Multi-event capture-recapture analysis in Alpine chamois reveals contrasting responses to interspecific competition, within and between populations

1. Understanding components of interspecific competition has long been a major goal in ecological studies. Classical models of competition typically consider equal responses of all individuals to the density of competitors, however responses may differ both among individuals from the same population, and between populations. 2. Based on individual long-term monitoring of two chamois populations in sympatry with red deer, we built a multi-event capture-recapture model to assess how vital rates of the smaller chamois are affected by competition from the larger red deer. 3. In both populations, mortality and breeding probabilities of female chamois depend on age and in most cases, breeding status the preceding year. Successful breeders always performed better the next year, indicating that some females are of high quality. In one population where there was high spatial overlap between the two species, the survival of old female chamois that were successful breeders the pre ceding year (high-quality) was negatively related to an index of red deer population size suggesting that they tend interspecific competition affects the demographic performances of female chamois. We showed that breeding proba bilities of female chamois could be influenced by the presence of red deer competitors. These effects of red deer population size index on chamois differed between the two populations, the age and the reproductive status of the female, suggesting that the effect of in terspecific competition on population dynamics operates through complex pathways.


| INTRODUC TI ON
Species live in communities and when common limiting resources are shared among two species, interspecific competition can occur.
Interspecific competition can ultimately lead to the exclusion of one of them, and cascading effects can change the composition of the entire community (Chesson, 2000;Kokkoris, Troumbis, & Lawton, 1999). Understanding components of interspecific competition has thus long been a major goal in ecological research across ecosystems (see Connell, 1983;Schoener, 1983 for reviews).
Nearly 100 years ago, the seminal work of Lotka (1925) and Volterra (1926) formulated the concept of interspecific competition mediated through shared and limited resources. They provided a well-known mathematical model of competition for finite resources in which the species-specific population growth rates depended on species-specific densities. This model is based on systems of differential equations where population sizes are state variables, and only focuses on population growth rates and competitive coefficients (Giacomini, DeAngelis, Trexler, & Petrere, 2013). It is by nature nonmechanistic, i.e. the specific competitive mechanisms are not explicitly stated or explored in the Lotka-Volterra model, assuming equal responses of all individuals to an increase in density of competitors.
Since then, applications and extensions of this model have flourished in the literature (McPeek, 2017;Terborgh, 2015). For instance, Gamelon et al. (2019) recently derived from the Lotka-Volterra's competition model an approach where species-specific population growth rates depended on species-and age-specific densities.
The authors applied this model to great tit Parus major and blue tit Cyanistes caeruleus, two competing species, and found that an increase in the density of the larger great tits resulted in a decrease of the population growth rate of the smaller blue tits. This pattern was observed at several sites across Europe and indicates a consistent marked negative effect of interspecific competition on blue tit's population growth rate across all study sites.
Evidence is accumulating that sequential changes of demographic rates occur as population density of the focal species increases (i.e. intraspecific competition). In large mammals, it involves first a decrease in juvenile survival, followed by a decrease in reproductive rates of prime-aged females and finally a decrease in their survival (Bonenfant et al., 2009;Eberhardt, 1977Eberhardt, , 2002Gaillard, Festa-Bianchet, Yoccoz, Loison, & Toïgo, 2000). Surprisingly, little is known on how population density of a competing species affects age-specific demographic rates of the focal species. However, to gain a good understanding on how an increase in density of a given competitor affects the population growth rate of the other species, it is crucial to identify whether individuals, according to their characteristics (e.g. age, reproductive state, from different populations), are differently affected in their demographic rates. Given the importance of individual heterogeneity in the dynamics of animal populations (Hamel et al., 2018), the time has come to challenge the assumption of equal responses of all individuals to an increase in density of competitors and to evaluate whether there are individual differences in responses to interspecific competition within a population (i.e. between individuals). Additionally, we need to explore whether the response to interspecific competition varies between populations. Exploring response to interspecific competition within and between populations will strengthen our understanding of competitive interactions under various environmental conditions.
Here, we take advantage of individual long-term monitoring of two Alpine chamois Rupicapra rupicapra populations living in sympatry with another ungulate species, the red deer Cervus elaphus.
Previous works have shown that the diet of chamois and red deer shows considerable overlap in areas where they co-occur (Bertolino, Montezemolo, & Bassano, 2009;Lovari et al., 2014;Redjadj et al., 2014) and that the larger red deer might be a superior competitor over the smaller chamois (Anderwald, Haller, & Filli, 2016). In both chamois populations, females have been individually monitored for more than 20 years to determine their annual survival and reproduction. Simultaneously, an index of red deer population size has been recorded annually. Using a multi-event approach (Pradel, 2005), we investigate how the demographic performances of female chamois are related to the index of red deer population size. In particular, we identify whether, according to their characteristics (age/reproductive state, belonging to different populations), female chamois are differently affected in their demographic rates (survival and breeding probability) by an increase in red deer population size.
As Alpine environments are heterogenous habitats in terms of resource quality and quantity depending on altitude and on the exposure of the slopes (Nagy & Grabherr, 2009), we expect interactions between chamois and red deer to differ even at a small spatial scale and thus to differ between the two studied chamois populations (Anderwald et al., 2016). More specifically, previous works have shown that in one population, the low amount of high primary productivity (measured as Normalized Difference Vegetation Index) leads red deer to select meadows with high NDVI located at low altitudes during summer (Anderwald et al., 2016). At high altitudes, the limited amount of primary productivity is large enough to sustain chamois, more constrained by food quality than food quantity (Belovsky, 1986). This heterogeneity in the distribution of resources along the altitudinal gradient leads to strong segregation by elevation between the two species during summer. We thus expect no effect of red deer population size on chamois females in this first population. In contrast, in the other chamois population, red deer select meadows with high primary productivity and high solar radiation, coinciding with a positive selection for elevation, similar to the altitudinal selection by chamois (Anderwald et al., 2016;Herfindal, Anderwald, Filli, Campell Andri, & Rempfler, 2019). In this site, there is little altitudinal segregation between the two species that occupy the same habitats in summer. We thus expect a significant effect of red deer population size on chamois females. Specifically, one can hypothesize that an increase in the red deer population size should affect the survival of the most vulnerable female chamois, such as senescent individuals. For females of other ages, we expect little effect of red deer, because the survival of long-lived species is known to be buffered against environmental variation (Gaillard & Yoccoz, 2003;Morris & Doak, 2004).
However, in order not to jeopardize their survival when the number of competitors increases, female chamois could skip reproduction.
We thus expect a negative effect of red deer population size on the breeding probability of female chamois.

| Study sites
This study was conducted on two chamois populations within the Swiss National Park in the central Alps (46°40′N, 10°12′E). One population is located in the 5,026 ha area of Il Fuorn (first population, low spatial overlap between chamois and red deer during summer) and one in the 2,000 ha area of Val Trupchun (second population, high spatial overlap between the two species; see Figure 1).
Both areas range between 1,800 and 2,800 m a.s.l. and are inhabited by two competing species, chamois and red deer. Hunting is not allowed in the National Park and the only predator is the Golden eagle

| Study species and data collection
Chamois females may reproduce for the first time at 2 years of age (Crampe et al., 2006;Morin, Rughetti, Rioux-Paquette, & Festa-Bianchet, 2016;Pioz et al., 2008;Figure 2). As births occur between May and June in the study areas, year was defined from 1 May in a given year to 30 April the next year ( Figure 3). Between 1995 and2016, 129 chamois females (87 at Il Fuorn and42 in Val Trupchun) were captured all year-round using box or sling traps and marked with ear tags. The age at first capture, determined by counting growth rings on the horns (Schröder & von Elsner-Schack, 1985), ranged between 0 and 17 years old (see Appendix S1 for the distribution of age at first capture). Most females were captured as prime age, and only eight females at Il Fuorn and five females in Val Trupchun were captured as kids (i.e. in their first year of life). Ear-tagged females were monitored annually between June and October to assess their reproductive status. During that period, females observed at least once with a kid were considered as successful breeders. Females observed at least twice without kid were considered as failed breeders. For females seen only once without a kid or not detected at all between June and October (but observed in the periods May-June and/or October-May), we assumed that the reproductive status was unknown (see Appendix S2).
In parallel with individual monitoring, counts of red deer and chamois were performed annually at maximum seasonal densities, i.e. during July-August by experienced park rangers ( Figure 3). Counts were performed in the same area within each study site for both species. Il Fuorn was divided into seven blocks and Val Trupchun into five blocks. Censuses were then conducted from the exact same points each year, selected for their optimal viewshed. Counts were performed for 2 weeks, chosen for their optimal viewing conditions (for further details, see Haller, 2006). Double counting of individuals at adjacent blocks was avoided by noting the time of the sightings, the exact location and the group composition and by sharing this information between rangers thanks to radio contact (Saether et al., 2002). Thus, the invested effort in avoiding double counts and the open landscape suggest that counts are precise compared to most other ungulate F I G U R E 2 Life cycle of the Alpine chamois. 1-year old females at t may survive until t + 1 with a probability 1 − m 0−1 . Females in age class 2-12 at t may survive until t + 1 with a probability 1 − m 2−12 . Senescent females (>12 years old) at t may survive until t + 1 with a probability 1 − m >12 . Females can start reproducing at age 2 with a breeding probability of ψ 2 and they reproduce with a probability ψ 3 at age 3. Females in age class 4-12 and senescent females have a breeding probability of ψ 4−12 and ψ >12 respectively 1 2 3 4 5 … 11 12 >12

F I G U R E 3
Timeline showing the periods of capture-mark (all year-round), resighting of marked chamois (from July to October) and red deer population censuses (second half of July). For each period, the type of data collected is indicated. Capital letters correspond to months population counts (Saether et al., 2002). The same protocol was applied twice during the 2-week counting period and a higher number of counted individuals was kept as a proxy of the minimum red deer Population counts may have some weaknesses. First, annual variations in red deer population size index can be confounded with annual variations in detectability (Pollock et al., 2002). Note that here, both the location of the censuses (counting points) and the period to perform population counts have been carefully chosen for their optimal viewing conditions by experienced park rangers thus minimizing the risk of spurious correlation between population size index and detectability.
Second, our population counts can lead to severe underestimates of the true population size but they provide reliable population indices to track temporal changes in red deer population size index (see Corlatti, Gugiatti, & Pedrotti, 2016 for a study in central Italian Alps).

| Capture-mark-recapture model
To estimate annual mortality, breeding and resighting probabilities, we used a multi-event approach (Pradel, 2005) implemented in E-SURGE (Choquet, Rouan, & Pradel, 2009). Chamois females at Il Fuorn and Val Trupchun are subjected to markedly different environmental contexts and are expected to exhibit contrasting demographic responses to an increase in the strength of interspecific competition, measured as an increase in the red deer index; therefore, we analysed the two chamois populations separately. There is currently no specific test to assess goodnessof-fit (GOF) of multi-event models (Pradel, 2005). Therefore, we ran the GOF test from the Cormack-Jolly-Seber (CJS) model using U-CARE (Choquet et al., 2009 with no kid), (2) successful breeder (i.e. with one kid) or (3) dead ( Figure 4). We dealt with state uncertainty by assessing the likelihood of a female state given the observation (i.e. event) in the field using a multi-event approach (Pradel, 2005). We considered four events for a female: (0) not detected; (1) detected as a failed breeder (i.e. observed at least twice with no kid between June and October); (2) detected as a successful breeder (i.e. observed at least once with a kid between June and October); (3) detected F I G U R E 4 Illustrative figure showing the between-state transition process (biological process) and the structure of the observation process (events). First, failed breeders (in green, FB) at year t may survive until t + 1 with a probability 1 − m FB or die with a probability m FB . Successful breeders (in grey, SB) at year t may survive until t + 1 with a probability 1 − m SB or die with a probability m SB . Second, failed breeders at year t may remain failed breeders at year t + 1 with a probability 1 − ψ FB−SB or become successful with a probability ψ FB−SB . Successful breeders at year t may remain successful at year t + 1 with a probability ψ SB−SB or fail with a probability 1 − ψ SB−SB . Four events (i.e. observations) are considered for a female: event 0-not detected; event 1-detected as a failed breeder; event 2-detected as a successful breeder; event 3-detected but reproductive status unknown. Failed breeders may not be detected with a probability 1 − p FB , detected as a failed breeder with a probability p FB × γ FB or detected with unknown reproductive status with a probability p FB × (1 − γ FB ). Successful breeders may not be detected with a probability 1 − p SB , detected as a successful breeder with a probability p SB × γ SB or detected with unknown reproductive status with a probability p SB × (1 − γ SB ). Dead females are not necessarily observed  often after the peak of juvenile mortality) and females of age 1 (Figure 2), mortality m 0−1 for this age class was likely underestimated. We thus focused on the age classes 2-12 and >12. For breeding probabilities, because reproduction is expected to be lower for 2 and 3 years old than for older females, we considered four age classes: age 2, age 3, age class 4-12 and age class >12 ( Figure 2).
We tested different biologically meaningful models for the effects of breeding status at t, age and red deer population size index on breeding and mortality probabilities in the two chamois populations (see Appendix S6 for a list of all models tested). We used the Akaike's information criterion (AIC; Burnham & Anderson, 2002) to select the best model. When AIC values were within two units, the most parsimonious model was retained. In addition, when red deer population size index was retained in the best models, we used an ANODEV to quantify the proportion of breeding/mortality probabilities for chamois explained by red deer population size index (Grosbois et al., 2008). The proportion of breeding/mortality probabilities for chamois explained by red deer population size index (R 2 ) was assessed by comparing deviance of models with the covariate on mortality m and/or breeding probabilities ψ (Dev deer ), to the constant (Dev const ) and the time-dependent models (Dev t ) (Skalski, Hoffmann & Smith 1993), such that:

| Population size index
Population

| No effect of interspecific competition on chamois survival
At Il Fuorn (site with low overlap), the most parsimonious model (model M1, Appendix S6) indicates that mortality is age-dependent, being the highest for senescents (>12 years of age; Figure 5). In addition, mortality In Val Trupchun (site with high overlap), the best model (model M40, Appendix S6) indicates that mortality is age-dependent, being higher for the oldest age class ( Figure 6). Mortality probability were 0.09 (SE: 0.02) at ages 2-12 and 0.39 (SE: 0.08) for senescents ( Figure 6). Red deer population size index had no effect on the mortality probability of successful breeders (M29, Appendix S6), failed breeders (M28, Appendix S6) or both successful and failed breeders (M27, Appendix S6). Thus, at Il Fuorn and Val Trupchun, chamois mortality probability was not influenced by interspecific competition from red deer, irrespective of the breeding status and age of the chamois.

| Effects of interspecific competition on chamois breeding probability are population-, age-and state-specific
At Il Fuorn, the site with low overlap, the best model indicates that breeding probability at t + 1 is strongly age-dependent, decreasing R 2 = Dev const − Dev deer Dev const − Dev t .
from the age class 4-12 to the senescent class (>12 years of age; In Val Trupchun where chamois spatially overlap with red deer, the best model indicates that breeding probability at t + 1 is also strongly age-specific ( Figure 6) and depended on breeding status in

| D ISCUSS I ON
Classical models of competition between two species such as Lotka (1925) and Volterra (1926) use linear combinations of two densities. These nonmechanistic models do not include the underlying demographic pathways through which interspecific competition operates. Here, we took advantage of unique individual long-term monitoring of two chamois populations in sympatry with red deer and used a multi-event capture-mark-recapture modelling approach to analyse how interspecific competition affects the demographic performances of female chamois. We showed that breeding probabilities of female chamois could be influenced by the presence of red deer competitors. These effects of red deer population size index on chamois differed between the two populations, the age and the reproductive status of the female, suggesting that the effect of interspecific competition on population dynamics operates through complex pathways.
In both populations, mortality and breeding probabilities of female chamois were age-dependent. Mortality increased from the prime-aged class (2-12 years old) to the oldest age class (females of age 13 and older), providing further evidence for actuarial senescence in wild populations (Loison, Festa-Bianchet, Gaillard, Jorgenson, & Jullien, 1999;Nussey, Froy, Lemaître, Gaillard, & Austad, 2013) and more specifically in this species (Bleu et al., 2015). Breeding probabilities for prime-aged females depended on their previous breeding status. Females that bred in the preceding year consistently had the highest breeding probabilities the following year (and the lowest mortality at Il Fuorn).
These results clearly indicate that females that bred at year t do not exhibit reduced survival and/or reproduction at year t + 1, contrary to the theory of reproductive trade-offs that predicts fecundity and/or survival costs at t + 1 for females that bred at t (Bleu, Gamelon, & Saether, 2016;Roff, 2002;Williams, 1966).
Regarding the effects of red deer population size index on chamois demographic rates, we provided evidence for population-specific responses to interspecific competition. At Il Fuorn (site with low overlap), red deer population size index had no effect on female chamois, in accordance with results from an earlier study in this site (Anderwald et al., 2016), which could not detect any effect of interspecific competition on horn growth in young, a proxy of body condition. Spatial heterogeneity in the distribution of resources may allow chamois to rely on food resources at higher altitudes than red deer (Anderwald et al., 2015(Anderwald et al., , 2016, decreasing the spatial overlap between the two species and thus the potential for competitive interactions. In Val Trupchun where the spatial overlap between red deer and chamois is higher, breeding probability at t + 1 of senescent successful breeders at t was reduced at high red deer population size index, and red deer population size index explained 26.9% of the observed variance in breeding probability. This indicates that when red deer population size increases, old high-quality females tend to skip reproduction instead of jeopardizing their own survival, a pattern classically observed in long-lived species (Gaillard & Yoccoz, 2003). We found the same demographic response to increasing red deer population size for young females of age 2 and 3, i.e. an increased propensity to skip reproduction with increasing density of competitors.
Accordingly, previous study at Val Trupchun found reduced horn growth in young chamois when red deer population size increases (Anderwald et al., 2015), providing additional evidence for interspecific competition in this area. High red deer population size can explain the marked effect of interspecific competition on chamois.
In addition, in Val Trupchun, red deer rely on food resources located at high altitudes, which coincide with the area occupied by chamois, preventing spatial segregation between the two species and increasing interspecific competition for resources.
Our findings clearly show that the effects of interspecific competition are context-, age-and state-dependent and that demographic rates are differently affected by interspecific competition.
Although interspecific competition explains a large proportion of the variance in some demographic rates (e.g. up to 91% of the breeding probability of 2-year old females), the remaining part of the variance still may be due to multiple environmental factors such as weather conditions or habitat quality. Comparative studies have revealed strong influence of weather conditions on many demographic traits in cervids (Saether, 1997). For instance, snow cover a given year and its resulting effect on the duration of the growing season of the vegetation may have negative long-lasting effects on chamois survival (Jonas, Geiger, & Jenny, 2008;Loison, Jullien, & Menaut, 1999;Willisch et al., 2013). The effects of harsh environmental conditions can also be age-dependent, and typically the young and senescent individuals are more sensitive to poor weather conditions (see e.g.  perspective to achieve such a goal could be to combine capturemark-recapture (CMR) data on chamois with population counts within the framework of an integrated population model (Zipkin & Saunders, 2018).
There is accumulating evidence that natural populations are influenced by the combined effects of environmental factors and intraspecific density dependence (Boyce et al., 2006;Coulson et al., 2001;Leirs et al., 1997), chamois making no exception (Willisch et al., 2013).
Interestingly, at Il Fuorn (site with low overlap), red deer and chamois population sizes exhibited similar temporal variation (Pearson's correlation coefficient = 0.570; p = 0.007) and similar average population sizes ( Figure 1). As we did not find any effect of red deer population size index on chamois demographic rates in this site, we can hypoth- Bayesian multi-population integrated model to assess the competitive interactions of two sympatric duck species. Here, we show that multi-event capture-recapture models can be powerful tools to understand how a competing species influences the demographic performances of a sympatric species. While we focused on pairwise interactions, demographic rates of chamois could also be influenced by other competitors, as for example ibex present at Val Trupchun (Herfindal et al., 2019). Expanding our approach to more than two species offers promising avenues of research (Levine, Bascompte, Adler, & Allesina, 2017).
We provide evidence for contrasting demographic responses to an increase in the density of competitors, the responses to interspecific competition being age-, state-, context-and rate-specific.
We thus strongly recommend relaxing the assumption of equal responses of all individuals to interspecific competition and to move towards more mechanistic approaches. Mechanistic models are crucial to better understand how natural populations respond to changes in their environment and will ultimately help us to predict their dynamics in a changing world (Urban et al., 2016).

ACK N OWLED G EM ENTS
We warmly thank Rémi Choquet, Guillaume Souchay, Anne Loison, Jean-Michel Gaillard and one anonymous reviewer for helpful comments on an earlier version of this manuscript. We also thank Stefano Focardi for stimulating discussions about ungulate monitoring. We

DATA AVA I L A B I L I T Y S TAT E M E N T
Data available from the Dryad Digital Repository https://doi. org/10.5061/dryad.c866t 1g4g (Gamelon, Filli, Saether, & Herfindal, 2020).