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I am interested in identifying sex-specific survival rates. I have a long-term dataset of individually marked birds from one breeding colony. Of these, I am able to genetically sex a subset. Additionally, I have access to mark-recapture data on nearby breeding colonies and so can estimate emigration from my target breeding colony. However, I am only able to sex individuals from my focal breeding colony.
My research project addresses both survival and dispersal (permanent emigration). So I'd like to disentangle these as much as possible and look at effects of sex. One approach is to only model the subset of birds I'm able to sex. Another approach would be to model all individuals, including unknown sex, and apply the techniques in Nichols et al. (2004) to apply probabilities of "male or female" to unknown-sex birds (I may be summarizing that poorly).
Can I use a multi-site model if I only include individuals marked on one colony, but do have data for permanent emigration to other colonies? Would it make sense to use a multi-site model with all individuals from all colonies but only have sex information from one colony?
Thanks in advance!
Nichols, J.D., Kendall, W.L., Hines, J.E. and Spendelow, J.A. 2004. Estimation of sex‐specific survival from capture-recapture data when sex is not always known. Ecology 85(12):3192-3201.
Estimate sex-specific survival from mark-recapture data using multi-site, sex-specific cormack-jolly-seber model? - Biology
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Estimating and Visualizing Fitness Surfaces Using Mark-Recapture Data
Olivier Gimenez, 1,2 Arnaud Grégoire, 1,3 Thomas Lenormand 1,4
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Understanding how selection operates on a set of phenotypic traits is central to evolutionary biology. Often, it requires estimating survival (or other fitness-related life-history traits) which can be difficult to obtain for natural populations because individuals cannot be exhaustively followed. To cope with this issue of imperfect detection, we advocate the use of mark-recapture data and we provide a general framework for both the estimation of linear and nonlinear selection gradients and the visualization of fitness surfaces. To quantify the strength of selection, the standard second-order polynomial regression method is integrated in mark-recapture models. To visualize the form of selection, we use splines to display selection acting on multivariate phenotypes in the most flexible way. We employ Markov chain Monte Carlo sampling in a Bayesian framework to estimate model parameters, assessing traits relevance and calculating the optimal amount of smoothing. We illustrate our approach using data from a wild population of Common blackbirds (Turdus merula) to investigate survival in relation to morphological traits, and provide evidence for correlational selection using the new methodology. Overall, the framework we propose will help in exploring the full potential of mark-recapture data to study natural selection.
© 2009 The Society for the Study of Evolution.
Olivier Gimenez , Arnaud Grégoire , and Thomas Lenormand "Estimating and Visualizing Fitness Surfaces Using Mark-Recapture Data," Evolution 63(12), 3097-3105, (1 December 2009). https://doi.org/10.1111/j.1558-5646.2009.00783.x
Received: 26 November 2008 Accepted: 1 May 2009 Published: 1 December 2009
Sharks play critical roles in top-down regulation of marine ecosystems (Ferretti et al., 2010 Estes et al., 2011). The white shark (Carcharodon carcharias) is a top consumer in oceanic and neritic ecosystems. Currently, little empirical data exist to estimate vital rates or population dynamics of this species due to challenges inherent in studying a large pelagic predator. White sharks are long-lived, late to mature, and produce few young making them vulnerable to overexploitation (Cailliet et al., 1985 Francis, 1996 Chapple and Botsford, 2013 Andrews and Kerr, 2015 Hamady et al., 2014). White sharks are protected internationally under the Convention on International Trade in Endangered Species (CITES, Appendix II) and listed as vulnerable under the World Conservation Union Red List (IUCN, Category VU A1cdưcd) (Dulvy et al., 2008).
Recent genetic studies have shown that the northeastern Pacific (NEP) white shark population is genetically distinct from other known white shark populations in South Africa, Australia-New Zealand, Northwest Pacific, Northwest Atlantic, and the Mediterranean (Pardini et al., 2000 Gubili et al., 2010, 2012 Jorgensen et al., 2010 Tanaka et al., 2011). Electronic tags have shown that NEP sub-adult (sharks Ϣ.4 m total length (TL) but not mature) and adult white sharks [females > 4.5 m TL (Francis, 1996) and males > 3.8 m TL (Pratt, 1996)] aggregate annually at two primary sites in the California Current: central California, USA (Klimley, 1985 Klimley and Anderson, 1996) and Guadalupe Island, Mexico (Domeier and Nasby-Lucas, 2008). Tracks generated from time series data recorded on pop-up satellite archival tags (PAT) indicate that both groups make similar and predictable offshore migrations into the subtropical gyre to a geographic area known as the “White Shark Café” (Weng et al., 2007a Jorgensen et al., 2010) located approximately 2200 kilometers west of the northern portion of the Baja Peninsula (Domeier and Nasby-Lucas, 2008 Jorgensen et al., 2010). In addition, white sharks tagged in the NEP neritic foraging areas travel as far west as the Hawaiian Archipelago (Boustany et al., 2002 Weng et al., 2007a Domeier and Nasby-Lucas, 2008 Jorgensen et al., 2010). To date, there are few data indicating that sharks visit both coastal aggregation sites off the North American coast but some migratory exchange is evident from acoustic tag information (Jorgensen et al., 2012b).
Satellite tagging has been combined with acoustic tagging data in the central California aggregation sites, which together have revealed that these annual migrations of white sharks inclusive of an onshore and offshore phase are predictable and repeatable. Males show a consistent “to and from” annual migration from coastal aggregation sites at central California to the White Shark Café and/or Hawaii and back. In contrast, females spend more time offshore, have a more expansive range, which includes more southerly coastal locations than those used by males (Klimley, 1985 Jorgensen et al., 2012a). After sharks experience offshore movements, tagging data indicates sharks of both sexes return to central California (Jorgensen et al., 2010). This migratory behavior supports the use of a mark-recapture framework for estimation of population parameters at coastal sites (Chapple et al., 2011). Several studies have demonstrated that the pattern on the trailing edge of the white shark first dorsal fin is stable over many years and can be used as a means of identifying individuals, i.e., serves as a natural “mark” (Gubili et al., 2009 Anderson et al., 2011 Towner et al., 2013). The population trend remains unknown in central California although interpretations of catch per unit effort data of young of the year white sharks in Southern California have been taken to suggest an increasing trend in the smaller length classes (ς m) (Lowe et al., 2012).
Mark recapture studies (Chapple et al., 2011 Sosa-Nishizaki et al., 2012) at both California Current aggregation sites indicate the sex ratio of sub-adult and adult white sharks is apparently skewed toward males at the coastal aggregation sites of central California and Guadalupe Island. Chapple et al. (2011) observed a ratio of 3.6:1 (69 males: 19 females). It should be noted that an additional 42 individuals were observed but could not be assigned to sex during the 3-year study making it impossible without further analysis to accurately assess the actual sample sex ratio. This uncertainty is especially interesting, given that Sosa-Nishizaki et al. (2012) observed a much more even sex ratio of 1.5:1 (67 males: 46 females) at Guadalupe Island in a 9-year study with no unknown sexed animals in their sample dataset. A recent abundance estimate of California Current white sharks (Dewar et al., 2013) assumed a 1:1 sex ratio although neither empirical dataset from central California or Guadalupe Island suggests this to be true. Outside of an observed ߡ:1 sex ratio at birth (Uchida et al., 1996), there are no data to suggest equal numbers of older (sub-adult and adult) males and females. A skewed ratio may in fact be true, a critical consideration for population studies. First, inflating the number of females to equal males could falsely increase the population (requiring there to be more females than evident in the data set) and may ignore underlying behavioral or physiological causes of the bias (affecting management and conservation efforts). Also, as females are likely a more important demographic for population trend and viability than males, artificially overinflating the number of females to establish parity with males could overestimate reproductive potential of the population and resilience to perturbation. Therefore, it will be important to determine if the observed skewed sex ratio at both central California and Guadalupe Island is in fact real.
The strongly skewed observed sex ratio for sharks in the California population could be a result of two very different processes. First, sex-specific behavioral differences could make females less likely to be sampled, which would bias the observed sex ratio away from the true ratio. Second, demographic differences could be at least partially responsible for the skewed sex ratio if mortality rates are higher for females. For example, migratory differences could expose females to greater mortality risks. Clearly, understanding the extent to which the observed skew in sex ratio is apparent (due to behavioral differences) or real (due to survival differences) is crucial for our evaluation of white shark population dynamics and management.
Because white sharks have a slow life history and survival of mature sharks is expected to be important to population persistence, disparate mortality in males and females could have important population level consequences and effect how this group is managed and assessed. To date, the only survival rate estimates that exist were developed with ad hoc methods (Smith et al., 1998 Cortés, 2002), and nothing is known about potential differences in mortality rates between the sexes. Clearly there is strong need to obtain survival rates and test for differences between sexes using rigorous estimation methods and multiple years of empirical data. An understanding of annual survival could be an important step toward gaging the sustainability of this population and used in predictive models to assess status (i.e., population viability analyses). Additionally, survival rates can inform current management strategy as to the effectiveness of current protective measures for white sharks off central California.
Annual apparent survival rates estimate the proportion of the population that will survive, on average, from 1 year to the next. The complement of apparent survival rate (i.e., 1 – apparent survival rate) includes an estimate of mortality and permanent emigration, or what proportion of the population is lost on average over the course of a year. However, when estimating survival rates, sex-based differences in survival could be obscured if sampling regimes do not explicitly account for differential detection probability (Lebreton et al., 1992). White sharks can be assigned to sex when visually observed in an aggregation site by noting the presence of claspers on males or absence of claspers for females. However, the probability of assigning sex is unequal, as it is easier to positively identify presence of claspers than confirm their absence (Chapple et al., 2011). Nichols et al. (2004) developed a model to test for differences in apparent survival between sexes when imperfect sex assignment occurs on sampling occasions, a viable model that can be used across taxa. Additionally, this model estimates the sex ratio of the sample population after probabilistically assigning sex to animals of unknown sex.
In this study, we used empirical mark-recapture data from 6 years at central California aggregation sites to estimate the apparent survival rates specific to this group of white sharks. The new model enabled testing if the observed skewed sex ratio of sub adult and adult sharks at coastal aggregation sites in central California is a result of disparate apparent survival rates, while accounting for imperfect detection and imperfect sex assignment.
In a conservation context, monitoring to determine trends in population size is crucial to inform assessments of wildlife populations (e.g., IUCN, 2017 ). The cause of a trend may be understood from knowledge of human-induced mortality, for example, but in other cases the cause may not be so easily revealed. In such cases, estimates of fecundity and survival can play an important role in helping to understand which element(s) of life history may be responsible for changes in population size (e.g., Gaillard, Festa-Bianchet, & Yoccoz, 1998 Currey et al., 2011 ).
Long-term individual-based studies are an effective tool to estimate population parameters from discrete populations in which individuals can be repeatedly captured over time (Clutton-Brock and Sheldon, 2010), and are particularly important in long-lived species for which the ability to detect changes in demographic parameters may require decades of data. Capture–recapture analyses of individual-based data have been used extensively in ecology (Burnham, Anderson, White, Brownie, & Pollock, 1987 Cormack, 1964 ) to estimate survival probabilities (e.g., Gaillard et al., 1998 Altwegg et al., 2008 ). Obtaining robust estimates of survival probabilities in cetacean populations remains challenging, and estimates of age- and sex-specific survival are scarce (e.g., Bradford et al., 2006 Currey et al., 2009 Ramp, Bérubé, Palsboll, Hagen, & Sears, 2010 ).
Our focus here is the east coast of Scotland bottlenose dolphin (Tursiops truncatus) population (Figure 1), which long-term photoidentification monitoring since 1989 indicates is increasing, especially since around 2000 (Cheney, Graham, Barton, Hammond, & Thompson, 2018 Wilson, Hammond, & Thompson, 1999 Wilson, Reid, Grellier, Thompson, & Hammond, 2004 ). Survival rates have been estimated for this population using eight (Sanders-Reed, Hammond, Grellier, & Thompson, 1999 ) and 13 (Corkrey et al., 2008 ) years of data collected in the 1990s to early 2000s. Data for both studies indicated a greater probability of a population decline than of an increase. However, this population expanded its distributional range during the 1990s (Wilson et al., 2004 ), meaning that these estimated declines are likely to be confounded with temporary emigration (Corkrey et al., 2008 ).
Here, we use a 27 year-long dataset of individual capture histories to investigate variations in age- and sex-specific survival rates in this small, discrete population of bottlenose dolphins. We explore whether changes in juvenile/adult survival could help explain the observed increase in population size and investigate variation in calf survival. We first estimate annual survival of juvenile/adult dolphins using robust design capture–recapture models, which incorporate the estimation of temporary emigration, including assessing the support for a trend over time. We then explore whether there is evidence for sex-specific survival using multistate capture–recapture models. We estimate calf survival during the first 3 years of life for a subset of dolphins followed since their year of birth using age-specific models, and investigate whether survivorship of first-born calves was different from calves born subsequently.
Sex is one of the main individual features shaping life-history traits in most organisms. It is known to influence survival, dispersal, recruitment and other life-history parameters that have important consequences for demography and population dynamics ( Greenwood 1980 Stearns 1992 Gowaty 1993 Clobert et al. 2001 ). Thus, it is essential to assess the potential effects of sex in ecological and evolutionary studies ( Krebs 2001 ). However, incorporating sex into these studies depends on the ability to assign sex with certainty. Difficulties may appear when studying monomorphic or slightly dimorphic species that are monitored in the field from a distance and when direct manipulation for gonadal inspection, biometrical or acoustical discrimination, or molecular sexing is not possible in such cases, field biologists often rely on sexual behaviour (e.g. courtship, copulation) to distinguish males from females (e.g. Moynihan 1955 Bustnes et al. 2000 ). In these cases, it may occur that an animal that has once been recorded as a male may be later referred to as a female or vice versa ( Pradel et al. 2008 ). This is because some of the behavioural criteria used in the field are wrongly assumed to be totally reliable or because some criteria are more prone to field observation errors. When such potential biases are recognized, field biologists tend to either refuse to estimate sex-specific parameters or to analyse only those individuals whose sex has been determined with a reasonable degree of certainty, thereby also leading to biased sampling (e.g. if the accuracy of sexing changes with animal age or condition). However, in the latter case, many individuals included in the data set have to be discarded (for instance, Pradel et al. 2008 discarded up to 80% of the total data set) owing to uncertainty regarding their sex assignment ( Nichols et al. 2004 ). Another option is to use animals that have not been sexed as a third group, but this approach yields biased (i.e. overestimated) demographic parameters for the two sex groups, because animals assigned to these groups are likely to have survived longer (i.e. to have been observed on more occasions) (see Oro, Pradel & Lebreton 1999 Nichols et al. 2004 Pradel et al. 2008 ). To overcome this bias, Oro & Pradel (2000) proposed that the survival of the unknown-sex individuals be considered as a weighted average of the survival of the two sexes, with the weights reflecting the proportions of males and females among the animals of uncertain sex. However, this method presupposes the existence of a given sex ratio in the population and does not use all the information available from field observations. Finally, Nichols et al. (2004) , in an attempt to overcome the fact that survival estimates for animals of known sex are positively biased, proposed a reliable multistate model approach with probabilistic transitions from unknown sex to known sex.
Nichols et al. (2004) showed that it is possible to estimate sex-specific demographic parameters such as survival when the sex is not known for all individuals. Nevertheless, these authors also acknowledged that their method relied on the assumption that animals were assigned to a specific sex with certainty. Furthermore, in most cases, the certainty of assigning sex increases with the number of times an individual is recaptured or resighted, and thus, sex is known with a higher degree of certainty for individuals who do not disperse permanently or for those that live longer (see Nichols et al. 2004 ). Pradel et al. (2008) developed the first capture–recapture survival model to account for uncertainty in the assessment of sex: they examined parameter redundancy and the usefulness of incorporating the least reliable sexing clues and the genetic determination of sex available for only a handful of individuals as a means of improving the efficiency of the optimization algorithm (see also Conn & Cooch’s (2009) application to disease modelling). Given that its efficiency has been proven, here we further develop this multi-event capture–recapture modelling to examine sex differences in a number of demographic parameters, namely survival and transience, as well as to analyse the sex ratio in the population. In other words, here we formulate a new parameterization and extend the multi-event model described by Pradel (2005) . Contrary to Nichols et al. (2004) , we treat the problem of reliability in the criteria used to sex individuals by estimating the probability of error for each field-sexing criteria, as well as the probability of judging (assigning sex) over time. Additionally, we explore the sexual behaviour of the study species during its reproductive season. For these purposes, we used a large, long-term capture–recapture data set for Audouin’s gull Larus audouinii, a monomorphic species breeding in the Ebro delta in the western Mediterranean, where 65% of the world’s breeding population occurs. Although the demography and population dynamics of this population have been studied in depth (e.g. Oro & Pradel 1999, 2000 Oro, Pradel & Lebreton 1999 Oro & Ruxton 2001 Cam et al. 2004 Oro et al. 2004 Tavecchia et al. 2007 ), few such analyses (except Oro, Pradel & Lebreton 1999 ) have ever considered the potential effects of sex given the inherent difficulties in distinguishing the sex of breeding birds.
We thank M. Bjorklund, E. Cooch, and K. Theodorou for helpful suggestions C. Crainiceanu for providing bits of WinBUGS and R codes, E. Kazakou for providing computing resources and support and the School of Environment at the University of the Aegean (Greece) for hospitality. We thank the CRBPO, the Ministère de l’Environnement, the Ville de Dijon and Jardin Botanique for licences and access to the study site. We are grateful to all volunteers for contributing to the field work.
SI Materials and Methods
Mark–Recapture Survival Analysis.
To estimate daily chick survival (DCS), we used Cormack–Jolly–Seber models with 1-day encounter intervals. Because there is a strong nonlinear age effect on DCS in plovers (73, 74), our design matrices included chick age as a quadratic covariate (i.e., age 2 ) with sex and year as factors. Thus, the probability of survival from hatching to fledging was calculated simply as the product of all 25 age-specific estimates of DCS. Likewise, we used Cormack–Jolly–Seber models to estimate juvenile and adult survival but with 1-year encounter intervals. Juvenile and adult survival models were constructed from design matrices that included sex, year, and stage as factors.
Because we were interested in stage- and sex-specific estimates of survival, all models included a ϕ ∼ sex × stage component in the case of juvenile and adult analyses or a ϕ ∼ sex × age 2 component in the case of chick analyses. Two-way interactions between all variables were assessed for encounter probability modeling. We constructed survival models with the R package “RMark” (75) and estimated demographic parameters via maximum likelihood implemented in program MARK (76). We evaluated whether our data was appropriately dispersed (29) (i.e., c-hat ≤ 3) by using the “median c-hat” goodness-of-fit bootstrap simulation in program MARK (76).
Estimating Hatching Sex Ratio.
To account for potential sex biases arising before the chick stage (i.e., sex allocation), we evaluated if the hatching sex ratio deviated significantly from parity using a general linear mixed effect model fit with binomial error and a logit function (R package “lme4”) (77). In this model, the response variable was chick sex, and brood identifier was included as a random factor to control for the nonindependence of siblings. Significance was inferred from the intercept estimate, with α = 0.05 . Because of the precocial nature of plover chicks, posthatch brood mixing can occur. Consequently, our dataset for analyzing hatching sex ratio included only complete broods (i.e., no missing chicks) that were captured at the nest on the same day of hatching.
Evaluating Uncertainty of the ASR.
To evaluate uncertainty in our estimate of ASR caused by sampling and process variation in our survival parameters, we implemented a bootstrapping procedure in which each bootstrap (i) randomly sampled our mark–recapture data with replacement, (ii) ran the survival analyses described above, (iii) derived stage- and sex-specific estimates of apparent survival based on the model with the lowest corrected Akaike’s information criterion (AICc), (iv) constructed the matrix model of these estimates, (v) derived the stable stage distribution through simulation of 1,000 time steps, and (vi) calculated ASR from the final stage distribution. This approach ensured that parameter correlations within the matrix were retained for each bootstrap and that the nonlinear mating function reached equilibrium. We ran 1,000 bootstraps and evaluated the accuracy of our ASR estimate by determining the 95% confidence interval of its bootstrapped distribution.
Our bootstrap procedure showed that variation in encounter probability of juveniles and adults was best explained by sex, year, and stage [model p ∼ year + stage × sex : median △ AICc = 0 (95% CI = 0–7.58), mean w i = 0.43 (95% CI = 0.02–0.99)] (Fig. S2). In contrast, the encounter probability of chicks was the same for males and females but varied among years and as a quadratic function of age [model p ∼ year × age 2 : median △ AICc = 0 (95% CI = 0–1.97), mean w i = 0.94 (95% CI = 0.18–1)] (Fig. S2). Our mark–recapture data were not overdispersed [median c-hat = 1.36 (95% CI = 1.11–1.62)].
In many animal populations, demographic parameters such as survival and recruitment vary markedly with age, as do parameters related to sampling, such as capture probability. Failing to account for such variation can result in biased estimates of population-level rates. However, estimating age-dependent survival rates can be challenging because ages of individuals are rarely known unless tagging is done at birth. For many species, it is possible to infer age based on size. In capture–recapture studies of such species, it is possible to use a growth model to infer the age at first capture of individuals. We show how to build estimates of age-dependent survival into a capture–mark–recapture model based on data obtained in a capture–recapture study. We first show how estimates of age based on length increments closely match those based on definitive aging methods. In simulated analyses, we show that both individual ages and age-dependent survival rates estimated from simulated data closely match true values. With our approach, we are able to estimate the age-specific apparent survival rates of Murray and trout cod in the Murray River, Australia. Our model structure provides a flexible framework within which to investigate various aspects of how survival varies with age and will have extensions within a wide range of ecological studies of animals where age can be estimated based on size.
Spatial capture–recapture reveals age- and sex-specific survival and movement in stream amphibians
Life-history information sets the foundation for our understanding of ecology and conservation requirements. For many species, this information is lacking even for basic demographic rates such as survival and movement. When survival and movement estimates are available, they are often derived from mixed demographic groups and do not consider differences among life stages or sexes, which is critical, because life stages and sexes often contribute differentially to population dynamics. We used hierarchical models informed with spatial capture–mark–recapture data of Ascaphus montanus (Rocky Mountain tailed frog) in five streams and A. truei (coastal tailed frog) in one stream to estimate variation in survival and movement by sex and age, represented by size. By incorporating survival and movement into a single model, we were able to estimate both parameters with limited bias. Annual survival was similar between sexes of A. montanus [females = 0.885 (95% CI 0.614–1), males = 0.901 (0.657–1)], but was slightly higher for female A. truei [0.836 (0.560–0.993)] than for males [0.664 (0.354–0.962)]. Survival of A. montanus peaked at mid-age, suggesting that lower survival of young and actuarial senescence may influence population demographics. Our models suggest that younger A. montanus moved farther than older individuals, and that females moved farther than males in both species. Our results provide uncommon insight into age- and sex-specific rates of survival and movement that are crucial elements of life-history strategies and are important for modeling population growth and prescribing conservation actions.
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Materials and Methods
The Meleager’s Blue Polyommatus daphnis (Denis & Schiffermüller, 1775) is a relatively large lycaenid butterfly (Lepidoptera, Lycaenidae) with a wing span of about 33–37 mm. It shows a striking sexual dimorphism, with males being pale shiny blue, while females are less brightly coloured and occur in two main forms, i.e. a pale sky-blue with broad dark borders, and a dark grey-brown (f. steeveni). Moreover, females are usually somewhat smaller and have a deeply scalloped outer margin of hind wings 47 .
Polyommatus daphnis has a Ponto-Mediterranean distribution ranging from NE Spain through Southern and Central Europe to S Ural, Transcaucasus and Iran 47 . The species inhabits nutrient-poor grasslands, usually on calcareous soils, often on hills and mountain slopes up to 2000 m above sea level. Vegetation on the sites is often encroached by scrub and the sites are typically surrounded by woodlands. Across its European range, P. daphnis is usually local and not abundant, except on the Balkan Peninsula. This univoltine butterfly is on the wing from mid-June until the end of August, depending on the latitude and altitude of the locality. Caterpillars feed on Securigera varia (L.) Lassen and/or Hippocrepis comosa L. They are facultatively myrmecophilous, attended by Lasius, Formica and Tapinoma ants. The butterfly overwinters as an egg or a young larva 47 , but in Poland only the former stage is reported 48 .
The study was conducted on a site (N53°02′ E22°55′, ca 120 m a.s.l.) in the Podlasie region (NE Poland), near the Uhowo village close to the Narew National Park. The biotope was relatively heterogeneous and encompassed dry and mesic meadows with diverse herbaceous vegetation and some shrubs. P. daphnis was encountered on an area of about 5 ha (i.e. half of the regularly explored area during sampling), but the highest density was within the vicinity of patches of S. varia (the only larval food plant in Central Europe) and along dirt roads where the vegetation was generally shorter and rich in nectar plants. The site was bordered by a forest and arable fields, and it had been unmanaged in at least the last five years before the study. The population was located close to the northern limit of the species’ distribution in Poland 48 . We assumed that it was an isolated population since we did not find any other occurrence of the butterfly in the vicinity (i.e. in the radius of about 3 km) and no observations were reported from the surrounding area.
The population was sampled using mark-release-recapture (MRR) on 38 days between 3 July and 18 August 2014. We aimed to cover the entire flight period of P. daphnis, and started sampling when only a few males were on wing yet. The site was visited almost every day, weather permitting, except at the end of the flight period when the frequency of visits was lower. The weather conditions were generally favourable and stable. The vast majority of days during the flight period were sunny with temperatures 22–32 °C and only in the beginning there were three rainy days (July 5, 11, and 12) that did not allow sampling. Each time, 1–3 people were engaged in sampling, and spent five hours per day on the site on average. Butterflies were captured by an entomological net, marked on the underside of their hind-wings with unique numbers (Fig. S1d) using a fine-tipped pen with waterproof, non-toxic ink, and released at the place of capture. Date, time and GPS coordinates of each (re)capture, as well as the sex of the individuals were recorded. Sampling was finished when only a single worn individual was captured during a two-hour sampling session on 18 August. Moreover, on the following day weather conditions became unfavourable for a longer period. Additionally we mapped all patches of S. varia at the site using GPS.
Mark-recapture data were analysed using Cormack–Jolly–Seber (CJS) and Jolly–Seber (JS) models. The CJS model has two parameters, apparent survival rate (φ) and recapture probability (p). Apparent survival (φ) is the probability that a marked individual that is alive at occasion i will be alive and present in the population at occasion i + 1, hence this parameter applies to sampling intervals. (In single-site MRR studies, we cannot distinguish between emigration and death of individuals, therefore we estimate apparent survival, i.e. the probability that an individual survived and did not emigrate. However, in isolated populations such as our study population, apparent survival is reasonably a very good proxy of true survival.) Recapture probability means the probability that a marked individual that is present alive in the population at occasion i will be captured, and it applies to sampling occasions. In the formulation that we used, known as POPAN, the JS model includes two additional parameters: size of a ‘superpopulation’ (N), i.e. the number of all individuals that were in the population (and available for capture) during any of the sampling occasions, and probability of entry (pent), which represents the probability that individuals of this hypothetical ‘superpopulation’ enter the population and become available for capture between occasion i and i + 1 49 . The JS model assumes that survival and capture probabilities are equal for both marked and unmarked individuals of a population, thus it enables estimation of the population size 50 . We analysed the data on males and females separately, and in the case of females, we also involved wing colour type (blue vs. brown) as a grouping factor.
We tested the dependency of model parameters from covariates such as time, age and cohort, by constructing a set of 35 CJS models: (i) a parameter could be constant, i.e. it had the same value for all sampling occasions/intervals (‘
1’) (ii) a parameter could change with time, i.e. it could have different values at each sampling occasion/interval (‘
time’) (iii) a parameter could change during the sampling period linearly (‘
Time_lin’) (iv) a parameter could linearly change with cohorts (a cohort is the group of individuals marked on the same sampling occasion) (‘
Cohort’) and (v) a parameter could change with the time elapsed after marking (‘
Age’) (see also 17 ). We can consider the latter one as an ‘Age’-model if we assume that all individuals were marked soon after eclosion. Given our high sampling intensity this assumption is likely not violated. We built three ‘Age’-models for apparent survival. In the logistic model, the logit-transformed survival changed linearly with age (time since marking), in the Gompertz-model the loglog-transformed survival changed with age, while in the Weibull-model the loglog-transformed survival changed with ln(age) linearly 51 . For recapture probability, we used the logistic model only. In ‘
Cohort’ models (iii & iv), the logit-transformed parameters (survival φ and recapture probability p) were related linearly with time and cohort number, respectively. In all these models (iii, iv & v) an intercept and a slope are estimated for each demographic parameter.
Since marked and unmarked animals are not distinguished in JS models, here ‘Age’ and ‘Cohort’ models are not applicable. In JS models, three parameters can be constrained (φ, p and pent N is constant), so we fitted twenty-seven models to each dataset. We performed a model selection based on AICc values 52,53 . We carried out ‘Goodnes of Fit’ (GOF) tests on the CJS models using different approaches (‘RELEASE’ and bootstrap). We estimated the overdispersion parameter ĉ and adjusted the model estimates with it when it was necessary (see the description of methods and results of GOF-tests in Supplementary information). Model construction was conducted using the ‘RMark’ package version 2.2.7 54 within the R statistical software 3.6.3 55 , which provides a flexible R-like interface to the core routines of MARK 9.0 software 49 that performs model fitting and estimations. GOF-tests were performed in MARK 9.0.
Based on the estimates of apparent survival rate (φ) of the CJS models, we calculated mean life span and plotted life span distribution for males and females. In the case of a constant survival rate, life span follows an exponential distribution, and mean life span can be estimated as (1−φ) −1 −0.5 56 . In the case of age-dependent survival, we calculated the probability of death at a certain age for each round number of days between 0 and 50, and used this distribution to calculate mean life span. In the case of cohort-dependent survival, we calculated an average survival weighted by the number of individuals belonging to each cohort. In all calculations, the day of marking was the zero day of life.
We wish to thank all those who assisted in the field seasons referred to in this work and who contributed to photo-id studies. This work was funded by NERC through core funding to SMRU and grants NER/A/S/2000/00368 and NE/G008930/1, and by the Esmée Fairburn Foundation. The Northern Lighthouse Board, Scottish Natural Heritage and the Coastguard Agency provided assistance in each field season. We also thank Sophie Smout for her valuable comments during the preparation of this manuscript.