issue of parsimony in the model fit taking into account the goodness of fit and the number of estimated parameters. The lower the AIC index the better the fit of the model (Schumacker and Lomax, 1996, Raycov and Marcoulides, 2000, Byrne, 2001, Loehlin, 2004). AIC = x 2 mod el + 2q Where, x2 is Chi-square and q is the number of parameters to be estimated. 2.9.7. Validation procedure: The replication approach is the most reliable method to validate a path model. The models were run with half of the data, randomly selected, and the other half was used for validation (Schumacker and Lomax, 1996, Pidd, 1996). Each stage of the 25 path analysis procedure was validated (including the different tests used to analyze the data). During the model trimming process, the validation procedure aimed to prevent eliminating proposed effects that did have a contribution in the model. Besides, the estimation of confidence intervals of path coefficients and four indices of fit contributed in the validation process. Even when bootstrapping works as validation procedure, the software “Amos”, used in the present thesis, estimates confidence intervals only for path coefficients and standard errors. However, it was also important to validate other path parameters such as squared multiple correlations, Chi-square and indices of fit, which justifies to have split the data to create running and validation procedures as indicated above. 26 3. Results: 3.1. Data analysis: The analysis revealed the characteristics of the data. Firstly, the inspection of the normal probability plots (See Appendix 7.1.3.) indicates that there are not extreme values that could not be logically explained. Secondly, most of the proposed effects included in the influence diagram of Figure 1-3 were not linear. The transformation that was used for each proposed effect is reported, in bold letters, in Appendix 7.1.1. All selected transformations had a significant correlation at a confidence level of 99% (2-tailed). Thirdly, the spatial autocorrelation test that was carried out revealed that all the evaluated variables of the path diagram are significantly spatial autocorrelated. Appendix 7.1.2 shows the Moran’s I index and significance levels. Fourthly, the normal probability plots and normality test show that the explanatory variables are not normally distributed. However, the low values of skewness and kurtosis revealed that the non-normality is not severe. Skewness, kurtosis, normality test and normal probability plots are reported in Appendix 7.1.3. Finally, the collinearity test shows that the relative total abundance of snakes, relative abundance of Rhinechis scalaris and the relative abundance of Malpolon monspesulanus have high VIF caused by high correlations between the relative abundance of M. monspesulanus and the relative abundance of R. scalaris (r = 0.938), and between the relative abundance of M. monspesulanus and the relative total abundance of snakes (r = 0.787). Appendix 7.1.4 shows the VIF for all the variables, and the way in which acceptable levels of collinearity were achieved. 3.2. Path analysis: The process of eliminating insignificant effects mentioned on the model trimming section, heading 2.9.5, was performed using the path coefficients displayed in Appendix 7.2. However, in order to clarify and emphasize that a proposed effect was eliminated only if both, running and validation procedures, indicated that the proposed effect had the lowest contribution in the model (lowest path coefficient). Each path coefficient of the running procedure was compared with the corresponding path coefficient of the validation procedure. The highest value of each proposed effect was displayed in the path diagrams, inside parenthesis. The proposed effect with lowest path coefficient is displayed with red numbers (See 27 below figures). Besides, the confidence interval of the lowest path coefficient, estimated using bootstrapping, is included below each figure. The path diagrams label each possible effect with a number from 1 to 12. Standardized direct effects, standard errors, critical ratios (computed dividing the regression coefficient by its standard error) and significance levels of critical ratios are included in Appendix 7.2. 3.2.1. Models A: As stated in heading 2.8.3., model A was constructed dropping the possible effect of the relative abundance of Malpolon monspesulanus on the relative abundance of short-toed eagle, in order to avoid unacceptable levels of collinearity. The initial A model was called 1A. Figure 3 1: Model 1A The path coefficient of the proposed effect 7 had a confidence interval of -0.053 to 0.030 in the running procedure, and -0.075 to 0.009 in the validation procedure, with a confidence level of 99%. A new model was re-specified deleting the proposed effect 7. 28 Figure 3 2: Model 2A The path coefficient of the proposed effect 8 had a confidence interval of -0.121 to 0.050 in the running procedure, and -0.151 to 0.031 in the validation procedure, using a confidence level of 99%. A new model was re-specified deleting the proposed effect 8. Figure 3 3: Model 3A 29 The path coefficient of the proposed effect 5 had a confidence interval of -0.017 to 0.127 in the running procedure, and -0.012 to 0.119 in the validation procedure, with a confidence level of 99%. A new model was re-specified deleting the proposed effect 5. Figure 3 4: Model 4A The path coefficient of the proposed effect 6 had a confidence interval of -0.056 to 0.062 in the running procedure, and -0.053 to 0.065 in the validation procedure, using a confidence level of 99%. A new model was re-specified deleting the proposed effect 6. 30 Figure 3 5: Model 5A The path coefficient of the proposed effect 10 had a confidence interval of -0.029 to 0.064 in the running procedure, and -0.055 to 0.041 in the validation procedure, using a confidence level of 99%. A new model was re-specified deleting the proposed effect 10. Figure 3 6: Model 6A 31 The path coefficient of the proposed effect 11 had a confidence interval of 0.118 to 0.269 in the running procedure, and 0.106 to 0.269 in the validation procedure, with a confidence level of 99%. A new model was re-specified deleting the proposed effect 11. Figure 3 7: Model 7A The squared multiple correlation of snake species richness in model 6A is 0.036 in the running procedure and 0.037 in the validation procedure, which indicates that around 3% of the variability of snake species richness was accounted for by forest area. In other words, forest area had no significant effect on snake species richness. Path analysis shows that the proposed effect 1 had the least contribution in model 7A. The path coefficient of the proposed effect 1 had a confidence interval of -0.282 to -0.090 in the running procedure, and -0.298 to -0.097 in the validation procedure, using a confidence level of 99%. A new model was re-specified deleting the proposed effect 1. 32 Figure 3 8: Model 8A Observing the squared multiple correlation of the relative abundance of short-toed eagle, in model 8A, can be observed that having eliminated the proposed effect 1 increased around 2% the squared multiple correlation of the relative abundance of short-toed eagle from 0.278 to 0.285 in the running procedure, and from 0.270 to 0.277 in the validation procedure. In other words, snake species richness had no effect on the relative abundance of short-toed eagle. Path coefficients of model 8A revealed that the proposed effects 2, 3, 9 and 12 could have a contribution in the model (See Appendix 7.2.1.8.). The proposed effect 12 has the lowest path coefficient. However it contributes explaining some of the variability of the relative abundance of short-toed eagle. If this proposed effect were eliminated, the squared multiple correlation of the relative abundance of short-toed eagle, Chi-square and the four indices of fit would worsen (See TABLE 3-1): 33 TABLE 3 1: Evaluation of model 8A compared to a new model that excludes the proposed effect 12. Running procedure Validation procedure Model 8A Without Model 8A Without effect 12 effect 12 Chi-square 500.889 657.811 541.943 686.858 2 R of short-toed eagle 0.285 0.201 0.277 0.202 IFI 0.682 0.666 0.582 0.576 NCP 494.889 535.943 650.811 679.858 ECVI 0.268 0.286 0.348 0.359 AIC 518.889 559.943 673.811 702.858 Higher values of the index of fit IFI indicate better fit than lower values. Lower values of the indices of fit NCP, ECVI and AIC indicate better fit than higher values. Therefore, the four indices of fit reveal a better fit of model 8A compared to a new model that excludes the proposed effect 12. Besides, the Chi-square differences between model 8A and a model without effect 12 were 156.9 in the running procedure and 144.9 in the validation procedure, which are much higher than the 24.32 Chi-square predicted by the Chi-square probability table, with 7 degrees of freedom, which indicates that all the proposed effects of model 8A may have a contribution in the model. 3.2.2. Models B: As stated in heading 2.8.3., a model B was constructed dropping the proposed effect of the relative total abundance of snakes on the relative abundance of short-toed eagle, in order to avoid unacceptable levels of collinearity. The initial B model was called 1B. 34 Figure 3 9: Model 1B The path coefficient of the proposed effect 6 had a confidence interval of -0.021 to 0.074 in the running procedure, and -0.060 to 0.033 in the validation procedure, with a confidence level of 99%. A new model was re-specified deleting the proposed effect 6. Figure 3 10: Model 2B The path coefficient of the proposed effect 5 had a confidence interval of -0.184 to 0.010 in the running procedure, and -0.175 to 0.02 in the validation procedure, with 35 a confidence level of 99%. A new model was re-specified deleting the proposed effect 5. Figure 3 11: Model 3B The path coefficient of the proposed effect 8 had a confidence interval of -0.071 to 0.041 in the running procedure, and -0.093 to 0.019 in the validation procedure, with a confidence level of 99%. A new model was re-specified deleting the proposed effect 8. Figure 3 12: Model 4B 36 The path coefficient of the proposed effect 11 had a confidence interval of -0.131 to -0.001 in the running procedure, and -0.190 to -0.044 in the validation procedure, with a confidence level of 99%. A new model was re-specified deleting the proposed effect 11. Figure 3 13: Model 5B The path coefficient of the proposed effect 7 had a confidence interval of -0.186 to 0.057 in the running procedure, and -0.209 to -0.084 in the validation procedure, with a confidence level of 99%. A new model was re-specified deleting the proposed effect 7. 37 Figure 3 14: Model 6B The path coefficient of the proposed effect 10 had a confidence interval of -0.107 to -0.020 in the running procedure, and -0.135 to -0.043 in the validation procedure, with a confidence level of 99%. A new model was re-specified deleting the proposed effect 10. Figure 3 15: Model 7B 38 The path coefficient of the proposed effect 1 had a confidence interval of -0.256 to 0.087 in the running procedure, and from -0.252 to -0.077 in the validation procedure, with a confidence level of 99%. A new model was re-specified deleting the proposed effect 1. Figure 3 16: Model 8B After having eliminated the proposed effect 1, the squared multiple correlation of the relative abundance of short-toed eagle dropped from 0.245 to 0.233 in the running procedure and from 0.242 to 0.229 in the validation procedure, which indicates that less than 2% of the variability of the relative abundance of short-toed eagle was accounted for by snake species richness. In other words, snake species richness had no significant effect on the relative abundance of short-toed eagle. Path coefficients of model 8B reveal that the proposed effects 2, 4, 9 and 12 could have a contribution in the model (See Appendix 7.2.2.8.). The proposed effect 12 has the lowest path coefficient. However it contributes explaining some of the variations of the relative abundance of short-toed eagle. If this proposed effect were eliminated, the squared multiple correlation of the relative abundance of short-toed eagle, Chisquare and indices of fit would worsen (See TABLE 3-2): 39 TABLE 3 2: Evaluation of model 8B compared to a new model that excludes the proposed effect 12. Running procedure Validation procedure Model 8B Without Model 8B Without effect 12 effect 12 595.598 Chi-square 545.451 657.811 686.858 R2 of short-toed eagle 0.233 0.201 0.229 0.202 IFI 0.654 0.582 0.633 0.576 NCP 539.451 650.811 589.598 679.858 ECVI 0.291 0.348 0.314 0.359 AIC 563.451 673.811 613.598 702.858 Higher values of the index of fit IFI indicate better fit than lower values. Lower values of the indices of fit NCP, ECVI and AIC indicate better fit than higher values. Therefore, the four indices of fit reveal a better fit of model 8B compared to a new model that excludes the proposed effect 12. Besides, the Chi-square differences between model 8B and a model without effect 12 were 112.36 in the running procedure and 91.26 in the validation procedure, which are much higher than the 24.32 Chi-square predicted by the Chi-square probability table, with 7 degrees of freedom, which indicates that all the proposed effects of model 8B may have a contribution in the model. 3.2.3. Model C: As stated in heading 2.8.3., model C was constructed exclusively to test if the relative abundance of the ‘main preys’ of short-toed eagle had a significant effect on the relative abundance of short-toed eagle. The initial model was called 1C. 40 Figure 3 17: Model 1C The path coefficient of the proposed effect 4,5,6 had a confidence interval of -0.072 to 0.083 in the running procedure, and -0.069 to 0.086 in the validation procedure, with a confidence level of 99%. Thereby, the relative abundance of “main preys” of short-toed eagle had not a significant direct effect on the relative abundance of short-toed eagle; therefore, no contribution in the model. 3.2.4. Comparison between models 8A and 8B: Chi-square and four indices of fit were used to compare models 8A and 8B, in order to know which one fits the data better. TABLE 3 3: Goodness of fit of models 8A and 8B Model 8A Running Validation procedure procedure Chi-square 500.889 541.943 Degrees of freedom 6 6 IFI 0.682 0.666 NCP 494.889 535.943 ECVI 0.268 0.286 AIC 518.889 559.943 41 Model 8B Running Validation procedure procedure 545.451 595.598 6 6 0.654 0.633 539.451 589.598 0.291 0.314 563.451 613.598 Higher values of the index of fit IFI indicate better fit than lower values. Lower values of the indices of fit NCP, ECVI and AIC indicate better fit than higher values. Therefore, the four indices of fit reveal a better fit of model 8A compared to model 8B. Besides, Chi-square of model 8B is significantly worse than Chi-square of model 8A, with a probability of 99%. The Chi-square difference between both models is 45.00 in the running procedure and 53.66 in the validation procedure. Which are higher than the 24.32 Chi-square predicted by the Chi-square probability table, with 6 degrees of freedom, which indicates that model 8A fits the data significantly better than model 8B. 3.2.5. Evaluation of “Additional model”: As stated in heading 2.9.3. in order to analyze if the best fitting model is model 8A or a combination of model 8A and 8B, a model called “Additional model” was constructed. Figure 3-18 shows the initial “Additional model”, and Figure 3-19 shows the final “Additional model”, after the process of model trimming. The final “Additional model” is the same than model 8A. Thereby, the best fitting model is model 8A, and not a combination of models 8A and 8B. The detailed modeltrimming process is included in Appendix 7.2.4. Figure 3 18: Initial “Additional model” 42 Figure 3 19: Final “Additional model” 3.2.6. Direct and indirect effects of model 8A: Standardized direct effects of model 8A are presented in TABLE 3-4, and its confidence intervals are included in TABLE 3-5. Standardized indirect effects of model 8A and its confidence intervals are presented in TABLES 3-6 and 3-7. The final 8A model is presented in Figure 3-20 as schematic diagram, and includes squared multiple correlations (R2) for running and validation procedures. A description of the table headings is shown below: SDE = Standardized direct effects. SIE = Standardized indirect effects. SE = Standard errors of the regression coefficients. CR = Critical ratios (Regression coefficient/standard error). P = Significance level of the critical ratios. Arrow = Proposed direct effect. Snake species richness Relative abundance of M. monspesulanus = Indirect effect of snake species richness on the relative abundance of Malpolon monspesulanus. 43 Snake species richness Relative abundance of C. gallicus = Indirect effect of snake species richness on the relative abundance of Circaetus gallicus (short-toed eagle). TABLE 3 4: Standardized direct effects of model 8A. 2 3 9 12 Running procedure SDE 0.784 0.437 0.872 0.308 SE 0.129 0.286 0.007 1.505 CR 53.621 20.924 67.946 13.574 Validation procedure P <0.001 <0.001 <0.001 <0.001 SDE 0.796 0.430 0.882 0.304 SE 0.122 0.266 0.007 1.548 CR 56.377 21.030 72.067 13.277 P <0.001 <0.001 <0.001 <0.001 TABLE 3 5: Confidence intervals of standardized direct effects (confidence level = 99%) of model 8A, estimated using bootstrap method. Running procedure Validation procedure 2 3 9 12 Lower bound 0.756 0.372 0.848 0.249 Upper bound 0.809 0.503 0.890 0.376 SE P 0.009 <0.001 0.024 <0.001 0.007 <0.001 0.023 <0.001 Lower bound 0.772 0.359 0.861 0.244 Upper bound 0.819 0.487 0.899 0.363 SE P 0.010 <0.001 0.025 <0.001 0.008 <0.001 0.023 <0.001 TABLE 3 6: Confidence intervals of standardized indirect effects (confidence level = 99%) of model 8A, estimated using bootstrap method, in running procedure. Running procedure Indirect effect SIE Snake species richness Relative abundance of M. monspesulanus Snake species richness Relative abundance of C. gallicus Lower Upper SE P bound bound 0.683 0.659 0.705 0.008 <0.001 0.342 0.289 0.398 0.025 <0.001 44 TABLE 3 7: Confidence intervals of standardized indirect effects (confidence level = 99%) of model 8A, estimated using bootstrap method, in validation procedure. Validation procedure Indirect effect Lower Upper SIE SE P bound bound Snake species richness Relative abundance of M. 0.702 0.681 0.723 0.009 <0.001 monspesulanus Snake species richness 0.342 0.287 0.390 0.021 <0.001 Relative abundance of C. gallicus 45 Figure 3 20: Schematic diagram of model 8A 46 4. Discussion: 4.1. eagle: Effect of snake species richness on the relative abundance of short-toed Path analysis revealed that, apparently, snake species richness has not a direct effect on the relative abundance of short-toed eagle, which could mean that each short-toed eagle does not specializes on different preys, as Moreno-Rueda and Pizarro (2007) thought. It also revealed that it is possible that snake species richness affect the relative total abundance of snakes. In fact, Moreno-Rueda and Pizarro (2007) noticed that in their study area, in south-eastern Spain, zones where snake species richness was higher, ophidian abundance was higher as well. The possible effect of snake species richness on the relative total abundance of snakes could indicate that competition among snake species is low. Spanish snake species prey on a wide range of preys (Regalado, 2004, Santos, 2004, Santos and Pleguezuelos, 2004), which could keep a low interespecific competition. On top of that, it is possible that snakes reduce competition for food with other snake species becoming active at a different time of the day (Moreno-Rueda and Pizarro, 2007). Besides, path analysis revealed that the relative total abundance of snakes could affect directly the relative abundance of short-toed eagle. In fact, Bakaloudis et al (1998) mention that Dadia forest, north-eastern Greece, supports the highest density of reptiles in Europe, and a very high density of short-toed eagles. The effect of the relative total abundance of snakes on the relative abundance of short-toed eagle could indicate that short-toed eagle is a generalist that feeds on many snake species according to their local abundance. Indeed, when Gil and Pleguezuelos (2001) analyzed the diet of short-toed eagle they found a correlation between the presence of Malpolon monspesulanus, Rhinechis scalaris and Hemorrhois hippocrepis in short-toed eagle’s pellets, and the abundance of those species in the study area. However, the effect of the relative total abundance of snakes on the relative abundance of short-toed eagle was not strong as expected, considering the relevance of food availability for predators (Newton, 1998). The strength of the relationship could have several possible explanations: Firstly, it is liable that not all snake species have the same probability to be captured by short-toed eagle. For example: Natrix maura spends most of the time in water bodies (Bakaloudis et al. 1998), Malpolon monspesulanus could get more exposed due to specific thermoregulation needs (Pleguezuelos, 2009), snakes could become less accessible in areas with dense 47 vegetation (Bakaloudis, 2009). Secondly, even though short-toed eagle has physiological adaptations as short-toes and a pointed heel to capture snakes (Breuil et al. 1998) it seems that when lizards, rodents and other small animals are abundant, the eagle does not miss the opportunity to get extra fat (Darawshi, 2007). Fat is the fuel that makes the long migration possible (Agostini et al. 2002, Faaborg, 2002). For example, Darawshi (2007) mentions that it is common to see, in Israel, groups of short-toed eagles hunting rodents, in agricultural fields, during plowing and harvesting activities. Under those specific agricultural events rodents constitute the main preys of short-toed eagle. The relative total abundance of snakes could not only affect the relative abundance of short-toed eagle, but also the relative abundance of Malpolon monspesulanus, which could indicate that M. monspesulanus is also a generalist that preys on many snake species according to their local abundance. However, apparently, the inclusion of M. monspesulanus in the estimation of the relative total abundance of snakes over-estimated the possible effect as shown in the additional analysis of Appendix 7.5. M. monspesulanus, as short-toed eagle, does not prey exclusively on snakes. It is reported that M. monspesulanus preys also on small mammals and birds (Pleguezuelos, 2009). Therefore, the stronger effect of the relative total abundance of snakes on the relative abundance of M. monspesulanus, compared to the effect of the relative total abundance of snakes on the relative abundance of short-toed eagle, could be an indication that accessibility to preys is not an important factor for M. monspesulanus as it could be for short-toed eagle. However, it could also indicate that the relative total abundance of snakes is a more relevant factor for M. monspesulanus than for short-toed eagle. Short-toed eagle requires not only preys but also forests for nesting, while M. monspesulanus nests on many kinds of habitats (Pleguezuelos, 2009). However, considering that path analysis does not prove causality, the effect of the relative total abundance of snakes on the relative abundances of short-toed eagle and M. monspesulanus could indicate not only that short-toed eagle and M. monspesulanus may feed on many snake species according to their local abundance, as stated before. The relative total abundance of snakes could be correlated to the total abundance of snakes and their common preys (small rodents for example) together, which could suggest that the total abundance of snakes and their common preys together could be the variable affecting the relative abundances of short-toed eagle and M. monspesulanus. 48 4.2. Effect of the relative abundances of M. monspesulanus, R. scalaris, H. hippocrepis and N. natrix on the relative abundance of short-toed eagle: Path analysis revealed that it is not so viable that any of the snake species, that were considered as possible main preys of short-toed eagle, have a significant effect on the relative abundance of the eagle. This finding could be the reason why Niamir (2009) could not increase the predictive power of a short-toed eagle distribution model, using the availability of the three ‘main preys’ of short-toed eagle. Malpolon monspesulanus, Rhinechis scalaris and Hemorrhois hippocrepis are the biggest and most abundant snakes of south-eastern Spain (Gil and Pleguezuelos, 2001). The method to evaluate the diet of short-toed eagle, used by Gil and Pleguezuelos (2001), in south-eastern Spain, consists in analyzing regurgitated pellets. This method makes possible to identify the parts of the preys that have not been digested (Mersmann et al. 1992, Vlachos and Papageorgiou, 1994, Redpath et al. 2001). However, there is evidence that diurnal raptors can digest even bones (Houston and Copsey, 1994, Bochenski et al. 1997, Katzner et al. 2006), which, apparently, adds bias to the method. Mersmann et al. (1992) tested the method using captive bald eagles. They conclude that the method over-represents medium sized and big sized preys, and under-represents small preys. Scientific research carried out by Redpath et al. (2001) and Jordan (2003) confirms that the analysis of regurgitated pellets under-represents small preys. Besides, according to Peeters and Peeters (1997) even preys of the same size may not be equally digestible. In consequence, the method “analysis of regurgitated pellets”, used by Gil and Pleguezuelos (2001), could have identified the snake species that are difficult to digest by the digestive juices of short-toed eagle, instead of the preys that the eagle preys on. Path analysis revealed that the relative abundance of M. monspesulanus, apparently, has no effect on snake species richness, consequently, no indirect effect on the relative abundance of short-toed eagle. Pianka (2000) mentions that predators as the ophidiophagous snake M. monspesulanus could reduce competition among preys allowing the presence of more species. However, generalizations, in ecology, do not mention the set of circumstances that need to be present for the generalization to become true (Cotgreave and Forseth, 2002, Jorgensen and Fath, 2007, Pickett et al. 2007). It is likely that the mentioned generalization is valid only under high interespecific competition. Interespecific competition takes place when different species require the same limiting resource (Cronk and Fennessy, 2001). In Spain, snake species feed on a wide range of preys (Regalado, 2004, Santos, 2004, Santos and Pleguezuelos, 2004), which could keep a low interespecific competition. On top 49 of that, apparently, snakes reduce competition for food with other snake species becoming active at a different time of the day (Moreno-Rueda and Pizarro, 2007). 4.3. Effect of forest area on the relative abundance of short-toed eagle: In Spain, forests are important habitats for several snake species. However, they are not the only habitat for those species (Galan, 2004, Pleguezuelos, 2005, Brito, 2006, Martinez-Freira, 2009), which could explain why path analysis did not detect a significant direct effect of forest area neither on the relative total abundance of snakes nor on snake species richness. Sanchez-Zapata and Calvo (1999) consider the possibility that the abundance of short-toed eagle could be affected by forest area, which is supported by the results of this thesis. The effect of forest area on the relative abundance of short-toed eagle could indicate that forest area is related to the abundance of suitable nesting sites. However, the relationship was not strong as expected, considering that short-toed eagle needs forests for nesting. The strength of the relationship could have several possible explanations: Firstly, only adult short-toed eagles and juveniles of less than three months old require forests for nesting (Cramp and Simmons, 1980, Darawshi, 2007), but the relative abundance of short-toed eagle was estimated using occurrence data that do not differentiate the eagle’s age. Secondly, considering that, apparently, short-toed eagle avoids forests for foraging, (Bakaloudis et al. 1998, Bakaloudis, 2009), it is reasonable to think that the occurrence data of the eagle could include some observations near forests and others far from them. Finally, forest area was computed using cells of forests of 100 x 100 m; however, it is possible that patches of forests of less that 100 x 100 m are also important nesting sites for short-toed eagle. Path analysis does not prove causality, as stated before. Therefore, it is also possible that forest area is related to a variable with stronger effect on the relative abundance of short-toed eagle. In 1980, logging was permitted for the first time in several areas of Dadia forest (north-eastern Greece), which caused the fragmentation of the forest. According to Bakaloudis et al (1998), forest fragmentation originated an increase in the population of several species of raptors included short-toed eagle. Therefore, forest area could be related to the abundance of forest fragments. Forest fragmentation could allow short-toed eagle to nest near foraging habitats, which could be important to reduce the energy costs of foraging (Fox et al. 2001). 50 4.4. Data limitations: The present research had several limitations: Firstly, Kernel density allowed copping with the absence of abundance data. However, kernel density could have estimated better approximations of abundance for habitat generalists than for habitat specialists. Besides, the low accuracy of the occurrence data could have also affected the quality of the abundance estimations. Secondly, as mentioned in heading 4.3, not having considered patches of forests smaller than 100 by 100 m, which is the finest spatial resolution of Corine 2000, could have affected the results. Finally, relative abundances were estimated based on occurrence data collected in an organized way, as described in heading 2.2. However, the abundance of occurrences may reflect not only how abundant a species is, but also how detectable it is. Therefore, it is possible that the use of occurrence data overestimated the actual abundances of some species and underestimated the abundances of others. 51 52 5. Conclusions and recommendations: Path analysis could not detect that the relative abundance of the snakes that are thought to be the main preys of short-toed eagle in Spain (Malpolon monspesulanus, Rhinechis scalaris and Hemorrhois hippocrepis) and in other countries (Natrix natrix) have a significant direct effect on the relative abundance of short-toed eagle. Besides, path analysis could not reveal the existence of direct relationships between the relative abundance of M. monspesulanus and snake species richness, forest area and snake species richness, forest area and the relative total abundance of snakes, and snake species richness and the relative abundance of short-toed eagle. However, the results show that snake species richness could affect the relative total abundance of snakes, which, apparently, affects directly the relative abundances of the shorttoed eagle and M. monspesulanus. In consequence, snake species richness could affect indirectly the relative abundances of both species. Moreover, forest area could also affect the relative abundance of short-toed eagle. Path analysis does not prove causality (Grace and Pugesek, 1998). Therefore, in order to increase the level of certainty that the results of this thesis may represent actual causal relationships, occurrence data from other countries should be analyzed. Besides, new theories should be tested. 53 54 6. References: Agostini, N., Baghino, L., Coleiro, C., Corbi, F., Premuda, G. 2002, ‘Circuitous autumn migration in the short-toed eagle (Circaetus gallicus)’, J. Raptor Res., vol. 36. pp. 111 – 114. 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A. of Circaetus Circaetus Gallicus Gallicus (Validation) Snake species richness Power3 0.274 0.254 Snake species richness Power2 0.306 0.286 Snake species richness Power1 0.316 0.302 Snake species richness Sqrt 0.291 0.285 Snake species richness 10log 0.290 0.286 Snake species richness Power-1 -0.192 -0.200 Snake species richness Power-2 -0.158 -0.176 Snake species richness Power-3 -0.132 -0.155 Relative total abundance of snakes Power3 0.241 0.208 Relative total abundance of snakes Power2 0.350 0.330 Relative total abundance of snakes Power1 0.438 0.436 Relative total abundance of snakes Sqrt 0.442 0.449 Relative total abundance of snakes Log10 0.406 0.420 Relative total abundance of snakes Power-1 -0.176 -0.244 Relative total abundance of snakes Power-2 -0.049 -0.095 Relative total abundance of snakes Power-3 -0.037 -0.056 R. A. of Malpolon monspesulanus Power3 0.180 0.176 R. A. of Malpolon monspesulanus Power2 0.262 0.273 R. A. of Malpolon monspesulanus Power1 0.328 0.356 R. A. of Malpolon monspesulanus Sqrt 0.285 0.331 R. A. of Malpolon monspesulanus Log10 0.154 0.216 R. A. of Malpolon monspesulanus Power-1 -0.020 -0.052 R. A. of Malpolon monspesulanus Power-2 -0.007 -0.035 R. A. of Malpolon monspesulanus Power-3 -0.007 -0.030 65 R. A. of Circaetus Gallicus Transformations R. A. of Rhinechis scalaris Power3 R. A. of Rhinechis scalaris Power2 R. A. of Rhinechis scalaris Power1 R. A. of Rhinechis scalaris Sqrt R. A. of Rhinechis scalaris Log10 R. A. of Rhinechis scalaris Power-1 R. A. of Rhinechis scalaris Power-2 R. A. of Rhinechis scalaris Power-3 R. A. of Hemorrhois hippocrepis Power3 R. A. of Hemorrhois hippocrepis Power2 R. A. of Hemorrhois hippocrepis Power1 R. A. of Hemorrhois hippocrepis Sqrt R. A. of Hemorrhois hippocrepis Log10 R. A. of Hemorrhois hippocrepis Power-1 R. A. of Hemorrhois hippocrepis Power-2 R. A. of Hemorrhois hippocrepis Power-3 R. A. of Natrix Natrix Power3 R. A. of Natrix Natrix Power2 R. A. of Natrix Natrix Power1 R. A. of Natrix Natrix Sqrt R. A. of Natrix Natrix Log10 R. A. of Natrix Natrix Power-1 R. A. of Natrix Natrix Power-2 R. A. of Natrix Natrix Power-3 R. A. of main preys Power3 R. A. of main preys Power2 R. A. of main preys Power1 R. A. of main preys Sqrt R. A. of main preys Log10 R. A. of main preys Power-1 R. A. of main preys Power-2 R. A. of main preys Power-3 66 0.195 0.276 0.340 0.301 0.175 -0.065 -0.051 -0.048 0.031 0.085 0.167 0.175 0.135 -0.049 -0.024 -0.016 0.160 0.228 0.298 0.315 0.281 -0.061 -0.019 -0.010 0.129 0.214 0.302 0.307 0.149 -0.037 -0.034 -0.037 R. A. of Circaetus Gallicus (Validation) 0.169 0.259 0.346 0.333 0.229 -0.065 -0.028 -0.020 -0.004 0.053 0.167 0.205 0.184 -0.046 -0.040 -0.038 0.156 0.207 0.264 0.285 0.271 -0.091 -0.063 -0.060 0.100 0.198 0.317 0.321 0.212 -0.053 -0.029 -0.020 R. A. of Circaetus 0.198 gallicus 0.245 0.300 0.327 0.325 -0.242 -0.132 -0.084 Transformations Forest area Power3 Forest area Power2 Forest area Power1 Forest area Sqrt Forest area Log10 Forest area Power-1 Forest area Power-2 Forest area Power-3 R. A. of Circaetus gallicus (Validation) 0.187 0.226 0.272 0.296 0.295 -0.228 -0.141 -0.096 Transformations R. A. of R. A. of Malpolon Malpolon monspesulanus monspesulanus (Validation) Snake species richness Power3 0.355 0.356 Snake species richness Power2 0.444 0.433 Snake species richness Power1 0.527 0.511 Snake species richness Sqrt 0.547 0.532 Snake species richness 10log 0.550 0.531 Snake species richness Power-1 -0.365 -0.359 Snake species richness Power-2 -0.368 -0.359 Snake species richness Power-3 -0.346 -0.337 Rel. tot. abundance of snakes Power3 0.597 0.588 Rel. tot. abundance of snakes Power2 0.696 0.689 Rel. tot. abundance of snakes Power1 0.780 0.774 Rel. total abundance of snakes Sqrt 0.787 0.780 Rel. total abundance of snakes Log10 0.753 0.743 Rel. total abund. of snakes Power-1 -0.351 -0.487 Rel. total abund. of snakes Power-2 -0.210 -0.199 Rel. total abund. of snakes Power-3 -0.048 -0.104 67 Total R. A. of snakes Sqrt Forest area Power3 Forest area Power2 Forest area Power1 Forest area Sqrt Forest area 10log Forest area Power-1 Forest area Power-2 Forest area Power-3 68 Snake species richness 0.246 0.253 0.260 0.256 0.245 0.245 -0.167 -0.041 Transformations 0.597 0.696 0.778 0.777 0.774 -0.524 -0.502 -0.463 0.139 0.142 0.146 0.152 0.133 -0.094 -0.052 -0.032 Snake species richness Snake species richness Power3 Snake species richness Power2 Snake species richness Power1 Snake species richness Sqrt Snake species richness 10log Snake species richness Power-1 Snake species richness Power-2 Snake species richness Power-3 Forest area Power3 Forest area Power2 Forest area Power1 Forest area Sqrt Forest area 10log Forest area Power-1 Forest area Power-2 Forest area Power-3 Total R. A. of snakes Sqrt (Validation) 0.603 0.700 0.784 0.783 0.781 -0.521 -0.504 -0.466 0.103 0.112 0.126 0.137 0.089 -0.037 0.002 0.012 Transformations 0.257 0.272 0.280 0.279 0.270 -0.199 -0.112 -0.071 Appendix 7.1.2: Moran’s I Spatial autocorrelation test: Moran’s I Explanatory variables index R. A. of short-toed eagle 0.10 R. A. of Hemorrhois hippocrepis 0.21 R. A. of Malpolon monspesulanus 0.19 R. A. of Rhinechis scalaris 0.18 R. A. of Natrix natrix 0.13 R. A. of 'main preys' of C. gallicus 0.19 Relative total abundance of snakes 0.15 Snake species richness 0.11 Forest area 0.14 69 P < 0.01 < 0.01 < 0.01 < 0.01 < 0.01 < 0.01 < 0.01 < 0.01 < 0.01 Appendix 7.1.3: Normal probability plots and normality tests for the variables included in models A, B and C. Appendix 7.1.3.1: Normal probability plot of the relative abundance of Circaetus gallicus. Appendix 7.1.3.2: Normal probability plot of the relative abundance of Hemorrhois hippocrepis. 70 Appendix 7.1.3.3: Normal probability plot of the relative abundance of Malpolon monspesulanus. Appendix 7.1.3.4: Normal probability plot of the relative abundance of Rhinechis scalaris. 71 Appendix 7.1.3.5: Normal probability plot of the relative abundance of Natrix natrix. Appendix 7.1.3.6: Normal probability plot of the relative total abundance of snakes. 72 Appendix 7.1.3.7: Normal probability plot of the relative abundance of the ‘main preys’ of short-toed eagle. Appendix 7.1.3.9: Normal probability plot of snake species richness. 73 Appendix 7.1.3.10: Normal probability plot of forest area. 74 Appendix 7.1.3.11: Shapiro-Wilk test for the explanatory variables. Running Validation Explanatory variables procedure procedure P P R. A. of short-toed eagle 0.000 0.000 R. A. of Hemorrhois hippocrepis 0.000 0.000 R. A. of Malpolon monspesulanus 0.000 0.000 R. A. of Rhinechis scalaris 0.000 0.000 R. A. of Natrix natrix 0.035 0.041 R. A. of 'main preys' of C. gallicus 0.009 0.003 Relative total abundance of snakes 0.000 0.004 Snake species richness 0.001 0.000 Forest area 0.005 0.002 P = Level of significance 75 Appendix 7.1.3.12: Skewness of the explanatory variables. Validation Running procedure Explanatory variables 1.124 procedure 1.002 R. A. of short-toed eagle 0.211 1.297 0.393 R. A. of Hemorrhois hippocrepis 0.183 0.898 0.950 R. A. of Malpolon monspesulanus 0.433 0.233 0.169 R. A. of Elaphe scalaris 1.081 0.369 R. A. of Natrix natrix 0.257 R. A. of 'main preys' of short-toed eagle 0.933 Relative total abundance of snakes 0.453 Snake species richness 0.128 Density of forest patches 1.022 Appendix 7.1.3.13: Kurtosis of the explanatory variables. Validation Running procedure Explanatory variables 2.882 procedure 0.987 R. A. of short-toed eagle 1.661 3.703 1.573 R. A. of Hemorrhois hippocrepis -0.336 0.490 1.879 R. A. of Malpolon monspesulanus -0.180 1.596 -0.588 R. A. of Elaphe scalaris 2.934 1.512 R. A. of Natrix natrix -0.19 R. A. of ‘main preys’ of short-toed eagle 1.560 Relative total abundance of snakes -0.364 Snake species richness -0.684 Density of forest patches 2.572 76 Appendix 7.1.4: VIF of explanatory variables: Appendix 7.1.4.1: VIF of the whole set of explanatory variables. Running Independent variables procedure R. A. of Hemorrhois hippocrepis 28.571 R. A. of Malpolon monspesulanus 111.111 R. A. of Rhinechis scalaris 76.923 R. A. of Natrix natrix 4.082 R. A. of 'main preys' of short-toed eagle 500.000 Relative total abundance of snakes 13.889 Snake species richness 2.950 Forest area 2.096 Validation procedure 26.316 100.000 76.923 4.098 500.000 12.821 2.994 2.000 Appendix 7.1.4.2: VIF of the explanatory variables to be included in models A and B, before removing collinearity. Running Validation Independent variables procedure procedure R. A. of Hemorrhois hippocrepis 3.185 2.857 R. A. of Malpolon monspesulanus 9.709 9.091 R. A. of Rhinechis scalaris 9.615 8.772 R. A. of Natrix natrix 4.082 4.098 Relative total abundance of snakes 12.821 11.905 Snake species richness 2.933 2.994 Forest area 2.079 1.976 Appendix 7.1.4.3: VIF of the explanatory variables to be included in model 1A. Running Validation Independent variables procedure procedure R. A. of Hemorrhois hippocrepis 3.165 2.857 R. A. of Rhinechis scalaris 4.975 4.630 R. A. of Natrix natrix 3.906 3.802 Relative total abundance of snakes 9.615 9.091 Snake species richness 2.933 2.907 Forest area 2.049 1.953 77 Appendix 7.1.4.4: VIF of the explanatory variables to be included in model 1B. Running Validation Independent variables procedure procedure R. A. of Hemorrhois hippocrepis 2.353 2.137 R. A. of Rhinechis scalaris 8.850 8.130 R. A. of Natrix natrix 1.996 2.132 R. A. of Malpolon monspesulanus 8.772 8.065 Snake species richness 2.725 2.833 Forest area 1.701 1.590 Appendix 7.1.4.5: VIF of the explanatory variables to be included in model 1C. Running Validation Independent variables procedure procedure R. A. of 'main preys' of short-toed eagle 5.208 4.695 Relative total abundance of snakes 6.803 6.667 Snake species richness 2.841 2.793 Forest area 1.901 1.773 Appendix 7.1.4.6: VIF of the explanatory variables to be included in “Additional model”. Running Validation Independent variables procedure procedure R. A. of Hemorrhois hippocrepis 3.155 2.849 R. A. of Natrix natrix 3.984 4.049 R. A. of Malpolon monspesulanus 5.000 4.831 Relative total abundance of snakes 9.709 9.434 Snake species richness 2.933 2.994 Forest area 1.946 1.838 78 7.2. Appendices for the path analysis procedure: A description of the table headings is shown below: SDE = Standardized direct effects. SE = Standard errors of the regression coefficients. CR = Critical ratios (Regression coefficient/standard error). P = Significance level of the critical ratios. Arrow = Proposed direct effect. * = It indicates the proposed effect with lowest path coefficient. Appendix 7.2.1. Model A Appendix 7.2.1.1. Path coefficients of model 1A 1 2 3 5 6 7* 8 9 10 11 12 Running procedure SDE -0.124 -0.087 0.122 0.077 0.044 -0.011 0.097 0.215 0.749 0.310 0.318 SE 7.645 0.154 6.772 2.922 1.199 4.945 0.013 0.024 0.036 0.008 5.784 CR -2.926 -1.959 0.929 2.179 1.397 -0.185 3.234 5.716 22.482 12.135 3.061 Validation procedure P 0.003 0.050 0.353 0.029 0.163 0.853 0.001 <0.001 <0.001 <0.001 0.002 79 SDE -0.109 -0.040 0.228 0.133 0.029 -0.030 0.004 0.120 0.723 0.356 0.252 SE 5.741 0.130 6.233 2.651 1.210 4.822 0.014 0.025 0.036 0.008 4.970 CR -3.154 -0.942 1.977 4.295 0.936 -0.559 0.130 3.216 21.042 14.621 2.853 P 0.002 0.346 0.048 <0.001 0.349 0.576 0.896 0.001 <0.001 <0.001 0.004 Appendix 7.2.1.2.: Path coefficients of model 2A 1 2 3 5 6 8* 9 10 11 12 Running procedure SDE -0.191 0.506 0.233 0.068 0.059 -0.033 0.136 0.406 0.532 0.360 SE 3.707 0.108 0.894 2.826 0.794 0.018 0.009 0.046 0.009 1.833 CR -6.415 27.524 5.532 2.208 2.296 -1.197 3.859 21.592 25.433 10.199 Validation procedure P <0.001 <0.001 <0.001 0.027 0.022 0.231 <0.001 <0.001 <0.001 <0.001 SDE -0.184 0.460 0.275 0.120 0.048 -0.057 0.109 0.434 0.575 0.356 SE 3.502 0.112 0.848 2.668 0.812 0.018 0.009 0.048 0.008 1.843 CR -6.497 23.621 6.949 4.151 1.981 -2.202 3.126 22.021 28.308 9.960 P <0.001 <0.001 <0.001 <0.001 0.028 0.048 0.002 <0.001 <0.001 <0.001 Appendix 7.2.1.3.: Path coefficients of model 3A 1 2 3 5* 6 9 10 11 12 Running procedure SDE -0.191 0.506 0.233 0.057 0.068 0.121 0.406 0.528 0.360 SE 3.690 0.107 0.893 2.848 0.796 0.009 0.046 0.009 1.843 CR -6.456 27.753 5.542 2.194 2.290 3.655 21.526 25.622 10.147 Validation procedure P <0.001 <0.001 <0.001 0.028 0.022 <0.001 <0.001 <0.001 <0.001 80 SDE -0.189 0.462 0.277 0.048 0.121 0.085 0.432 0.569 0.357 SE 3.487 0.111 0.849 2.726 0.818 0.008 0.048 0.008 1.860 CR -6.664 24.024 6.983 1.976 4.115 2.563 21.843 28.559 9.918 P <0.001 <0.001 <0.001 0.048 <0.001 0.010 <0.001 <0.001 <0.001 Appendix 7.2.1.4.: Path coefficients of model 4A 1 2 3 6* 9 10 11 12 Running procedure SDE -0.185 0.540 0.250 0.004 0.546 0.397 0.559 0.409 SE 3.776 0.159 0.940 0.931 0.012 0.065 0.009 2.198 CR -5.882 22.680 4.786 0.151 19.104 18.244 26.680 10.085 Validation procedure P <0.001 <0.001 <0.001 0.880 <0.001 <0.001 <0.001 <0.001 SDE -0.189 0.475 0.284 0.007 0.493 0.452 0.598 0.394 SE 3.550 0.170 0.967 0.940 0.013 0.069 0.009 2.377 CR -6.378 17.981 5.480 0.267 15.839 18.992 28.986 8.964 P <0.001 <0.001 <0.001 0.790 <0.001 <0.001 <0.001 <0.001 Appendix 7.2.1.5.: Path coefficients of model 5A 1 2 3 9 10* 11 12 Running procedure SDE -0.20 0.789 0.556 0.860 0.018 0.208 0.288 SE 3.723 0.130 0.451 0.012 0.099 0.021 1.428 CR -6.233 51.333 16.894 35.618 0.873 5.565 13.010 Validation procedure P <0.001 <0.001 <0.001 <0.001 0.383 <0.001 <0.001 SDE -0.204 0.798 0.568 0.873 -0.005 0.184 0.283 SE 3.540 0.124 0.426 0.013 0.112 0.025 1.469 CR -6.329 53.756 17.502 34.933 -0.218 4.428 12.711 P <0.001 <0.001 <0.001 <0.001 0.828 <0.001 <0.001 Appendix 7.2.1.6.: Path coefficients of model 6A 1 2 3 9 11* 12 Running procedure SDE -0.20 0.790 0.562 0.864 0.192 0.287 SE 3.722 0.121 0.440 0.009 0.018 1.422 CR -6.262 55.504 17.505 47.322 5.803 13.043 Validation procedure P <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 81 SDE -0.204 0.798 0.567 0.872 0.189 0.283 SE 3.540 0.117 0.424 0.009 0.021 1.470 CR -6.326 56.931 17.572 48.414 5.476 12.701 P <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 Appendix 7.2.1.7.: Path coefficients of model 7 1* 2 3 9 12 Running procedure SDE -0.185 0.778 0.573 0.873 0.283 SE 3.859 0.128 0.433 0.007 1.521 Validation procedure CR -5.758 53.182 18.255 67.704 12.443 P <0.001 <0.001 <0.001 <0.001 <0.001 SDE -0.193 0.791 0.577 0.882 0.277 SE 3.687 0.121 0.420 0.007 1.569 CR -5.900 55.979 17.986 71.913 12.042 P <0.001 <0.001 <0.001 <0.001 <0.001 Appendix 7.2.1.8.: Path coefficients of model 8A 2 3 9 12* Running procedure SDE 0.784 0.437 0.872 0.308 SE 0.129 0.286 0.007 1.505 Appendix 7.2.2. CR 53.621 20.924 67.946 13.574 Validation procedure P <0.001 <0.001 <0.001 <0.001 SDE 0.796 0.430 0.882 0.304 SE 0.122 0.266 0.007 1.548 CR 56.377 21.030 72.067 13.277 P <0.001 <0.001 <0.001 <0.001 Models 1 to 8 B Appendix 7.2.2.1.: Path coefficients of model 1B 1 2 4 5 6* 7 8 9 10 11 12 Running procedure SDE -0.152 -0.089 -0.035 0.028 0.025 -0.033 0.097 0.215 0.751 0.310 0.425 SE 4.490 0.148 3.916 3.969 1.187 3.806 0.013 0.023 0.036 0.008 1.580 CR -6.066 -2.093 -0.723 0.580 0.787 -0.751 3.306 5.915 22.567 12.260 14.876 Validation procedure P <0.001 0.036 0.469 0.431 0.562 0.453 <0.001 <0.001 <0.001 <0.001 <0.001 82 SDE -0.156 -0.043 -0.090 0.031 -0.013 -0.066 0.004 0.121 0.726 0.356 0.449 SE 3.887 0.129 3.738 4.009 1.214 3.772 0.014 0.024 0.036 0.008 1.596 CR -6.634 -1.012 -1.959 0.653 -0.404 -1.541 0.148 3.276 21.049 14.635 15.686 P <0.001 0.312 0.050 0.513 0.686 0.123 0.882 0.001 <0.001 <0.001 <0.001 Appendix 7.2.2.2.: Path coefficients of model 2B 1 2 4 5* 7 8 9 10 11 12 Running procedure SDE -0.154 0.131 -0.085 -0.084 -0.109 0.108 0.262 0.310 0.195 0.386 SE 4.624 0.159 4.151 6.246 2.462 0.013 0.026 0.038 0.008 1.457 CR -5.786 3.392 -1.504 -1.241 -3.066 3.707 5.653 10.213 7.465 13.975 Validation procedure P <0.001 <0.001 0.133 0.215 0.002 <0.001 <0.001 <0.001 <0.001 <0.001 SDE -0.149 0.209 -0.155 -0.073 -0.124 0.014 0.159 0.267 0.233 0.410 SE 3.928 0.136 4.128 5.641 2.453 0.014 0.029 0.038 0.009 1.492 CR -6.067 5.533 -2.953 -1.168 -3.559 0.483 3.154 8.469 9.128 14.686 P <0.001 <0.001 0.003 0.243 <0.001 0.429 0.002 <0.001 <0.001 <0.001 Appendix 7.2.2.3.: Path coefficients of model 3B 1 2 4 7 8* 9 10 11 12 Running procedure SDE -0.169 0.168 0.436 -0.163 -0.017 0.803 -0.241 -0.089 0.279 SE 4.410 1.935 0.607 2.218 2.054 0.016 0.118 2.090 1.207 CR -6.027 7.874 16.562 -5.069 -1.065 47.686 -5.294 -2.091 11.535 Validation procedure P <0.001 <0.001 <0.001 <0.001 0.945 <0.001 <0.001 0.231 <0.001 83 SDE -0.168 0.120 0.379 -0.200 -0.032 0.873 -0.271 -0.097 0.313 SE 3.901 1.660 0.623 2.003 2.178 0.017 0.111 2.076 1.209 CR -6.159 8.189 13.495 -6.494 -2.065 49.371 -5.989 -3.013 12.162 P <0.001 <0.001 <0.001 <0.001 0.910 <0.001 <0.001 0.048 <0.001 Appendix 7.2.2.4.: Path coefficients of model 4B 1 2 4 7 9 10 11* 12 Running procedure SDE -0.16 0.457 0.440 -0.12 0.932 -0.36 -0.07 0.256 SE 4.243 0.187 0.595 1.812 0.013 0.054 0.008 1.228 CR -6.007 19.655 17.063 -4.315 58.936 -17.787 -2.723 10.838 Validation procedure P <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 SDE -0.160 0.405 0.378 -0.145 0.937 -0.453 -0.119 0.289 SE 3.711 0.173 0.610 1.553 0.015 0.049 0.008 1.235 CR -6.268 17.111 13.752 -5.660 55.398 -22.376 -4.785 11.329 P <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 Appendix 7.2.2.5.: Path coefficients of model 5B 1 2 4 7* 9 10 12 Running procedure SDE -0.159 0.469 0.438 -0.123 0.930 -0.353 0.257 SE 4.261 0.186 0.596 1.840 0.014 0.054 1.221 CR -5.937 20.226 17.233 -4.357 57.625 -17.342 11.024 Validation procedure P <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 SDE -0.155 0.420 0.372 -0.143 0.936 -0.449 0.295 SE 3.745 0.174 0.611 1.546 0.016 0.048 1.216 CR -6.105 17.313 13.896 -5.597 51.898 -22.038 11.870 P <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 Appendix 7.2.2.6.: Path coefficients of model 6B 1 2 4 9 10* 12 Running procedure SDE -0.17 0.767 0.565 0.888 -0.06 0.161 SE 3.790 0.133 0.764 0.008 0.082 1.526 CR -5.223 50.166 17.279 65.383 -3.626 6.527 Validation procedure P <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 84 SDE -0.169 0.777 0.561 0.901 -0.087 0.161 SE 3.566 0.126 0.760 0.007 0.084 1.548 CR -5.066 52.873 16.618 68.789 -5.044 6.403 P <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 Appendix 7.2.2.7.: Path coefficients of model 7B 1* 2 4 9 12 Running procedure SDE -0.163 0.778 0.562 0.883 0.189 SE 3.939 0.128 0.813 0.007 1.633 CR -4.770 52.675 16.492 69.540 7.526 Validation procedure P <0.001 <0.001 <0.001 <0.001 <0.001 SDE -0.161 0.791 0.562 0.895 0.188 SE 3.765 0.122 0.831 0.007 1.712 CR -4.587 55.576 15.743 73.338 7.227 P <0.001 <0.001 <0.001 <0.001 <0.001 Appendix 7.2.2.8.: Path coefficients of model 8B 2 4 9 12* Running procedure SDE 0.789 0.433 0.878 0.213 SE 0.128 0.508 0.007 0.493 CR 53.878 20.299 68.877 9.035 Validation procedure P <0.001 <0.001 <0.001 <0.001 Appendix 7.2.3.: SDE 0.801 0.429 0.890 0.212 SE 0.121 0.502 0.007 1.552 CR 56.625 19.860 72.730 8.741 P <0.001 <0.001 <0.001 <0.001 Model 1 C Appendix 7.2.3.1.: Path coefficients of model 1C 1 2 3 4-6* 8 9 10 11 12 Running procedure SDE -0.20 0.552 0.260 0.008 -0.07 0.166 0.341 0.516 0.355 SE 3.732 0.103 0.792 5.687 0.016 0.007 0.041 0.008 1.455 CR -6.583 31.824 6.903 0.488 -3.129 6.016 19.613 26.234 12.016 Validation procedure P <0.001 <0.001 <0.001 0.626 0.002 <0.001 <0.001 <0.001 <0.001 85 SDE -0.188 0.523 0.287 0.011 -0.110 0.139 0.356 0.545 0.366 SE 3.520 0.104 0.747 7.724 0.017 0.006 0.042 0.008 1.429 CR -6.593 29.331 8.131 -0.748 -4.819 5.101 19.856 28.506 12.630 P <0.001 <0.001 <0.001 0.454 <0.001 <0.001 <0.001 <0.001 <0.001 Appendix 7.2.4. “Additional model” Arrow Appendix 7.2.4.1.: Path coefficients of model 1 1 2 3 4 6* 7 8 9 10 11 12 Running procedure SDE -0.114 0.284 0.084 0.070 0.018 -0.023 -0.310 0.301 0.250 0.304 0.310 SE 8.1 0.300 7.226 2.992 1.402 3.218 0.010 0.134 0.010 0.079 4.889 CR -4.21 8.495 0.878 0.989 0.575 -0.502 -6.506 2.935 6.448 8.224 3.540 Validation procedure P 0.024 <0.001 0.380 0.322 0.630 0.616 <0.001 0.003 <0.001 <0.001 <0.001 SDE -0.118 0.262 0.091 0.014 0.004 -0.065 -0.288 0.288 0.291 0.289 0.314 SE 7.9 0.226 8.272 3.132 1.490 3.193 0.010 0.145 0.011 0.077 5.405 CR -2.34 7.888 1.003 0.190 0.091 -1.414 -6.844 3.290 7.999 8.190 3.222 P 0.021 <0.001 0.316 0.850 0.927 0.157 <0.001 <0.001 <0.001 <0.001 0.001 The path coefficient of the proposed effect 6 had a confidence interval of -0.040 to 0.051 in the running procedure, and -0.053 to 0.037 in the validation procedure, using a confidence level of 99%. A new model was re-specified deleting the proposed effect 6. 86 Appendix 7.2.4.2.: Path coefficients of model 2 1 2 3 4 7* 8 9 10 11 12 Running procedure SDE -0.144 0.270 0.426 0.025 0.017 -0.068 0.680 -0.068 -0.266 0.354 SE 3.805 0.559 0.213 2.142 1.290 3.043 0.037 3.043 0.111 1.395 CR -5.805 8.742 3.788 0.270 0.182 -1.524 37.580 -1.524 -5.973 12.400 Validation procedure P <0.001 <0.001 <0.001 0.787 0.811 0.127 <0.001 0.137 <0.001 <0.001 SDE -0.142 0.412 0.368 0.117 0.012 -0.040 0.628 -0.081 -0.238 0.313 SE 4.416 1.854 2.100 2.186 2.050 3.325 0.016 2.741 0.118 1.368 CR -5.182 8.246 3.456 1.269 0.092 -0.863 37.871 -1.792 -5.263 11.787 P <0.001 <0.001 <0.001 0.205 0.928 0.388 <0.001 0.241 <0.001 <0.001 The path coefficient of the proposed effect 7 had a confidence interval of -0.036 to 0.045 in the running procedure, and -0.056 to 0.033 in the validation procedure, using a confidence level of 99%. A new model was re-specified deleting the proposed effect 7. Appendix 7.2.4.3.: Path coefficients of model 3 1 2 3 4 8* 9 10 11 12 Running procedure SDE -0.218 0.802 0.448 0.152 -0.042 0.862 0.206 0.009 0.248 SE 3.745 0.292 0.675 1.343 0.024 0.013 0.021 0.101 1.668 CR -6.730 23.260 9.079 3.010 -0.413 33.492 5.455 0.398 9.629 Validation procedure P <0.001 <0.001 <0.001 0.003 0.680 <0.001 <0.001 0.690 <0.001 SDE -0.213 0.808 0.498 0.095 -0.030 0.013 0.181 -0.013 0.258 SE 3.563 0.312 0.704 1.428 0.026 0.013 0.023 0.112 1.768 CR -6.552 21.712 9.262 1.706 -0.264 33.987 4.782 -0.566 9.622 P <0.001 <0.001 <0.001 0.088 0.792 <0.001 <0.001 0.571 <0.001 The path coefficient of the proposed effect 8 had a confidence interval of -0.093 to 0.038 in the running procedure, and -0.078 to 0.014 in the validation procedure, 87 using a confidence level of 99%. A new model was re-specified deleting the proposed effect 8. Arrow Appendix 7.2.4.4.: Path coefficients of model 4 1 2 3 4 9 10 11* 12 Running procedure SDE -0.21 0.798 0.498 0.094 0.873 0.184 0.005 0.258 SE 3.581 0.118 0.693 1.428 0.008 0.017 0.087 1.762 CR -6.519 56.417 9.408 1.705 56.503 6.392 -0.265 9.658 Validation procedure P <0.001 <0.001 <0.001 0.088 <0.001 <0.001 0.791 <0.001 SDE -0.218 0.789 0.448 0.152 0.858 0.207 0.019 0.249 SE 3.778 0.123 0.662 1.344 0.008 0.015 0.081 1.658 CR -6.671 54.228 9.259 3.009 54.767 7.522 1.116 9.687 P <0.001 <0.001 <0.001 0.003 <0.001 <0.001 0.268 <0.001 The path coefficient of the proposed effect 11 had a confidence interval of -0.065 to 0.054 in the running procedure, and -0.021 to 0.128 in the validation procedure, using a confidence level of 99%. A new model was re-specified deleting the proposed effect 11. Appendix 7.2.4.5.: Path coefficients of model 5B 1 2 3 4* 9 10 12 Running procedure SDE -0.213 0.798 0.498 0.094 0.872 0.189 0.258 SE 3.582 0.116 0.688 1.427 0.007 0.017 1.764 CR -6.517 57.499 9.475 1.707 60.454 6.676 9.645 Validation procedure P <0.001 <0.001 <0.001 0.088 <0.001 <0.001 <0.001 SDE -0.218 0.790 0.449 0.154 0.862 0.191 0.249 SE 3.774 0.120 0.680 1.349 0.008 0.015 1.650 CR -6.679 55.709 9.017 2.997 59.116 6.955 9.735 P <0.001 <0.001 <0.001 0.003 <0.001 <0.001 <0.001 The path coefficient of the proposed effect 4 had a confidence interval of -0.033 to 0.145 in the running procedure, and 0.088 to 0.204 in the validation procedure, using 88 a confidence level of 99%. A new model was re-specified deleting the proposed effect 4. Arrow Appendix 7.2.4.6.: Path coefficients of model 6 1* 2 3 9 10 12 Running procedure SDE -0.20 0.790 0.562 0.864 0.192 0.287 SE 3.721 0.120 0.437 0.008 0.015 1.422 CR -6.264 55.722 17.625 59.091 7.012 13.045 Validation procedure P <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 SDE -0.204 0.798 0.567 0.872 0.189 0.283 SE 3.539 0.116 0.423 0.007 0.017 1.470 CR -6.327 57.503 17.612 60.437 6.699 12.702 P <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 The path coefficient of the proposed effect 1 had a confidence interval of 0.129 to 0.276 in the running procedure, and 0.133 to 0.278 in the validation procedure, using a confidence level of 99%. A new model was re-specified deleting the proposed effect 1. Appendix 7.2.4.7.: Path coefficients of model 7 2 3 9 10* 12 Running procedure SDE 0.797 0.411 0.863 0.184 0.285 SE 0.121 0.274 0.008 0.015 1.431 CR 56.290 20.254 59.079 6.597 12.705 Validation procedure P <0.001 <0.001 <0.001 <0.001 <0.001 SDE 0.804 0.411 0.872 0.181 0.282 SE 0.117 0.260 0.007 0.017 1.479 CR 58.056 20.487 60.398 6.316 12.450 P <0.001 <0.001 <0.001 <0.001 <0.001 Observing the squared multiple correlation of the relative abundance of short-toed eagle, in model 7, can be observed that having eliminated the proposed effect 1 improved the squared multiple correlation of the relative abundance of short-toed eagle from 0.277 to 0.287 in the running procedure, and from 0.276 to 0.285 in the validation procedure. In other words, snake species richness had no significant effect on the relative abundance of short-toed eagle. Path coefficient of the proposed effect 10 had a confidence interval of 0.126 to 0.231 in the running procedure, and 0.133 89 to 0.235 in the validation procedure, using a confidence level of 99%. A new model was re-specified deleting the proposed effect 10. Arrow Appendix 7.2.4.8.: Path coefficients of model 8 2 3 9 12 Running procedure SDE 0.784 0.437 0.872 0.308 SE 0.129 0.286 0.007 1.505 CR 53.621 20.924 67.946 13.574 Validation procedure P <0.001 <0.001 <0.001 <0.001 SDE 0.796 0.430 0.882 0.304 SE 0.122 0.266 0.007 1.548 CR 56.377 21.030 72.067 13.277 P <0.001 <0.001 <0.001 <0.001 The squared multiple correlation of snake species richness in model 7A is 0.034 in the running procedure and 0.033 in the validation procedure, which indicates that around 3% of the variability of snake species richness was accounted for by forest area. In other words, forest area had no significant effect on snake species richness. The final “Additional model” is the same 8A model. 90 Appendix 7.3. Pictures and average sizes of the 13 snake species of Spain Figure 8 1: Hemorrhois hippocrepis Figure 8 2: Hierophis viridiflavus (100 cm) (100 cm) Figure 8 3: Coronella austriaca Figure 8 4: Coronella girondica (50 cm) (50 cm) Figure 8 5: Macroprotodon brevis Figure 8 6: Zamenis longissimus (30 cm) (110 cm) 91 Figure 8 7: Rhinechis scalaris Figure 8 8: Malpolon monspesulanus (100 cm) (120 cm) Figure 8 9: Natrix maura Figure 8 10: Natrix natrix (40 cm) (100 cm) Figure 8 11: Vipera aspis Figure 8 12: Vipera latastei (60 cm) (55 cm) 92 Figure 8 13: Vipera seoanei (55 cm) Image source: http://www.mma.es/secciones/biodiversidad/inventarios/inb/anfibios_reptiles Average size source: Virtual encyclopedia of Spanish vertebrates: http://www.vertebradosibericos.org Ministry of Environment of Spain: http://www.mma.es. 93 Appendix 7.4. Relative abundances of the 13 snake species of Spain, estimated using kernel density. 94 Arrow Appendix 7.5. Additional analysis: 9! Running procedure SDE 0.702 SE 0.000 CR 43.325 Validation procedure P <0.001 SDE 0.711 SE 0.000 CR 44.757 P <0.001 The relative abundances of all the snakes except M. monspesulanus were added up. Arrow 9! is the possible effect of the relative total abundance of snakes, except M. monspesulanus, on the relative abundance of M. monspesulanus. 95