Population estimates , density – dependence and the risk of disease outbreaks in the Alpine ibex Capra ibex

Estimas de poblaciones, densidad-dependencia y riesgo de aparicion de brotes de enfermedades en el ibice de los Alpes, Capra ibex 
El seguimiento de la fauna silvestre y la identificacion de los factores asociados con los brotes de enfermedades son algunos de los objetivos principales de la conservacion de la fauna silvestre. En el presente estudio examinamos los datos demograficos y epidemiologicos del ibice de los Alpes, Capra ibex, entre los anos 1975 y 2013 para caracterizar la dinamica de la distribucion y la abundancia de la especie a gran escala. Asimismo, analizamos los sesgos metodologicos del seguimiento y estudiamos los factores que podrian estar relacionados con el riesgo de aparicion y persistencia de brotes de enfermedades. Nuestros resultados revelaron que la abundancia y la distribucion del ibice de los Alpes parecen estar aumentando tanto a escala nacional como internacional, de forma acorde con el estado de conservacion de la Union Internacional para la Conservacion de la Naturaleza (UICN) de Preocupacion Menor a escala internacional, y en el ambito nacional para Italia, Suiza y Francia. Nuestro analisis comparativo de los metodos convencionales de seguimiento pone de relieve el hecho de que los valores de abundancia obtenidos a partir de los conteos son infravaloraciones y sugiere que el ibice de los Alpes es mas abundante de lo que se suele registrar. La aparicion y la persistencia de los brotes de enfermedades (p. ej. la sarna sarcoptica, la queratoconjuntivitis o la brucelosis) estan relacionadas con la densidad y la abundancia del ibice a escala local. La correlacion observada entre el crecimiento de las poblaciones de ibice y los brotes de enfermedades sugiere que el riesgo de padecer epizootias podria estar creciendo o ser ya elevado en varias poblaciones de Capra ibex.


Introduction
The genus Capra includes flagship species living in rupicolous and mountain environments that were the subject of conservation, reintroduction and manage� ment programs during the past century (Stüwe & Niev� ergelt, 1991;Pérez et al., 2002).Capra ibex, known as the Alpine ibex due to its distribution (Sarasa et al., 2012), is a good example of this phenomenon.This species is present in the wild in at least six countries (Italy, Switzerland, France, Austria, Germany and Slovenia) and national reports from Italy and France reveal that its abundance and distribution is increasing (Apollonio et al., 2009;Corti, 2012).It was threatened by extinction at the beginning of the twentieth century but today is found in numerous colonies that are occasionally exposed to risk of disease outbreaks (Couturier, 1962;Gauthier et al., 1991;Stüwe & Nievergelt, 1991;Apollonio et al., 2009).
The improvement of wildlife monitoring and the identification of factors associated with disease outbreaks in animal populations are major goals in wildlife management and conservation (Lloyd-Smith et al., 2005;Putman et al., 2011).Nevertheless, the understanding of potential associations between the demography of host species and the causes of disease outbreaks (e.g.introduction, spread and persistence) is hampered by limited availability of data (Lloyd-Smith et al., 2005).The investigation of the potential correlation between host demography and epidemiology is of crucial interest for wildlife biologists aiming to conserve wild animal populations.Such research can aid in the identification of key factors regarding the compatibility -defined as a population's predisposition as a suitable environment for potential outbreaks (Combes, 2001)-to disease outbreaks on a population scale.
Several reviews of the recovery process and abundance of this ibex have been published (Cou� turier, 1962;Shackleton, 1997), and a number of national-wide reports on ibex populations have recently appeared highlighting increasing trends in Italy and France (Apollonio et al., 2009;Corti, 2012).Nevertheless, a novel synthesis of the management challenges facing the Alpine ibex populations on an international scale could help improve knowledge of the current status of the species and lead us to reas� sess the potential links between ibex demography and the risk of outbreaks of diseases such as sarcoptic mange, keratoconjunctivitis, and brucellosis.
Our first objective was to review the most recent demographic data to test the hypothesis that both the overall abundance and distribution of Alpine ibex are increasing on an international scale.In light of information contained in national reports (Apollonio et al., 2009;Corti, 2012), we also expected to observe an improvement in populations on a European scale.
The second objective was to assess the accu� racy of abundance estimates and methodological limits.All evaluations of species abundance are conditioned by the inherent difficulties involved in monitoring wildlife populations.Although other methods such as capture-mark-recapture (CMR) have been tested, counts (or censuses) performed in different seasons (depending on the population in question) are the most commonly used method for population estimates of the Alpine ibex (Toïgo et al., 2007;Apollonio et al., 2009;Guerra, 2010;Corti, 2012).Direct and indirect counts of ungulates have been reported in different environments (e.g.African forests and the boreo-nemoral zone on the west coast of Norway) but seem to be poor for predicting population changes below 10-50% (Plumptre, 2000;Mysterud et al., 2007).Nevertheless, as counts are still frequently used in the long-term monitoring of Alpine ibex (regardless of the population size and season) and, before any detailed analysis of the available data was carried out, we explored potential methodological biases.In line with previous esti� mates for this species (Gaillard et al., 2003;Largo et al., 2008;Giordano et al., 2012), we expected to find underestimated values in (1) census-based estimates vs. CMR estimates and in (2) summer censuses vs. winter censuses.
The third objective was to explore the factors potentially associated with the risk of disease out� break in the Alpine ibex.Previous studies of Capra species have highlighted the fact that disease may be a strong destabilizing factor in population dynamics or even a conservation threat for Capra populations around the world (Couturier, 1962;Vyrypaev, 1985;Pérez et al., 2002).Epidemiological models predict that host density and local population size will be key factors controlling the transmission dynamics of infectious diseases (Anderson & May, 1979;Lloyd-Smith et al., 2005).The demographic characteristics of populations may determine host group size (Pat� terson & Ruckstuhl, 2013), for instance, and may set the threshold for successful parasite invasion and/ or persistence (Lloyd-Smith et al., 2005;Jansen et al., 2012).We tested for potential links between host demography (density and population size) and the characteristics of disease outbreak (appearance and persistence).

Demographic data
Demographic and distribution data were compiled from scientific publications and official reports from institu� tions involved in the monitoring and management of Alpine ibex (table 1).We searched for data from all the countries in which Alpine ibex exist in the wild (Italy, Switzerland, France, Austria, Germany and Slovenia); nevertheless, most published data came from Italy, France and Switzerland.Comparisons between the different available sources enhance reliability and completeness of the compiled dataset.The name of the population, year of the population estimate, the estimated number of ibex and the estimation method used (censuses, CMR, monitoring season) were entered into a specially constructed database.The distribution of each colony or population was recorded using ArcGIS (ver.10.1).

Disease data
Data on the occurrence of disease outbreaks were gathered from scientific publications and official reports from institutions monitoring and managing Alpine ibex populations (table 1-2).Previous studies have reported that macro-and micro-parasites have uneven and context-dependent impacts on ibex individuals and populations and may give rise to endemic or epidemic (e.g.outbreaks) interactions (Couturier, 1962;Hars & Gauthier, 1994).Thus, we only included disease outbreaks in our database when the host-parasite interaction was characterized as such by the authors of a publication.Moreover, the spread or the incidence of parasites does not necessarily predict the potential impact of parasites on host demography.Only a few diseases are ever associated with the occasional destabilization of ibex populations or actually have the potential -by affecting ecological, health and socio-economic factors-to jeopardize their futures.The most important diseases are sarcoptic mange (caused by Sarcoptes scabiei), pneumonia (for in� stance caused by Mycoplasma agalactiae) and kera� toconjunctivitis (caused by Mycoplasma conjonctivae), although contagious agalactia, foot-rot, brucellosis and paratuberculosis are also of concern from health and socio-economic points of view (Couturier, 1962;Hars & Gauthier, 1994;Mick et al., 2014).Thus, we included in our dataset disease outbreaks that were both identi� fied as such in previous studies and were concomitant with population decreases.We recorded the start of the outbreaks (pathogen invasion) as binary data.The persistence of the outbreaks (outbreak persistence) was the number of years it took for the epidemic to become inactive (based on previous studies) or to be no longer associated with any demographic decline.This proxy for outbreak persistence takes into account the fact that the causal agents of diseases might exhibit non-lethal or asymptomatic interactions that could be potentially widespread but not necessarily associated with any demographic impact on ibex populations (Ryser-Degiorgis et al., 2009).

Missing data inference
Previous reviews of the overall distribution and abun� dance of mountain ungulate have sometimes inferred missing data from previously reported estimates (Shackleton, 1997;Pérez et al., 2002).We also used this approach in the analyses focused on the descrip� tive characterization of the overall abundance and dis� tribution of Alpine ibex populations.This conservative approach may underestimate population abundances and distributions in species whose populations are increasing but it can also provide robust estimates of minimum population size that are methodologically comparable with previous estimates.
We used a different approach in the analyses focused on the potential associations between de� mographic estimates and the occurrence of disease outbreaks.Values for all the considered factors were not available for every year.Thus, to avoid the loss of key information (in particular, of information on disease outbreaks), we performed a few (< 5%) missing-data inferences for population size and area estimates.Missing data were inferred using the predictions of linear models based on neighbouring available data.This approach is conservative and takes into account the reported dynamics of Alpine ibex populations over the past half-century, which were mainly characterized by population increases (Darinot & Martinot, 1994;Girard et al., 1998).

Connectivity between populations
The identification and delimitation of independent population units is a complex task in population ecol� ogy.As a first proxy for population units, we took the population units that for practical reasons are used by the institutions that monitor and manage ibex popula� tions (management units) (Apollonio et al., 2009;Corti, 2012).We also looked for information on reported connections between management units in scientific publications and in official reports to build a second proxy for meta-population units that group together connected management units.We considered a con� nected management unit to consist of populations (1) between which individuals are recorded to move or (2) with tangent/overlapping distributions.As the required information for testing potential associations between demography and epidemiology was only available for Italy and France (see below), population groups were only identified for these countries (table 2, fig.1).We used a conservative approach, and when potential -but unconfirmed-connections were mentioned in reports, we distinguished between populations units (e.g.G4-G5, G11-G13; fig.1).

Statistical analyses
In order to focus our study on the dynamic recovery of Alpine ibex on an international scale in recent decades and to reduce potential bias from unreliable former estimations we only used data from 1975 onwards.
Count (or census) data is the commonest form of population data for Alpine ibex.Thus, the overall popu� lation abundance and distribution of Alpine ibex were first predicted using count data and generalized additive models (GAM) (Wood, 2006).For some areas, popula� tion estimates inferred from CMR procedures were also available and the overall population abundance was also estimated using this data to quantify its effect on the total abundance estimates.Studies and reports on a local scale are essential for ibex management, and review analyses should support the dissemination of such studies.Thus, to maintain the large-scale focus of our analyses, to avoid pseudoreplication, and to encourage readers to refer directly to primary sources, local estimates are not presented and the references consulted for constructing the demographic dataset are given in table 1.
Paired abundance data (count vs. CMR estima� tes; end of spring-early summer counts vs. end of autumn-early winter counts) were analyzed with Student's t-test for paired samples.
Long-term monitoring of epidemiology, demography and distribution was only available from Italy and Fran� ce.Thus, the association between demography and disease outbreaks could only be analysed for these two countries.We analyzed the potential association between the start of disease outbreaks and the demo�  Hars & Gauthier (1994) graphic factors characterizing Alpine ibex populations (density, abundance, year) using generalized additive models (GAM) and a model selection procedure based on Akaike's information criterion (Burnham & Anderson, 2002;Wood, 2006).We repeated this procedure to analyze the potential association between the persis� tence of disease outbreaks and factors characterizing Alpine ibex populations.In our models, we included spatial and temporal factors (population, meta-popu� lation, country, season and year).
Using only the count data from countries with Alpine ibex populations (Italy, Switzerland, France, Austria, Germany, Slovenia), our GAM model predicted (esti� mate ± se) an overall population of 49,037 ± 1,012 in� dividuals in 2013.Predicted values using only count data were also estimated for the three main countries with Alpine ibex (Italy, Switzerland and France; table 4, fig.2).Data compiled for the other countries include several count estimations, but no long-term series that would have allowed us to build accurate and comparable models at a national scale for Austria, Germany and Slovenia.Nevertheless, in table 4 we summarize the population estimates reported in pre� vious studies.Using CMR data when available and count data if not available, our GAM model predicted an overall population of 50,195 ± 1,012 individuals in 2013 (see table 4 for national predictions).

Estimated distribution
Using the available data on spatial distribution from the main countries harbouring Alpine ibex populations (Italy, Switzerland and France), our GAM model predicted (estimate ± se) a distribution of 5,058 ± 109 km² in Italy and 2,568 ± 88 km² in France (table 4, fig.3) for 2013.Data compiled for other countries (Switzerland, Austria, Germany and Slovenia) were too limited to be able to build reliable models or to predict estimated distributions for the whole range of the Alpine ibex.

Disease outbreaks
Several disease outbreaks associated with population decreases between 1975 and 2013 have been repor� ted in the literature (table 2).The best model of the factors associated with the start of disease outbreak (AIC weight = 0.16) included only the factor 'density' (table 5, fig.4A).Five other models were within 2 AIC units of the best model, all of which included the factor 'density' within other factors (year, abundance and country).The deviance explained by these six models ranges from 15.6% to 19.2% (table 5).The relative importance of variables underlined once more the fact that, of the tested variables, local density was the key factor associated with the appearance of a disease outbreak, although local abundance, year and country might also play role (table 5).
The best model for the persistence of disease out� break (AIC weight = 0.41) included four parameters: density, local abundance, year and meta-population.Two other models were within 2 AIC units of the best model and include (in addition to the previous four parameters) 'monitoring season' or 'country'.The deviance explained by these best models was about 70% (table 6, fig.4B-4D).

Abundance and distribution
The predicted values of the GAMs suggest that, in agreement with national reports, at both national and international scales, the Alpine ibex has increased in abundance (fig.2) (Apollonio et al., 2009;Corti, 2012).Only the three countries with the largest ibex populations (Italy, Switzerland and France) have information from long-term monitoring schemes and up-to-date data from Austria, Germany and Slovenia would improve the overall estimates of ibex abun� dance in Europe.Analyses of paired data show that methodological designs have a major impact on the  Switzerland estimates of population abundance: abundances are underestimated in summer vs. winter counts and in census counts vs. CMR estimates.Although count data is the main source of population information in the literature, judging from our sample, on average they underestimate by half the Alpine ibex abundance when compared with results from CMR.Thus, most available information on ibex abundance (including the estimates in table 4) should be handled with care and is best thought of as an indicator of relative abundance rather than an accurate estimate of po� pulation size.The biases observed suggest that the Alpine ibex is probably more abundant that usually reported.Our total population estimate for Alpine ibex (about 50,200 individuals) is derived essentially from counts, while the total estimate for the Iberian ibex Capra pyrenaica population (about 50,000 individuals according to Pérez et al. (2002)) are largely derived from line transects and distance sampling.Our results show that the mean bias of Alpine ibex counts leads to underestimations.However, the mean bias of Iberian ibex estimates -as for other mountain ungulates-is an issue that is still unresolved because the use of data truncation in distance sampling analysis can overestimate densities of mountain ungulates, and consequently, their abundance (Pérez et al., 2015).Thus, Alpine ibex may well be the most abundant ibex in Western Europe.Further studies will be required to refine monitoring methods and population estimates of mountain ungulate species.
Tabla 5. Selección de modelos para determinar los factores asociados con la aparición de brotes de enfermedades en el íbice de los Alpes, Capra ibex, a escala poblacional en Francia e Italia.D. Densidad; A. Abundancia; Y. Año; G. Metapoblación; C. País; S. Estación de los censos; P. Población; n.Tamaño muestral; K. Número de parámetros estimados; AIC.Criterio de información de Akaike; ∆AIC.Diferencia del AIC entre el modelo y el modelo de máxima parsimonia; L(gi/x).Probabilidad de que el modelo sea el mejor dado el conjunto de datos; Wi.Peso de Akaike del modelo; Dev-expl.Desviación explicada del modelo ajustado; RI.Importancia relativa de los factores.Solo se muestran los diez modelos mejores según Burnham & Anderson (2002) y Wood (2006).In agreement with the predictions of ibex dynamics, information on the distribution of the Alpine ibex sug� gests that overall increases in ibex populations have occurred in Italy and France (fig.3).The structure of the observed values (figs.2-3) suggests that infor� mation on distribution has been updated less often than abundance estimates.Thus, further studiesparticularly in ibex populations in Switzerland, Austria, Germany and Slovenia-would improve the present understanding of ibex distribution across Europe.
Abundance and distribution data, taken together, suggest that the IUCN 'Least Concern' conservation status is probably accurate at an international scale and at a national scale for Italy, Switzerland and France.

Population units
Analyses of epidemiological vs. demographic data show that the population units used for historical or practical reasons by institutions to monitor and manage ibex populations are excluded from the best models.However, the proxy for meta-populations that take into account the reported connections between populations is selected in the best models.Thus, the spatial struc� ture and connectivity of ibex colonies must also be taken into account.These results also underline the relevance of trans-boundary monitoring and manage� ment, such as the programmes already underway in the Vanoise (France), Gran Paradiso (Italy) (Girard et al., 2009)

Disease outbreaks
In agreement with theoretical models (Anderson & May, 1979;Lloyd-Smith et al., 2005), our results highlight the link between the local density of Alpine ibex and appearance and persistence of disease outbreaks (fig.4), a finding that agrees with the results of recent studies of pneumonia epizootics in bighorn sheep (Sells et al., 2015).Moreover, ibex abundance and year were associated with at least the persistence of disease outbreaks (fig.4C-4D).For the start of outbreaks, the deviance explained by the best models (15.6-19.2%)suggests that most of the variability in the appearance of disease outbreaks for the available data is not explained by local density and the other parameters included in our analyses.Thus, exposure to pathogens (encounter filter), defined as the probability of contact between the pathogen and the potential host population (Combes, 2001), rather than compatibility (compatibility filter), defined as the population predisposition as suitable environments for potential outbreaks, might be key to the appearance of disease outbreaks.In terms of outbreak persistence, the deviance explained by the best models was about 70%, which suggests that the considered factors of population compatibility to outbreaks explain most of the observed variability in the persistence of disease outbreaks.Thus, our results match the hypothesis of density-dependence for pathogen transmission and highlight the idea that disease outbreaks may persist longer in high-density populations, at least in the areas with the commonest high-density values (7-10 ibex/km²).Nevertheless, our results also re� veal a decrease in the persistence index at greatest density and abundance values (density greater than 10 ibex/km² and abundance over 4,000 individuals in the population), probably due to the low sample size for this range of values and the poorer accuracy of demographic and epidemiological data in the lar� gest populations.The non-linear pattern linking the persistence of outbreaks and ibex abundance also suggests a localized decreasing pattern for small po� pulations (0-350 ibex in the population).This pattern might be a localized artefact for this range of values due to the early intensive monitoring of reintroduced populations.However, it could also indicate an 'Allee  effect' linked to pathogens (Krkošek et al., 2013).The persistence index of outbreaks was greatest in very small and in large populations, that is, populations that are possibly at the edge and the core, respec� tively, of the ibex's range.Increased persistence in very small populations (edge of range) might be the result of repeated exposure or greater compatibility of colonies to pathogens, of contact or competition with livestock (Sells et al., 2015), or of high gregariousness in very small populations.Increased persistence in large populations (core of range) might be linked to areas with the high density of potential hosts that usually characterizes large populations.The observed links between outbreaks and density were non-linear and the patterns suggest relative threshold values (Lloyd-Smith et al., 2005) close to five and seven, respectively, for the appearance and persistence of disease outbreaks.As discussed in previous articles on wild species (Gortazar et al., 2006;Cross et al., 2010), environments favouring overabundant and aggregated populations (e.g., protected areas in the case of the Alpine ibex) sometimes also leave popu� lations more prone to persistent disease outbreaks.Many threatened populations, species and rich ecosystems throughout the world are now protected.
A new conservation challenge is emerging because protected populations on the increase may suffer from repeated disease outbreaks due to over-abundance facilitated by protection (Gortazar et al., 2006;Cross et al., 2010).Further studies will have to explore these conservation trade-offs (Leader-Williams et al., 2010) to ensure that management plans that are designed in one particular year but are then implemented yearafter-year do not evolve into conservation threats.Additionally, our results suggest that disease rose in the Alpine ibex in 2000-2010 despite its decrease in the 1980s.This decrease in the 1980s was pro� bably the result of technical advances in diagnosis and increased investment in livestock prophylaxis (e.g., Fensterbank, 1986), coupled with research in eco-pathology and the management of disease risk at the wildlife-livestock interface during this period (e.g., Mayer et al., 1996).Nevertheless, the positive trends in Alpine ibex populations and the observed association between the demographic rise of ibex and disease outbreaks suggest that compatibility to epizooties may be increasing -or may already be high-in several populations of Capra ibex.Burnham & Anderson (2002) and Wood (2006).Tabla 6. Selección de modelos para determinar los factores asociados con la persistencia de brotes de enfermedades en el íbice de los Alpes, Capra ibex, a escala poblacional en Francia e Italia.D. Densidad; A. Abundancia; Y. Año; G. Metapoblación; S. Estación de los censos; C. País; P. Población; n.Tamaño muestral; K. Número de parámetros estimados; AIC.Criterio de información de Akaike; ∆AIC.Diferencia del AIC entre el modelo y el modelo de máxima parsimonia; L(gi/x).Probabilidad de que el modelo sea el mejor dado el conjunto de datos; Wi.Peso de Akaike del modelo; Dev-expl.Desviación explicada del modelo ajustado; RI.Importancia relativa de los factores.Solo se muestran los diez modelos mejores según Burnham & Anderson (2002) y Wood (2006) The heterogeneity of Alpine ibex monitoring between populations prevented us from inferring abundance or distribution estimates for Switzerland, Austria, Germany or Slovenia.Further investment aimed at updating missing information would thus complete the data presently available for Alpine ibex.Potential double counts in trans-boundary popula� tions might also have affected abundance estimates.Nevertheless, the observed propensity to undercount probably compensates for double counts and further trans-boundary monitoring will probably minimize this potential bias.
Population structures are still too poorly document� ed, however, to be incorporated into our analyses (even though they may modulate demographic processes) (Yoccoz & Gaillard, 2006;Mignatti et al., 2012).Thus, further studies should explore the role of population structure as a potential modulating factor of population compatibility to disease outbreaks.
Outbreaks are relatively rare events and the avail� able data do not allow for each disease to be analysed separately.In light of fresh outbreaks in the future, analysis should continue in the future, as should the search for potential variability in threshold values be� tween pathogenic agents.Even so, our analysis permits us to explore factors that may determine associations with disease outbreaks at population scales.
In conclusion, our reappraisal of the available demographic and epidemiologic data on Alpine ibex highlights the methodological limitations, the increa� se in ibex populations, the increased risk of disease outbreaks and the links between host demography and disease outbreaks.A challenge for the future is how to integrate knowledge on density-dependent processes in wild species (e.g.disease outbreaks in the Alpine ibex) into the management of such species and ecosystems.

Fig. 1 .
Fig. 1.Distribution of the Alpine ibex colonies, Capra ibex.Lakes and the sea are depicted in dark grey, black lines are national boundaries.Redrawn from Apollonio et al. (2009),Corti (2012)  and Office fédéral de l'environnement (2013a).See table 2 for the identity of the meta-populations.

Fig. 2 .
Fig. 2. Evolution of the abundance of the Alpine ibex, Capra ibex, between 1975 and 2013 in the whole of the Alps (A), Italy (B), Switzerland (C) and France (D).The solid lines represent the predicted patterns estimated by the generalized additive models, the grey shaded areas indicate the standard error, and the open circles are the observed values.The left-hand y-axis represents the centred values and specifies the smoothing factor 'Year', with the approximate degrees of freedom.The right-hand y-axis represents the estimated ibex abundance.

Fig. 3 .
Fig. 3. Evolution of the spatial distribution of the Alpine ibex, Capra ibex, between 1975 and 2013 in Italy (A) and France (B).The solid lines represent the predicted patterns estimated by the generalized additive models, the grey shaded areas indicate the standard error, and the open circles are the observed values.The left-hand y-axis represents the centred values and specifies the smoothing factor 'Year', with the approximate degrees of freedom.The right-hand y-axis represents the estimated spatial distribution of ibex (km²).

Fig. 4 .
Fig. 4. Link between the appearance and the persistence of disease outbreaks in the Alpine ibex, Capra ibex, and density estimates (A, B), abundance (C) and year (D).The solid circles represent the predicted values estimated by the best generalized additive models for the available data, the grey bars indicate the standard error, and the thick lines represent the values with available observed data.The left-hand y-axis represents the relative probability of a disease outbreak (A) and the relative persistence of disease outbreaks (B, C, D).

Table 3 .
Meta-populations or groups of populations (G) included in the analyses of potential associations between demography and epidemiology in the Alpine ibex Capra ibex.

Table 4 .
Abundance and distribution of Alpine ibex Capra ibex in 2013: Scd.Sum of count data only; P-GAM.Predicted by a GAM (generalized additive model) of count data; S-CMR.Sum of count plus CMR data when available; P-GAM-CMR.Predicted by a GAM of count data plus CMR data when available; Srp.Sum of reported population ranges; P-GAMrd.Predicted by a GAM of reported range data; * Reported from previous estimates; -Insufficient data available.

Table 5 .
Model selection for factors associated with the appearance of disease outbreaks in Alpine ibex Capra ibex at population scale in Italy and France.D. Density; A. Abundance; Y. Year; G. metapopulation; C. Country; S. Season of counts; P. population; n.Sample size; K. Number of estimated parameters; AIC.Akaike's information criterion; ∆AIC.Difference of AIC between the model and the most-parsimonious model; L(gi/x).Probability of the model being the best model given the data set; Wi.Akaike weight of the model; Dev-expl.Explained deviance of the fitted model; RI.Relative importance of factors.Only the ten best models are reported following

Table 6 .
Model selection for factors associated with persistence of disease outbreaks in Alpine ibex Capra ibex at population scale in Italy and France.D. Density; A. Abundance; Y. Year; G. metapopulation; S. Season of counts; C. Country; P. population; n.Sample size; K. Number of estimated parameters; AIC.Akaike's information criterion; ∆AIC.Difference of AIC between the model and the most-parsimonious model; L(gi/x).Probability of the model being the best model given the data set; Wi.Akaike weight of the model; Dev-expl.Explained deviance of the fitted model; RI.Relative importance of factors.Only the ten best models are reported following .