The Population Decline and Extinction of Darwin’s Frogs

Darwin’s frogs (Rhinoderma darwinii and R. rufum) are two species of mouth-brooding frogs from Chile and Argentina. Here, we present evidence on the extent of declines, current distribution and conservation status of Rhinoderma spp.; including information on abundance, habitat and threats to extant Darwin’s frog populations. All known archived Rhinoderma specimens were examined in museums in North America, Europe and South America. Extensive surveys were carried out throughout the historical ranges of R. rufum and R. darwinii from 2008 to 2012. Literature review and location data of 2,244 archived specimens were used to develop historical distribution maps for Rhinoderma spp. Based on records of sightings, optimal linear estimation was used to estimate whether R. rufum can be considered extinct. No extant R. rufum was found and our modelling inferred that this species became extinct in 1982 (95% CI, 1980–2000). Rhinoderma darwinii was found in 36 sites. All populations were within native forest and abundance was highest in Chiloé Island, when compared with Coast, Andes and South populations. Estimated population size and density (five populations) averaged 33.2 frogs/population (range, 10.2–56.3) and 14.9 frogs/100 m2 (range, 5.3–74.1), respectively. Our results provide further evidence that R. rufum is extinct and indicate that R. darwinii has declined to a much greater degree than previously recognised. Although this species can still be found across a large part of its historical range, remaining populations are small and severely fragmented. Conservation efforts for R. darwinii should be stepped up and the species re-classified as Endangered.


Introduction
There are two species of Darwin's frogs: the Northern Darwin's frog (Rhinoderma rufum) and the Southern Darwin's frog (R. darwinii), both of which inhabit temperate forests in central and south Chile and, in the case of the latter, also in adjacent areas of Argentina [1,2].Rhinoderma darwinii was named in honour of Charles Darwin [3], who first found this frog on December 1834, on the Island of Lemuy, Chiloe ´Archipelago [4].Rhinoderma rufum was originally described in 1902 [5], but after some debate (for some time it was considered a form of R. darwinii) [6,7], it was confirmed as a separate species in 1975 [8].With the snout-vent length of adults ranging from 2.2 to 3.2 cm [6,8,9,10], Darwin's frogs have a fascinating method of parental care that sets these frogs apart from all other known amphibians (7,044 spp.) [11].Males care for their young by incubating them in their vocal sacs for part of their development, a process first documented by Jime ´nez de la Espada [12] and since termed neomelia [6,8,13,14,15,16].Along with seahorses (genus Hippocampus), Rhinoderma spp.are the only known living vertebrates where males incorporate developing embryos into a specialized sac, giving the appearance of being ''pregnant''.The two Rhinoderma spp.differ in their expression of this reproductive behaviour: while R. rufum expels larvae into water bodies prior to metamorphosis, R. darwinii males do not release the young until they have metamorphosed [17].The two species can also be distinguished morphologically: R. rufum has a welldeveloped, transparent interdigital membrane between all five toes of the hind feet, a prominent metatarsal external tubercle and a diffuse pattern of white marks on a black background on the ventral surface of the body.Whereas in R. darwinii, the interdigital membrane is thicker, but present only between hind toes III-IV and IV-V; the metatarsal tubercle is smaller; and the white ventral markings are generally larger and extend farther caudally to include the hind feet [8,18].Other differences include: smaller intra-vocal sac larvae of R. darwinii, compared to the larger larvae of R. rufum [14,19]; differences in call patterns [8,20]; and characteristic karyotypes [21].
Rhinoderma rufum has not been recorded since 1980 [20,22] while R. darwinii is no longer found at some locations from which the species was recently abundant [23].The reasons for these apparent disappearances remain poorly understood.Throughout the historical distribution of R. rufum, and within the northern range of R. darwinii, there has been extensive habitat degradation, mainly due to the large-scale replacement of native forest with pine (Pinus radiata) and eucalypt (Eucalyptus globulus) plantations [1,2,24,25].Habitat loss, however, does not fully explain the enigmatic disappearances of R. rufum from its entire historical range or of the declines of R. darwinii from wild protected areas (WPAs), such as National Parks and other undisturbed ecosystems.
Rhinoderma rufum is classified as Critically Endangered by the IUCN [2], and is ranked #45 on the amphibian evolutionarily distinct and globally endangered (EDGE) list [26], while R. darwinii is listed as Vulnerable [1], but there is little information on their current distributions or abundances.Such information is required in order to develop adequate conservation strategies for these species.Here, we present evidence on the extent of the declines, current distribution and conservation status of Rhinoderma spp., including information on the relative abundance, population size, population density and habitat of, and threats to, extant R. darwinii populations.

Ethics Statement
This study was carried out in strict accordance with the recommendations in the guidelines for use of live amphibians and reptiles in field research compiled by the American Society of Ichthyologists and Herpetologists (ASIH).Research was approved by the ZSL Ethics Committee and was conducted following Chilean and Argentinian wildlife regulations and according to permits 1241/08, 7377/09, 7993/10 and 300/12 of the Livestock and Agriculture Service (SAG) and 20/09, XI-01/09, 28/11 and X-03/11 of the National Forestry Corporation (CONAF) both in Chile, and permit 1119/11 of the National Parks Administration (APN) in Argentina.Archived amphibians were examined in their museum of origin, by the authors or museum staff, with specific permission given by all 50 zoological institutions specified in Appendix S1.

Historical Distribution
A review of the scientific literature and of museum records was conducted to establish the historical distributions of R. darwinii and R. rufum.Museums known to us to contain Rhinoderma spp. in their collections were either visited or contacted to obtain information on the dates and locations from which their specimens had been collected.The largest collections in Europe and South America were visited and each metamorphosed specimen in these collections was examined to confirm the species identity.From the museums not visited, herpetologists in charge of the collections examined the individuals, and photographs of specimens of uncertain identification were examined by us to confirm the species identity.Using these data, historical distribution range maps were created for each Rhinoderma spp.following the aminimum convex polygon method [27].

Current Distribution
Extensive surveys throughout the historical distribution of R. rufum and R. darwinii in Chile and Argentina were carried out from October 2008 to March 2012.Directed surveys were designed based on the results of the historical distribution and were conducted at locations where the presence of Rhinoderma spp.had been identified in publications or museum records.In addition, an awareness-raising campaign throughout the historical distributions of Rhinoderma spp.(and covering all habitat types with the ranges) was conducted with the use of informative leaflets, presentations and interviews with local people and park rangers.This allowed coverage of large areas to help identify current presence/absence of Darwins frogs.Also, a small number of sightings during the period of this study were obtained from reliable sources (knowledgeable herpetologists or photographic proof) for sites that could not be visited.
Darwin's frogs are diurnal [9], therefore surveys were conducted during daylight hours.In order to maximise the likelihood of finding frogs, all surveys were conducted between October and March, when the frogs are reproductively active and call more frequently [8].Accessible areas at each visited location were carefully searched by 2-6 herpetologists for visual and auditory encounters with Rhinoderma spp.Absence of Rhinoderma spp. in a site was determined after completing a minimum of two visits carried out in different years, each search effort of no less than 5 hours duration.

Estimated Date of Extinction
For R. rufum, all years for which records of historical sightings had been recorded in museum archives and in the scientific literature, were obtained.Following Solow [28], these were analysed using the non-parametric method, optimal linear estimation (OLE), within the statistical package, R (v. 2.13.1), to test the null hypothesis that the species is extant.

Habitat
For each population of Darwin's frog found, the vegetation coverage of the site was characterised as: a) forest; b) shrub and bushes; and c) grassland, moss and coarse woody debris (CWD).Temperature and relative humidity were measured at 1-2 cm above the ground at each site visited.For those areas with historical presence of Rhinoderma spp., but no evidence of an extant population, current type of land use and presence of other amphibians were recorded.The degree of habitat perturbation was categorised as none, low, high or severe, according to the status of protection of the land, proximity to humans, and/or exploitation of the immediate forest.

Abundance
It is known R. darwinii generally form colonies with high site fidelity in small areas (e.g. a clearing in the forest) [9].At locations where Darwin's frogs were found, sites were delimited and a standardised search effort of one hour by two researchers was conducted in order to obtain information on relative abundance.Searches were done in such a manner that survey effort was equal throughout each site.Captured frogs were temporarily removed, safely contained in individual sealed plastic bags and put back immediately after the capture session in the exact place of capture.Each frog was handled using new, disposable nitrile gloves (prior to release, morphometric data and non-invasive skin swabs for complementary studies were obtained).This procedure was conducted for at least two visits for each population in order to estimate a relative abundance index (RAI), which was calculated for each population as follows: RAI = C6F 21 , where C is the sum of counts (captures) and F is the frequency of capture sessions at each population [29,30,31].Populations were geographically classified as Coastal, Andes, Chiloe ´Island and South.Statistical analyses were performed using SPSS (v.20.0) to detect any significant difference in relative abundance between geographical groupings and between different degrees of human impact.
For those populations with at least four consecutive standardised capture sessions (1 hour by two researchers per session), each session separated by 24 hours, capture histories were created through a modified non-invasive capture-mark-recapture (CMR) technique, based on the individually-unique black-and-white coloration patterns of the ventral body recorded in each captured R. darwinii (Figure 1).The selection of these populations was based on three criteria: 1) representation of all four geographic regions within the distribution range of R. darwinii; 2) different degrees in R. darwinii abundance, previously obtained by RAI values; and 3) accessibility, i.e. closeness to a road or village.Simple, behaviour, time and heterogeneity models, and mixtures of them, were performed using the closed captures Huggins full heterogeneity function in programme MARK (v.6.1) to estimate population sizes [32].The area of the site containing each population was measured in order to calculate population densities.

Historical Distribution
A total of 2,244 Rhinoderma specimens from 50 institutions were examined.Based on anatomical features; 789 of the specimens which had been catalogued as R. darwinii were re-classified as R. rufum.As a consequence, a total of 1,226 R. darwinii and 1,018 R. rufum were identified (see Appendix S1 in supplementary data).
Thirteen unique locations for R. rufum were reported in the scientific literature [5,8,13,20,33,34,35], seven additional unique locations were identified from the collection data for archived specimens, and a further location was provided by G. Medina-Vogel, pers.comm.(see Appendix S2).For R. darwinii, 24 unique locations were reported in the scientific literature [4,6,9,13,16,23,36,37,38] and an additional 90 unique locations were established from the collection data for archived specimens.Based on these results, and the new locations of R. darwinii found in the current study (see below), the historical ranges for R. rufum and R. darwinii are presented in Figure 2.

Current Distribution
A total of 223 sites were surveyed for Darwin's frogs: 46 within the historical range of only R. rufum, 157 within the historical range of only R. darwinii, and 20 sites within the area of sympatry (Figure 2).Despite the extensive search effort and surveys of every recorded location of the species, no individuals of R. rufum were either observed or heard.For R. darwinii, however, we found 26 areas (Figure 3) with extant frogs within which the species was present in a total of 36 sites.Generally these areas were extremely isolated from each other, except for populations in southern Chiloe ´Island (Figure 3).Rhinoderma darwinii sites .2km from each other were determined to be separate populations (and therefore different areas), whilst sites ,2 km apart were considered to be subpopulations (and therefore sites).This distinction was based on studies of other amphibians with poor dispersal abilities [39,40], as is the case for Rhinoderma spp [9].To facilitate our abundance analyses, however, we treated each of the 36 R. darwinii sites as separate ''populations''.In 10 additional areas, the presence of the species was confirmed either by the detection of a single R. darwinii (Cochamo ´and Caulı ´n), or through obtaining reliable information about the species' presence: Cayucupil, Isla Mocha, Chaihuı ´n, Hueicolla, Huinay, Rı ´o Marchant and Rı ´o Cuervo in Chile; and Puerto Blest in Argentina (Figure 3).These 10 areas were not included in our abundance analysis as the population status was uncertain.

Estimated Date of Extinction
Years of sightings for R. rufum are detailed in Appendix S2.

Habitat
Details of the habitat and identified threats at specific locations surveyed for Rhinoderma spp. at which they were known to have been present but were not found during the current study are presented in Table 1.Briefly, 20 of 24 such sites were classified as having moderate to severe anthropogenic habitat perturbation, while four sites (1 R. rufum site, 3 R. darwinii sites) were identified as having no or low anthropogenic habitat perturbation.One of these last sites (Amarillo), however, has suffered from volcanic activity, which has been associated with the recent disappearance of R. darwinii (C.S-A.& A.V-S., personal observations).
A description of the habitat at each site where R. darwinii was found is given in Appendix S3.In all cases, Darwin's frogs were

Abundance
A total of 648 different R. darwinii were captured (120 brooding males, 111 non-brooding males, 218 females and 199 juveniles).Local relative abundances are shown in Figure 4.The RAI values for each R. darwinii population gave an average of 7.0 frogs/ population (95% CI, 5.0-9.0).Differences in abundance between the four geographical regions were found (one-way ANOVA; F 3.32 = 8.32, P,0.001).Post-hoc comparisons revealed a higher abundance of frogs in Chiloe ´when compared with Coast, Andes and South populations (Tukey's HSD: P = 0.001, P = 0.008, P = 0.002 respectively).Differences in abundance according to the degree of human impact were found.Sites with no disturbance showed higher abundance of frogs when compared with sites with anthropogenic disturbance (Mann-Whitney U-test; U = 57.0,P = 0.005).
With CMR data from five populations (El Natre 1, Villarrica 1, Inio 1, Queulat 2 and 3), population size and density averaged 33.2 frogs/population (range, 10.2-56.3)and 14.9 frogs/100 m 2 (range, 5.3-27.4),respectively.The probability of detection per search was highly variable, ranging from 0.04 to 0.64 across sites, and with evidence for behaviour effects, individual heterogeneity and time-dependent variation in detection probability, at least in the site where search effort was most intense (Inio 1; Table 2).

Historical Distribution
Using as many published and unpublished (museum) records of Rhinoderma spp. as we could obtain, we established the historical range of R. rufum and R. darwinii (Figure 2).According to our    results, the distribution of R. rufum was much larger than previously recognized [2], as it has been recorded from the foothills of the Andes in the VI Region [33] as well as from the coastal forests of the V Region of Chile (C.Moreno, pers.comm.)[8].In contrast, according to our data, the historical range of R. darwinii has been overestimated [1], as we were unable to locate any records of the species having been found south of the city of Coyhaique or on the Chonos Archipelago.

Current Distribution and Extent of Declines
Despite multiple, extensive searches, including all previouslyknown locations for R. rufum, we were not able to locate this species.This is in accordance with many other search efforts that have been made over the past 10 years for this species [2,15,18,22,43].
Identifying the extinction of a species is problematic [41,44].There is reluctance to declare a species extinct because of the large conservation implications involved and so as not to facilitate the Romeo effect (giving up on a species too early) or the Lazarus effect (bringing a species back from extinction) [28].Using the OLE model developed by Solow [28] the sighting record indicates that this species most likely became extinct in the early 1980s.The OLE method does not take into account multiple sightings in a given location, though assumes that sightings effort never falls to zero in intervening years.We felt that the sparse dataset, which we have collated, would not be suitable for an Ederer-Myers-Mantel test [45], although that alternative method should be considered in the future should additional data become available.
We found extant R. darwinii in all four main geographic regions (Coastal, Andes, Chiloe ´Island and South) within its historical range, but only as small and fragmented populations.The current area of occupancy of R. darwinii most likely represents a small fraction of its former range.Our data, and those of Crump [9] and Crump and Veloso [23], indicate that this species has disappeared from, or markedly declined in, multiple locations, including those in which was recently abundant.For instance, in the remote area of Melimoyu, Crump [9] studied 146 individuals in 1998 and 120 in 1999 during fieldwork sessions of 10 and 16 days respectively.Although shorter in time, successive expeditions by the authors to the same area during the reproductive season failed to locate any Darwin's frogs in 2009 (6 days of searching) and found only two individuals in 2011 (5 days).This represents a drastic population decline over the last 12 years in an area of southern Chile only accessible by sea and characterized by an undisturbed ecosystem with a low human presence (,57 people, Figure 3).
Archived material and scientific literature have shown that both species of Darwin's frogs have been abundant, at least at some locations [6,8,13,33].Charles Darwin himself stated among his notes: ''It inhabits thick and gloomy forests, and is excessively common in the forest of Valdivia'' [46].In the area of Chiguayante and Cerro Caracol (Concepcio ´n) prior to the 1980s, Rhinoderma spp.were commonly heard and seen in house gardens (albethey gardens incorporating native forest).In this context, we documented 838 R. rufum specimens deposited in different museums, collected by two wildlife collectors from the same area in Chiguayante over the period 1975-1979.An area with high abundance of R. darwinii in the past, but apparent current absence, is the Nahuelbuta National Park.In this protected area and its surroundings, the extraction of R. darwinii for the illegal pet trade to the United States and Europe was a common practice until the late 1980s [47].Over-extraction of Darwin's frogs could have acted as an extinction driver at some localities.

Habitat Perturbation
No Darwin's frogs were found near urban or rural settlements; instead they were always associated with specific conditions within native forest.Furthermore, of the Rhinoderma spp.populations that have recently disappeared, 22 of 24 suffered anthropogenic habitat perturbation to differing degrees (Table 1).Chilean temperate forests are being rapidly destroyed to supply the increasing global demand for wood and paper products [48].Echeverria et al. [24] calculated a reduction of natural forest area in the coastal range of central-south Chile of 67% for the period 1975-2000.By 1993, P. radiata reached 1.24 million ha in central-south Chile, becoming the largest pine plantations worldwide [49].Together with eucalypts, they produce drastic changes in atmospheric/substrate humidity, air temperature, luminosity and wind speed [50].They also promote erosion in environments previously rich in ground cover and may facilitate the dissemination of invasive species [51].In addition, the conversion of native forest to agriculture has occurred to a large extent, especially towards central Chile [24,25].Other causes of habitat loss, such as urbanization and infrastructure development projects, might also play an important role in the disappearance of R. rufum.For example, the land surrounding Lake Vichuque ´n and Zapallar, has been drastically changed for urban and tourist purposes.Urban sprawl in the Greater Concepcio ´n area, with over one million inhabitants, now incorporates areas from which the Darwin's frog populations of Cerro Caracol, Chiguayante, Hualqui and San Pedro have disappeared.

Other Threats
Small populations are more prone to extinction from environmental and demographic stochasticity [52].Although volcanic events could be considered as beneficial over geological timescales, generally they are considered as catastrophic over human time-scales [53].Two high magnitude plinian volcanic eruptions in the southern Andes have recently affected R. darwinii populations.First, the Chaite ´n volcano eruption from May 2008 to June 2009 and which produced a total of 4 km 3 of magma and an ash column up to 22 km high [54], is associated with the disappearance of a R. darwinii population located 22 km SW from the crater (Amarillo; Table 1, Figure 3).More recently, from June 2011 to May 2012, the Caulle-Puyehue volcano erupted producing ash columns up to 12 km high and with pyroclastic material accumulating in large amounts in the surrounding area [55].As a consequence, one of two R. darwinii populations known in this area (Pajaritos) has apparently disappeared (C.S-A.& A.V-S., personal observations), although additional surveys are required to confirm this (Figure 3).
In the early 1970s, the African clawed frog (Xenopus laevis) was introduced to Chile, apparently near Santiago [56].Mainly by colonization movements, but also with human assistance, X. laevis today inhabits an extensive area of central Chile [57,58].We detected the presence of this invasive frog near only one site with an historical presence of R. rufum (Hualan ˜e ´; Table 1), however, this species is unlikely to be found at Darwin's frogs sites as X. laevis generally inhabits open lentic waters and human disturbed environments [57].Xenopus laevis has been associated with the emergence and global spread of the amphibian disease chytridiomycosis, caused by Batrachochytrium dendrobatidis (Bd) [59,60].Recently, Bd has been identified in wild populations of X. laevis in Chile [61] and chytridiomycosis has been reported as a cause of mortality of R. darwinii in captivity [36,43].The impacts of Bd on sympatric wild amphibians, including Darwin's frogs, in Chile have not been investigated.Further research is required to investigate if Bd has been involved in the decline of Darwin's frogs, in particular their enigmatic declines in, and disappearances from, protected areas.
Other factors that have been cited as possibly causing amphibian declines elsewhere, such as pollution, UV radiation and climate change [62], have not been assessed for Darwin's frogs.It is possible, however, that global warming with concomitant changes in, for example, precipitation patterns, might negatively impact terrestrial, high humidity dependent, nonmigratory species such as Darwin's frogs, whilst also favouring the dynamics of emerging pathogens [63,64,65,66].

Habitat Requirements of Rhinoderma darwinii
Rhinoderma darwinii is known to inhabit small open areas within native forest [9], however, we also found this species in dense forest, i.e. in areas with $90% mature forest coverage (Oncol, Puma, Pajaritos and Puyehue 2).Even though R. darwinii was found in a great variety of vegetation types (Appendix S3), it appears that a mixture of grassland/moss/CWD and young trees/ bushes, within a predominantly mature native forest matrix is required for the species' survival.Short vegetation increases water retention while decreasing temperature at the soil level and provides a good refuge from predators [50,67].The microhabitats of all monitored populations showed .70%relative humidity and ,22uC air temperature (Appendix S3).These data were all obtained in the daytime during the Austral spring-summer and, therefore, most likely represent values near the minimum humidity and maximum temperature requirements for the species.Studies on habitat selection of Darwin's frogs are required to better understand the impacts of habitat loss as well as to develop adequate conservation management practices [67].

Abundance of Rhinoderma Darwinii
Capture-mark-recapture analysis indicated considerable variability detection probability between sites (0.04-0.64 per site visit), suggesting that a degree of caution is needed in interpreting the RAI values.Nonetheless, the magnitude of RAI differences between sites is large enough to give some confidence that the broad pattern of higher abundance on Chiloe ´Island than elsewhere is real, particularly for the eight sites located in the southern third of the island.It is probably not coincidental that human perturbation is minimal in this area, much of which is protected.
As R. darwinii exhibits a high degree of site fidelity [9], the use of non-invasive closed population CMR analysis, appears to be a reliable method to estimate population size in this species.There was, however, strong support for heterogeneity and behaviour effects on detection probability at the one site where there were many (16) visits, but not at sites with fewer (4) visits.This is likely because of insufficient data at the less-intensively visited sites to identify these effects in capture probability, suggesting that abundances at these sites could had been under-estimated to some extent.Nonetheless, any such underestimation is likely to be modest, since the estimated degree of heterogeneity in capture probability was not great.Furthermore, the sites at which CMR analysis was applied included both large and small populations, as indicated by RAI values.Taken together, these lines of evidence suggest that all of the sites visited have population sizes below 100, giving a picture of highly fragmented, small and vulnerable populations.

Conservation Status
Rhinoderma rufum.More than three decades has passed since R. rufum was last detected [20].This species' habitat, the Maulino forest, is today scarcely represented within the Coastal range of central-south Chile [24].Although there are no objective records about the presence of this species within WPAs, there are eight National Reserves and one National Park within its historical range.However, most of these are small (45-9,262 ha), have been explored in detail by park rangers, herpetologists and other scientists and are frequently visited by tourists.In this respect, it is important to note that Rhinoderma spp. is not the hardest species to find and identify, particularly during their reproductive season, since they have a: 1) unique anatomy; 2) characteristic call (both sexes); 3) diurnal activity; and 4) gregarious behaviour.Given the size of its historical distribution, hope remains that R. rufum still survives somewhere to this day [43].Therefore, we suggest the species should be considered as a candidate for the new IUCN Red List category Critically Endangered (Possibly Extinct; CR [PE]), currently under review by the IUCN [68].
Rhinoderma darwinii.Although R. darwinii abundance has not been previously recorded, and hence the extent of population declines cannot be accurately measured, our results indicate that there has been a recent rapid population decline of this species, based on the severe reduction in distribution range, anecdotal data on severe population declines (e.g. at Melimoyu) and local extinctions registered within WPAs, remote areas and undisturbed ecosystems.Alarmingly, the causes of these declines are not understood.Even though the species remains widely distributed, mainland populations are small and highly fragmented.Following the A2abc IUCN Red List criteria, our new data suggest this species should be re-classified at least as Endangered (EN).Should further work show the observed decline to be greater than 80% over 10 years, then the species would qualify for a listing of Critically Endangered (CR).

Table 1 .
Characteristics of known locations of Darwin's frogs (Rhinoderma darwinii and Rhinoderma rufum) from which the species apparently disappeared during or since the 20 th Century.

Table 2 .
Estimated population sizes, calculated using Huggins closed population models and densities of five populations of the Southern Darwin's frog (Rhinoderma darwinii).aNumber of counts.bModelselected (Model: letter codes indicate detection probability dependence: t = time; b = behaviour; and h = heterogeneity).cDetectionprobability.Recapture probability at Inio 1 showed a pattern of initially low values for the early capture occasions, higher values during the middle of the period, then low values, similar to those at the start.A simpler model with only two time periods (t 1 : early/late and t 2 : mid) was therefore preferred to a fully time varying model.h1 and h2 refer to recapture probabilities for heterogeneity mixtures, and p1 to the estimated proportion of the population in mixture 1. doi:10.1371/journal.pone.0066957.