# Trap-dependence in capture-recapture studies: empirical evidence in vertebrates and biological meaning

Jessica Cachelou, Jean-Michel Gaillard, Agathe Chassagneux, Eric Baubet, Marlène Gamelon

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Jessica Cachelou, Jean-Michel Gaillard, Agathe Chassagneux, Eric Baubet, Marlène Gamelon. Trap-dependence in capture-recapture studies: empirical evidence in vertebrates and biological meaning. Oikos, In press, 10.1002/oik.11715 . hal-05323190

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OIKOS

Forum

Trap-dependence in capture–recapture studies: empirical
evidence in vertebrates and biological meaning

Jessica Cachelou ID 1,2,3, Jean-Michel Gaillard<fnref n="1" />, Agathe Chassagneux<fnref n="2" />, Eric Baubet<fnref n="3" />, Marlène Gamelon ID<fnref n="1" />

Correspondence: Jessica Cachelou (jessica.cachelou@gmail.com)

Oikos

2025: e11715

doi: 10.1002/oik.11715

Subject Editor:
Melanie Dammhahn
Editor-in-Chief:
Paulo R. Guimaraes

Accepted 5 September 2025

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Capture–recapture (CR) models have been used for decades to estimate population size and demographic rates in natural populations from the monitoring of individuals. One of the most frequent deviations from assumptions required in CR studies is the immediate trap-dependence that corresponds to the correlation between capture events. We review empirical evidence of immediate trap-dependence across vertebrate populations where several capture types exist, record possible variation in the occurrence and the sign of trap-dependence and discuss its biological meaning. We highlight that when trap-dependence occurs, trap-happiness, the higher probability for an individual to be captured again at *i* + 1 if captured at *i*, is the rule rather than the exception, whatever the type of capture. However, the occurrence of trap-dependence varies among populations of a given species and only displays a moderate repeatability in a given species. It also varies within a population depending on sex, age, or type of mark, and reflects among-individual variation in personality (bold versus shy), social status, or ecological context. We argue that immediate trap-dependence can be seen as a form of dynamic heterogeneity, reflecting clear among-individual differences. Although trap-dependence is generally considered simply as a noise to account for, it has a clear biological meaning in terms of among-individual differences.

Keywords: capture-mark-recapture, goodness-of-fit test, individual heterogeneity, individual monitoring, inter-individual differences, resighting, unequal catchability

Introduction

Capture–recapture (hereafter, CR) studies consist in monitoring over time individu-
als in the wild. Individuals are captured (physically or not), marked, and recaptured.
Originally developed to estimate population size of demographically closed popula-
tions (Petersen 1896, Lincoln 1930), single-state CR methods have rapidly evolved
to estimate variation over time in survival rates (Cormack 1964) and population size

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<footnote n="1">¹Université Claude Bernard Lyon 1, CNRS, VetAgro Sup, UMR 5558 Biométrie et Biologie Evolutive, Villeurbanne Cedex, France.</footnote>

<footnote n="2">²Fondation François Sommer, Pôle Nature, Paris, France</footnote>

<footnote n="3">³Office Français de la Biodiversité, DRAS-Service Conservation et Gestion des Espèces à Enjeux, Montfort, Birieux, France</footnote>
(Jolly 1965, Seber 1965) in demographically open popula-
tions, based on the same statistical model (i.e. the so-called
Cormack–Jolly–Seber (CJS) model; Brownie 1986). This
model has then been extended to cases where individuals are
detected in several states (e.g. breeding versus non-breeding,
multiple sites), these more complex models being called mul-
tistate CR models (Lebreton et al. 2009).

Two main sources of lack of fit in CR studies come from
transience and trap-dependence. First, transience is well
understood (Pradel et al. 1997, Genovart and Pradel 2019)
and can arise when “individuals captured for the first time
(‘new individuals’) have a lower expectation of being re-
observed in the future, as compared to individuals of the same
sample that had been captured previously (‘old individuals’)”
(Pradel et al. 1997, Genovart and Pradel 2019, p. 2). This can
result from various biological effects, such as aging, costs of
first reproduction, emigration (resident versus transient indi-
viduals) or permanent dispersal from the study area. Second,
trap-dependence corresponds to different capture probabili-
ties between individuals captured previously or not (Pradel
1993). Historically, trap-dependence has been interpreted
as the unequal catchability among individuals caused by the
direct response to capture event (Pollock 1980). However,
the definition of trap-dependence has changed through time,
and many authors currently define trap-dependence more
broadly as any source of unequal catchability among indi-
viduals (Pradel and Sanz-Aguilar 2012).

In closed populations, there is a set of models (*M*) that allows incorporating variation in capture probabilities due to heterogeneity among individuals (*M*<sub>b</sub>), trap response (*M*<sub>t</sub>), time variation in capture probabilities (*M*<sub>v</sub>) and possible combinations of these factors (e.g. *M*<sub>b,t</sub>, *M*<sub>t,t</sub>; Pollock 1991). The null model (*M*<sub>0</sub>) considers a constant capture probability for each animal at each capture event. These models can be compared using

model selection procedure, leading to the occurrence of trap
response when the model retained is M<sub>b</sub> (i.e. behavioral response
to capture). In open populations, to assess the fit of single- and
multi-state CR models to data collected in the field, some
goodness-of-fit (GOF) tests have been developed (see Box 1 for
a description of the test of immediate trap-dependence). In this
review, we define immediate trap-dependence as described by
Pradel and Sanz-Aguilar (2012, p. 1): “any correlation between
capture events whatever its nature”. Following this defini-
tion, the null hypothesis H<sub>0</sub>(i) is: “there is no difference in
the probabilities of being reencountered at i + 1 between those
encountered and not encountered at occasion i conditional on
presence at both occasions” (Choquet et al. 2005, p. 26; Box
1). Alternatively, if H<sub>0</sub> is rejected, this means that successive
capture events are correlated. In that case, ‘trap-happiness’ (or
its opposite ‘trap-shyness’) corresponds to a higher (or lower)
probability to be recaptured at i + 1 for an individual previously
caught at i, compared to an individual not previously caught.
Up to now, immediate trap-dependence has been typically
viewed as a nuisance process that needs to be corrected for in
CR models (Pradel 1993, Lebreton 1995, Abadi et al. 2013).
However, the extent immediate trap-dependence is widespread
in nature, its biological meaning in terms of among-individual
differences in catchability and its consideration in CR studies
have not yet been systematically reviewed and assessed.

This review aims at filling this knowledge gap by focusing
on the literature pertaining to immediate trap-dependence
(Box 1) in open populations using a GOF test. We explore the
diversity of trap-dependence patterns across and within spe-
cies. In particular, we discuss the type of capture used in the
studies, the biological meaning inferred through trap-depen-
dence at both inter- and intra-specific levels, and the diver-
sity of models proposed to assess immediate trap-dependence.
Finally, we raise some conceptual challenges and propose some

**Box 1. Goodness-of-fit (GOF) test: a focus on immediate trap-dependence.**

To test the applicability of the Cormack–Jolly–Seber model and the presence of immediate trap-dependence, Tests 2.CT and M.ITEC of GOF are used. The null hypothesis H₀(i) of the tests 2.CT / M.ITEC is: “there is no difference in the probabilities of being reencountered at i + 1 between those encountered and not encountered at occasion i conditional on presence at both occasions” (Choquet et al. 2005, p. 26). This null hypothesis corresponds to an absence of among-individual differences in recapture / resighting probability. If the test (2.CT or M.ITEC) is statistically significant, then it means that H₀ should be rejected, and that there is a difference in the probabilities of being reencountered at i + 1 between those encountered and not encountered at occasion i conditional on presence at both occasions. This indicates the occurrence of immediate trap-dependence.

The test also gives the sign of the immediate trap-dependence through the statistic z. The statistic z is based on the following hypothesis: “H<sub>1</sub>(i): there is a difference in the probability of being reencountered at i + 1 between those encountered and not encountered at occasion i conditional on presence at both occasions” (Choquet et al. 2005, p. 27), and the z sign is calculated as the difference between the observed number of individuals encountered at i + 1, knowing that they are not encountered at i; and the expected number of individuals encountered at i + 1, knowing that they are not encountered at i. The alternative hypothesis is: “HT1(i): among individuals alive at both occasions i and i + 1, those encountered at i tend to be less (if trap-shy) or more (if trap-happy) reencountered at i + 1” (Choquet et al. 2005, p. 27). If the z sign is negative, a given individual has a higher probability to be recaptured if it was captured earlier: this corresponds to ‘trap-happiness’. If the z sign is positive, a given individual has a lower probability to be recaptured if it was captured earlier: this corresponds to ‘trap-shyness’ (Choquet et al. 2005).
perspectives to enhance the biological meaning of trap-dependence in CR studies, particularly with regards to individual differences.

## Literature search

We conducted an extensive literature search on immediate trap-dependence in CR studies in open populations, specifically focusing on papers citing the pioneering work of Pradel (1993) on immediate trap-dependence, and those citing Pradel and Sanz-Aguilar (2012) that provided a new methodological approach to account for immediate trap-dependence in CR models. Moreover, we looked for papers containing the following key words: 'Release + trap-dependence + Burnham' and 'U-Care + trap-dependence', in Google Scholar in September 2023. We added these key words because 1) Release (Burnham et al. 1987) was the first software allowing proper tests of trap-dependence in CR studies, and 2) the more recently proposed U-Care software (Choquet et al. 2000) is nowadays commonly used tool to test for trap-dependence. Using these key words helped to record most CR studies that tested the assumption of unequal catchability among individuals between two successive capture events. In the selected studies, several outputs of the GOF test can be provided, such as test 3, test 2, and test of positive association (Table 8 in Jeyam et al. 2018). While the test 3.SR is well suited to test transience effects, the test 2.CT (or M.ITEC for multistate models) is particularly appropriate to test for immediate trap-happiness and trap-shyness (Jeyam et al. 2018). We thus focused specifically on the test 2.CT (or M.ITEC for multistate models). It is thus important to remind that a statistically significant test 2.CT in GOF may be related to trap-dependence effect but also to individual heterogeneity (i.e. among-individual variation in terms of phenotypic attributes or life-history traits). Specific tests for individual heterogeneity have been available only recently (in 2018 with the test of positive association from Jeyam et al. 2018). Consequently, a lot of papers in this review highlight both trap-dependence and / or individual heterogeneity with a statistically significant test 2.CT. Nowadays, we argue that it is crucial to test for individual heterogeneity when test 2.CT is statistically significant to better disentangle true immediate trap-dependence and individual heterogeneity at capture.

We excluded Master and PhD dissertations, resulting in the consideration of 633 papers, including 586 research articles, 30 methodological papers, 4 books and 13 reviews (Step 1, Supporting information). We did not find any paper on spatial capture-recapture studies, even when the type of capture is camera traps. We excluded the paper by Viallefont et al. (1999) on human *Homo sapiens*. Due to the low number of case studies on invertebrates (e.g. insects, arachnids, malacostraca, gastropoda) and plants (i.e. 2.6% of the papers – 15 papers in total), hereafter, we focused our analysis on vertebrates, which represented up to 97.4 % of the recorded case studies (i.e. 570 papers; see Step 2, Supporting information). As expected, the number of papers

explicitly testing for immediate trap-dependence has markedly increased since 1995, but the proportion of CR studies testing for trap-dependence has not changed in the last 25 years (i.e. 75%; Supporting information).

After keeping only studies that provided explicit test of immediate trap-dependence (tests 2.CT and M.ITEC of the GOF, Box 1), we retrieved 483 papers. Some of them included several species, while others included several populations of a given species (i.e. 1228 case studies in total; see Supporting information for all case studies). There was a large range of life histories, going from fast-living species like deer mouse *Peromyscus maniculatus* or great tit *Parus major* to slow-living species such as blue whale *Balaenoptera musculus* or black-browed albatross *Thalassarche melanophris*. Importantly, we found that 44% provided evidence for immediate trap-dependence, while 56% did not (Step 3, Supporting information). Among those studies that reported statistical evidence of immediate trap-dependence, only 39.8% (i.e. 215 case studies) provided a biological interpretation of this effect (27% interpreted as among-individual differences – 146 case studies, and 12.8% interpreted as observer effect – 69 case studies), leaving 60.2% (i.e. 325 case studies) that did not give any biological explanation for this immediate trap-dependence effect. Moreover, among the studies that reported statistical evidence of immediate trap-dependence, nearly half of the studies (46.1%, i.e. 247) did not give any information on the sign of trap-dependence. This lack of information prevents any biological interpretation of the identified trap-dependence, and indicates that in a substantial proportion of studies, authors only considered trap-dependence as a nuisance parameter without providing a biological interpretation of this effect. When the sign of trap-dependence was provided, it was most often negative (268 cases out of 291 case studies, see Box 1 for an explanation of the sign). This corresponds to trap-happiness, i.e. that individuals captured in time *i* are more likely to be captured again in time *i* + 1. For instance, in the european storm petrel *Hydrobates pelagicus*, the probability for a bird to be recaptured at *i* + 1 if it was seen at time *i* was 0.783, while it was 0.639 for a bird not seen before (Sanz-Aguilar et al. 2010). Trap-shyness represented only 7.9% of the case studies. For instance, in common toad *Bufo bufo* (Schmidt et al. 2002), the capture probability of individuals not seen before was higher (0.898) than individuals seen before (0.561).

## What does ‘capture’ mean?

There are several types of ‘capture’ allowing individuals to be monitored over time. We divided them into three categories, from the less invasive (i.e. the individual is not physically caught) to the most invasive (i.e. the individual is physically captured at each sampling event). If several methods are used to monitor individuals, and all of the information are combined in the same dataset, we just kept the most invasive type of capture in our dataset (e.g. combination of photo-identification and genetic samples in Tardy et al. 2023).
In some case studies, the population monitoring is based on marks left by individuals rather than on individuals themselves. Thus, scat/faecal or feather samples (Marucco et al. 2009, Cayuela et al. 2019a), generally collected along a transect, do not require the physical capture of individuals. Genetic analyses are performed to identify each individual, leading to record their life history (e.g. wolf *Canis lupus*, Marucco et al. 2009). Camera traps are included in this category because there is no contact with humans (e.g. ocelot *Leopardus pardalis*, Sternberg et al. 2023). We pooled these studies in a first category called 'indirect capture'.

A widespread type of capture involves 'mark and resighting', corresponding to individuals physically captured only once, when they are marked and individually identified thereafter. The recapture events are resighting events with a telescope, binoculars, antennas or transmitters (Verkuil et al. 2010). This type of capture is commonly used in birds (e.g. white stork *Ciconia ciconia*, Sanz-Aguilar et al. 2015; lesser black-backed gull *Larus fuscus*, Rock and Vaughan 2013), and mammals (e.g. fur seal *Arctocephalus tropicalis*, Beauplet et al. 2006; hoary marmot *Marmota caligata*, Carrier et al. 2022), and sometimes used in reptiles (e.g. fence lizard *Sceloporus undulatus*, Darracq et al. 2017) and fish (e.g. coho salmon *Oncorhynchus kisutch*, Hwan et al. 2018) and constitutes the second category. Photo-identification (not camera traps) is

also included. Individuals are identified by unique notches or scars (e.g. in marine mammals) or by unique stripe / spot pattern (e.g. plains zebra *Equus quagga*). Researchers need to get close to individuals to take high-quality photos inducing a response behavior (i.e. attraction or fright).

Lastly, the third category 'mark and recapture' capture type brings together all studies where individuals are physically captured at each sampling event, involving active captures. In that case, individuals are captured by entering into traps (baited or not) or cannot avoid capture, e.g. teleanesthesia. Studies with skin biopsy samples (Baker et al. 2013) are also included in this category, which corresponds to the most invasive capture type. Studies with sample design similar to a trap are also included in this category (e.g. hair sampling, Herreman and Peacock 2013).

Whatever the type of capture, we found evidence for trap-dependence, but the occurrence of immediate trap-dependence varied with the type of capture (Fig. 1). For instance, for the less invasive method, 'indirect capture', trap-dependence was recorded in less than 30.77% of case studies, while it was recorded in more than 53.28% of case studies for a more invasive method as 'mark and resighting' (Fig. 1). To test explicitly the influence of the type of capture on the occurrence of immediate trap-dependence, we built a generalized mixed model with the occurrence of immediate

<figure><img src="image_5.png" /><figcaption>Figure 1. The occurrence of immediate trap-dependence in case studies that included an explicit test, according to the type of capture (N<sub>indirect capture</sub> = 13; N<sub>mark and resighting</sub> = 533; N<sub>mark and recapture</sub> = 665, and 17 case studies with no information on the type of capture). 'Mark and recapture' is less likely to detect trap-dependence than 'mark and resighting' and 'indirect capture'.</figcaption></figure>
trap-dependence as binomial response variable (i.e. coded
1 for 'yes' and 0 for 'no'). We included the type of capture
as categorical variable, and species was entered as a random
variable to account for repeated measures within a given
species. We compared with a null model by using Anova
(analyses were performed with R, ver. 4.1.1; www.r-project.
org). The model retained showed evidence for an effect of
the type of capture on the occurrence of trap-dependence
(χ² = 9.91, df = 2, p-value = 0.007). By looking more specif-
ically at the type of capture, we found that 'mark and recap-
ture' (–0.86, SD = 0.17, p-value < 0.01) is less likely to
detect immediate trap-dependence than 'mark and resight-
ing' (–0.20, SD = 0.18, p-value = 0.27) and 'indirect cap-
ture' (–0.53, SD = 0.90, p-value = 0.55) (Fig. 1). Indeed,
resighting individual is typically easier than recapturing it,
and allows increasing the size of the dataset by monitor-
ing many individuals during many years, which enhances
the statistical power and helps detect trap-dependence. As
an illustration, Nevoux et al. (2007, 2010) focused on the
exact same population with contrasting study duration, and
they showed a switch from no statistical evidence of trap-
dependence (for the shorter duration) to a statistically sig-
nificant test in the second (longer) study. Strikingly, among
the studies that found evidence for immediate trap-depen-
dence, whatever the type of capture used, the sign was most
often negative (trap-happiness; Box 1) with some evidence
for trap-shyness for all types of capture (Fig. 2, Supporting
information).

Intraspecific variation in the occurrence of
trap-dependence

For a given species, several populations could be studied, rang-
ing from one single population for whale shark *Rhincodon
typus* to 58 populations for yellow-bellied toad *Bombina var-
iegata*. The type of capture did not vary a lot for a given spe-
cies. For instance, the cory's shearwater *Calonectris diomedea*
is only monitored through 'mark and resighting' and 'mark
and recapture' (Fig. 3, Supporting information). Importantly,
the outcome of the immediate trap-dependence test can dif-
fer among populations. To test intraspecific variation in the
occurrence of immediate trap-dependence, we partitioned
the variance from the previous generalized mixed model, and
estimated the repeatability (R) of the occurrence of immedi-
ate trap-dependence within a given species (Nakagawa and
Schielzeth 2010). Repeatability and its sampling variance
were estimated from 1000 bootstrap iterations using 'rptR'
ver. 0.9.22 (Stoffel et al. 2017) in R. This repeatability cal-
culated from the model including the random effect 'species'
was of 0.378 on the link-scale (SE: 0.055; CI: 0.22-0.41,
p_value <0.01) and 0.348 (SE: 0.08, CI: 0.19-0.5, p_value
<0.01) on the original scale, which is slightly higher than
the mean repeatability value expected for behavioural traits
(reviewed by Bell et al. 2009). This value thus indicates a
moderate among-population heterogeneity in the occur-
rence of immediate trap-dependence within a species (e.g.

detection of trap-dependence for 1 out of 5 populations in
field vole *Microtus agrestis*, Graham and Lambin 2002, Fig. 2,
Supporting information).

The occurrence of trap-dependence can also vary within
populations. Between-sex differences are widespread in the
reviewed studies. For instance, in blue whale *Balaenoptera
musculus* and greater flamingos *Phoenicopterus roseus*,
trap-dependence occurred in females but not in males
(Ramp et al. 2006, Rendón et al. 2014). However, some
studies (e.g. on the ruff *Philomachus pugnax*) showed the
opposite response with trap-happiness detected in males
but not in females (Schmaltz et al. 2015). Similarly, trap-
dependence can be age-specific. In wild boar *Sus scrofa*,
(Toïgo et al. 2008), juveniles showed trap-happiness while
adults did not. For a given population, trap-dependence
can even vary over time. In red knot *Calidris canutus*, trap-
dependence was detected in some years, but not in others
(Lok et al. 2019). Trap-dependence was also dependent
on the type of mark used. In the pink-footed geese *Anser
brachyrhynchus* of the Eastern flyway for example, trap-
happiness was detected for individuals equipped with neck
collars, whereas no trap-dependence occurred in individuals
marked with leg rings (Madsen et al. 2014).

Intraspecific variation in the non-independence among
two successive capture events is thus the rule rather than the
exception. To what extent this is related to biological pro-
cesses and whether this corresponds to true among-individual
differences is crucial to decipher for a full understanding of
trap-dependence.

What does the non-independence among
capture events tell us?

Among-individual differences in behaviour (animal personality)

Personality corresponds to consistent among-individual dif-
ferences in behavioural traits (Biro and Stamp 2008, Sih et al.
2015). Different behavioural types may show different behav-
iours in front of traps, with individuals that can be classified as
'bold' or 'explorative' when they have a low latency to enter a
trap, and individuals that can be classified as 'shy' or 'avoider',
when they take a long time to enter a trap (Réale et al. 2007).
A bold individual should enter traps easily, favouring suc-
cessive recapture probabilities, leading to trap-happiness. At
the opposite, a shy individual should avoid traps, decreasing
successive recapture probabilities, leading to trap-shyness,
and causing different capture probabilities depending on the
personality (e.g. bighorn sheep *Ovis canadensis*; Réale et al.
2000). In contrast, if all individuals display the same per-
sonality in a population, they should respond similarly to
the trap (e.g. no among-individual differences in personal-
ity), leading all individuals to have equal recapture probabil-
ity. Therefore, non-independence among successive capture
events revealed by the test of immediate trap-dependence can
highlight behavioural differences among individuals within a
population.
<figure><img src="image_6.png" /><figcaption>Figure 2. Number of case studies depending on the sign (i.e. trap-shy or trap-happy) of the immediate trap-dependence, and according to a sample of species for mammals (A), birds (B) and actinopterygii, amphibians and reptiles (C) (see the Supporting information for the full figure). ‘Sign unknown’ corresponds to case studies with evidence for immediate trap-dependence but where there is no information on the sign (i.e. trap-happy or trap-shy). ‘No’ is for case studies with no evidence for immediate trap-dependence.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 3. Number of case studies depending on the type of capture, and according to a sample of species for mammals (A), birds (B) and actinopterygii, amphibians and reptiles (C) (see the Supporting information for the full figure). ‘NA’ corresponds to case studies that did not give any information on the type of capture.</figcaption></figure>
Previous studies have shown that individual differences in catchability, quantified as the number of captures for a given individual or as the ratio between the number of visited traps and the number of available traps, could be interpreted in terms of boldness and of exploration. These are common metrics of personality (Boon et al. 2008, Le Coeur et al. 2015, Santicchia et al. 2018) that have been shown to be repeatable (Boon et al. 2008).

## Among-individual differences in responses to capture

As individual differences in behavioural type can induce different behaviours in front of traps, the capture event can also influence the behaviour of individuals, leading to either avoidance (i.e. trap-shyness) or attraction (i.e. trap-happiness). In this case, whatever the behavioural type of the individual, the capture event may influence the behaviour of individuals caught (i.e. behavioural response to capture). For instance, if traps contain food, individuals previously captured can be more likely to enter the trap at the next capture event, subsequently affecting their probability of recapture. This results in different recapture probabilities between individuals trapped at the previous occasion and those not trapped due to food attraction (e.g. 0.427 versus 0.164, respectively; Crespin et al. 2008). Likewise, the manipulation can induce a high level of stress for some individuals, potentially leading to trap avoidance in subsequent captures (Choquet et al. 2013), as for red squirrels (Bossom et al. 2012) or reindeer (Trondud et al. 2022). In the same way, the repeated presence of observers may induce an avoidance for a specific location. For instance, blackcaps *Sylvia atricapilla* exhibited trap-shyness because previously caught birds avoided mist-net locations, and birds not trapped before had thus a higher recapture probability (0.18 versus 0.07 for birds trapped before; Belda et al. 2007).

## Among-individual differences in habitats

Within a population, individuals can have varying degrees of fidelity to specific breeding or feeding sites. For instance, in whale sharks *Rhincodon typus* from Western Australia, some individuals move between two geographic locations, while others remain in their area (Holmberg et al. 2008). Since sampling design generally focuses on a specific area, individuals that are more territorial may exhibit higher recapture or resight rates (Bearhop et al. 2003), generating trap-dependence in successive capture events. Similarly, birds demonstrate high site fidelity, particularly at nesting or breeding sites. For black-legged Kittiwakes *Rissa tridacodyla*, if an individual successfully breeds at a specific site, the probability of being resighted in subsequent years will be higher than for failed breeders, which will disperse to a new breeding site (Ponchon et al. 2018), generating again immediate trap-dependence (i.e. when individuals move between different sites or stay in a specific site among years). Therefore, non-independence among successive capture events can highlight among-individual differences in habitat use.

## Among-individual differences in breeding performance

For many species, individuals that successfully breed at year *i* may have a higher probability to reproduce at year *i + 1*, as observed in lesser black-backed gulls *Larus fuscus* (Rock and Vaughan 2013). On the other hand, individuals that fail breeding at year *i* may have a higher probability to skip again reproduction the following year *i + 1*. In contrast, some species tend to skip reproduction after a successful breeding event, the most obvious pattern being biennial reproduction. In black-footed albatross *Phoebastria nigripes*, the first reproduction is highly costly for young birds, leading some individuals to skip reproduction the following year and thereby be not present on breeding islands (Fisher 1976). All these scenarios where the capture event is linked to the breeding status, such as only breeders are present on the sampling location and can be resighted, can cause non-independence between successive capture events and lead to immediate trap-dependence.

## Among-individual differences in social status

Social status can be revealed by the test of immediate trap-dependence. Studies using indirect captures (i.e. scat sample) have demonstrated that dominant wolves (*Canis lupus*) have a higher probability to be recaptured than subordinates (Caniglia et al. 2012, Fletcher et al. 2012). Dominant wolves mark their territory by using faeces and are thus more detectable from scat samples than others (Fletcher et al. 2012). Similarly, when traps with food are used to capture individuals, social status may influence catchability. For instance, in their study on wild boar *Sus scrofa*, Rossi et al. (2011) assumed that groups with a dominant status have a better access to food and are thus more likely to enter traps (i.e. higher recapture probability) than groups with lower social status. Therefore, non-independence among successive capture events can highlight among-individual differences in social status within a population.

## Observer effect

Non-independence among successive capture events does not always reflect among-individual differences. Sometimes, non-independence among successive capture events simply results from the sampling design. For example, experienced observers who know that some nests or burrows contain individuals can regularly return to these sites (Kéry et al. 2006). This trap-dependence is generated by observers, not by animals. Visibility, accessibility, or size of the studied area (Bjorndal et al. 2003) can thus induce heterogeneity in detection probabilities and generate trap-dependence.

While trap-dependence has been initially interpreted as the unequal catchability among individuals caused by the direct response to capture event (Pollock 1980), our review highlights that trap-dependence encompasses a large range of biological processes. In particular, trap-dependence can be the signal of among-individual differences in habitat use, breeding performance or behaviour. It is crucial to interpret these among-individual differences in the context of the studied
species, its biology, the studied area, and also the sampling
design to understand better the underlying biological pro-
cesses and to distinguish a real biological effect from a simple
observer effect. For instance, in birds, when all individuals
have the exact same potential probability of being resighted,
observer sampling in closed areas will get a lower resight rate
than those sampling in open areas (Ratcliffe et al. 2008). The
observer effect, either due to the observer ability or to the
area characteristics sampled by the observer, is a 'mimicked'
trap-dependence.

Although trap-dependence occurred in each type of cap-
ture, whether it reflects true among-individual differences
in terms of e.g. personality, age and social status or rather
corresponds to methodological or observer effects has to be
discussed. For indirect capture (e.g. camera trap, sampling of
faeces), the trap-dependence detected is more likely generated
by the sampling design (e.g. camera locations) or by observer
effect (e.g. observer heterogeneity occurring in repeated tran-
sects) than by individual differences in behaviour or other
phenotypic attributes. For mark and resighting type of cap-
ture, the occurrence of immediate trap-dependence is more
likely caused by spatial heterogeneities in sampling effort
either due to differences among observers or to the geo-
graphical context that influence the detection rate; except for
species that can skip reproduction (like birds or turtles) or
temporary migrate. Finally, the mark and recapture type of
capture seems to be the best way to assess among-individual
differences in behaviour through trap-dependence, and is less
likely influenced by the study design or differences among
observers (but it can be biased towards certain behavioural
types, such as bold or explorative).

**Methodological and conceptual challenges**

Most of the retrieved case studies tested for immediate trap-
dependence to ensure that single- or multi-state CR models
satisfactorily fit the data. If not, the authors often used statis-
tical approaches to account for trap-dependence and obtain
unbiased estimates of population size, survival or reproduc-
tive parameters.

The first encounter may induce trap-dependence for sub-
sequent encounter events, particularly when the first cap-
ture involves juveniles (Souchay et al. 2013). Historically,
excluding the first capture event for all individuals provided
a simple way to correct for trap-dependence in early CR
studies (Lebreton et al. 1992, p. 105). Another method
consists to fit an age effect on capture probabilities when
marked individuals have the same age, or a time-since-
marking effect on capture probabilities if it is difficult to
know the exact age of the individuals (Omeyer et al. 2019).
Trap-dependence in CR analyses can also be handled by
including an individual covariate based on whether the
individual was captured in the previous occasion or not
(Huggins 1989, Schleimer et al. 2019).

A different method to properly account for trap-dependence
is the model proposed by Gimenez et al. (2003), which extends
Pradel's model (1993) into a multistate framework. This model
includes an unobservable state for non-captured individuals in

the previous occasion. In some studies, transition probability
between recapture states and non-recapture states are explicitly
added in multistate models (Toigo et al. 2007). A commonly
used model to account for trap-dependence is the model of
Pradel and Sanz-Aguilar (2012). It includes a trap-awareness
transition matrix, with a capture probability of trap-aware
individuals, and a capture probability of trap-unaware indi-
viduals. Trap-aware individuals are individuals that are caught,
regardless of whether they will be attracted to the traps or tend
to avoid them at the next occasion, unlike trap-unaware indi-
viduals that are not caught (Pradel and Sanz-Aguilar 2012).
An individual caught at time *i*, but not caught at time *i* + 1, is
reverting from state aware to unaware (i.e. naive state).

Concluding remarks

Individual heterogeneity corresponds to among-individual
differences in a population, which can involve phenotypic
attributes such as sex, age, body mass, size, or behavioural
traits, leading to different individual states. Besides these eas-
ily measurable individual differences, individual heterogeneity
can also be unobserved, when individuals with the same phe-
notypic attributes still differ in performance (e.g. reproduc-
tion or survival; Cam et al. 2002, reviewed by Gimenez et al.
2018). Immediate trap-dependence can be related to indi-
vidual heterogeneity and particularly to dynamic heteroge-
neity because the probability to be recaptured at time *i* + 1
is conditional on the previous state (i.e. captured or not) at
time *i*. Indeed, dynamic heterogeneity corresponds to the
within-individual differences generated by random processes
(e.g. change in climate, resource availability, parasite abun-
dance), leading to change over the life course of the indi-
viduals, through transitions between different states (e.g. age,
Plard et al. 2012). It can be defined as “a Markovian process in
which experiencing an event affects an individual and changes
its propensity to re-experience the event” (Authier et al. 2017,
p. 3349). Therefore, immediate trap-dependence, involving
that the probability to be recaptured at time *i* + 1 is condi-
tional to the previous state (i.e. captured or not) at time *i*, can
be interpreted as a form of dynamic heterogeneity.

In this review, we highlighted that trap-happiness fre-
quently occurs across taxa, with a variable propensity
among populations within a given species. This strong
intraspecific variation in catchability may be due to differ-
ences in individual attributes or environmental conditions
(i.e. among-individual variation in response to capture,
habitat use, breeding performance, or social status). The
type of capture is closely related to the focal species, and
it influences the occurrence of trap-dependence (i.e. more
likely to detect with ‘mark and resighting’ and ‘indirect
capture’). Regardless of the type of capture, it is crucial
to test for trap-dependence in CR studies for at least two
reasons: 1) properly accounting for trap-dependence leads
to unbiased estimates of demographic parameters (Pradel
1993, Lebreton 1995, Abadi et al. 2013); 2) beyond sta-
tistical aspects, our review demonstrates that testing for
trap-dependence sheds key insights on intraspecific variation in the wild. Consequently, we recommend that authors investigate trap-dependence, not by simply accounting for it to get unbiased parameter estimates, but by looking for an interpretation of the trap-dependence test that most likely uncovers a real biological signal of intraspecific variation.

*Acknowledgements* – We warmly thank the Office Français de la Biodiversité (OFB), the Association Nationale de la Recherche et de la Technologie (ANRT), the Fondation François Sommer and the CNRS to support our study. We thank the Editor, Marco Festa-Bianchet and Ana Sanz-Aguilar for insightful comments on the previous draft.

*Funding* – This study was funded by the Office Français de la Biodiversité (OFB), the Association Nationale de la Recherche et de la Technologie (ANRT), the Fondation François Sommer and was supported by the CNRS. MG was supported by the ‘PURE’ ANR JCJC program (ANR-23-CE02-0028).

*Conflict of interest* – The authors declare no conflict of interest.

## Author contributions

**Jessica Cachelou:** Formal analysis (lead); Writing – original draft (lead); Writing – review and editing (equal).

**Jean-Michel Gaillard:** Writing – review and editing (equal).

**Agathe Chassagneux:** Writing – review and editing (equal).

**Eric Baubet:** Writing – review and editing (equal).

## Data availability statement

Data sharing is not applicable to this article as none new data were created or analyzed in this study.

## Supporting information

The Supporting information associated with this article is available with the online version.

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