Evaluating population recovery for sea turtles under nesting beach protection while accounting for nesting behaviours and changes in availability

Authors


Correspondence author. E-mail: jimthor@uw.edu

Summary

1. Sea turtles and sea birds generally have high conservation importance world-wide and are often difficult to survey except when present on nesting grounds. Consequently, many such surveys tag nesting individuals and use tag-resighting models to estimate population size and assess anthropogenic impacts. However, the conventional Cormac–Jolly–Seber (CJS) tag-resighting model is problematic for these species for three reasons: individuals often return to nesting areas in alternating years because of high energetic costs for nesting, estimated detectability confounds changes in survey efficiency with availability on the surveyed beach, and tag loss is confounded with mortality.

2. We develop a robust design model that uses higher-order Markovian transitions to approximate skip-nesting behaviours and incorporates multiple observations for each nesting individual to estimate changes in availability (the probability of returning to the surveyed area rather than alternative nesting areas). We approximate time-varying effects using a flexible spline method and demonstrate the model using data for leatherback sea turtles Dermochelys coriacea and loggerhead sea turtles Caretta caretta in South Africa.

3. The apparent lack of recovery for leatherback sea turtles after implementing beach protection, as observed in nest count data, is likely to be due to declining detectability caused by decreased availability during population recovery (e.g. habitat expansion). By contrast, loggerhead sea turtles have approximately constant detectability and stable abundance since the 1970s.

4. We find that increased fishing effort has no explanatory power regarding changes in survival for either species.

5.Synthesis and applications. Based on study results, we recommend that future tag-resighting programmes for sea turtles and birds are accompanied periodically by count surveys beyond the regularly monitored nesting areas to evaluate evidence of range expansion. However, the identification of range expansion in historical data is only possible using model-based inference and robust design methods such as presented in this study.

Introduction

Sea turtles and sea birds undergo long migrations between nesting and feeding grounds, and many populations are easiest to survey on their nesting grounds (Dutton et al. 2005; Veran et al. 2007; Kendall et al. 2009; Cubaynes et al. 2010; Monk, Berkson & Rivalan 2010). The application of tags to nesting individuals, and subsequent resighting of these tags, allows tag-resighting models to simultaneously estimate survival and detectability (i.e. the probability that a tag will be detected when it is present). Detectability can then be combined with the number of unique detections per year to estimate female or total abundance (Horvitz & Thompson 1952). Abundance would be otherwise difficult to estimate for such species, for which adults range over wide spatial areas.

However, conventional tag-resighting methods such as the Cormack–Jolly–Seber model (CJS; Cormack 1964; Jolly 1965; Seber 1965) have several limitations when applied to sea turtle and sea bird populations. First, sea turtles and birds exhibit skip-nesting behaviours, where individuals generally avoid nesting in consecutive years because energetic costs are high (Rivalan et al. 2005; Cubaynes et al. 2010), which causes tagged individuals to have variable detectability over time. Secondly, changes in CJS detectability can be caused by either sampling design issues (i.e. changes in sampling effort or protocol) or changing availability (i.e. individuals leaving the sampled area to nest in other nearby beaches), causing difficulties when interpreting estimated detectability. Thirdly, loss of tags will be confounded with annual mortality (Bjorndal et al. 1996).

These three issues can be accommodated using extensions to the CJS model (Kendall & Bjorkland 2001; Conn, Kendall & Samuel 2004; Kendall et al. 2009). Accounting for skip-nesting behaviours is possible by modelling unobserved nesting returns as a latent process (Rivalan et al. 2005; Monk, Berkson & Rivalan 2010). The confounding of sampling design and availability in CJS detectability can be resolved using a ‘robust design’ model (Pollock 1982; Kendall, Nichols & Hines 1997) that includes the number of observations for each observed turtle in a nesting season. Finally, tag loss rates can be estimated using data from double tagging (Nichols et al. 1992). These extensions have been previously developed, but are rarely integrated into a single model.

As one example of the importance of skip-nesting and changing availability, leatherback sea turtles Dermochelys coriacea (Vandelli, 1761) and loggerhead sea turtles Caretta caretta (Linnaeus, 1758) nest on beaches in the KwaZulu-Natal region of South Africa near the southern Mozambique border. Although mortality at this beach is assumed to have decreased because of regulations on the harvest of turtle eggs, mortality at sea is caused by bycatch in tuna longline fisheries and entanglements in beach protection nets (Petersen et al. 2009; Brazier et al. In press). A beachside monitoring study has been conducted on this beach since the 1960s and yields an annual count of observed nests that can serve as a relative index of abundance (R. Nel, A. Punt & G.R. Hughes unpublished data). Analysis of nesting count data indicates that loggerhead sea turtles have recovered because of nesting beach protection, but shows little evidence for the recovery of leatherback sea turtles. This difference between species is counterintuitive given that leatherback sea turtles have a younger age-at-maturity (Van Buskirk & Crowder 1994) and leatherback populations elsewhere have recovered under nesting beach protection (Dutton et al. 2005). One possible explanation is differential response to bycatch in longline fisheries. Alternatively, apparent differences in recovery could be caused by changes in detectability arising either from skip-nesting behaviours, changing availability or sampling design issues. The inability to estimate these three factors contributing to detectability makes any interpretation of nesting count data difficult.

We present a tag-resighting model that simultaneously accounts for skip-nesting, availability, sampling design issues and tag loss. We demonstrate this model for the KwaZulu-Natal leatherback and loggerhead sea turtle populations to provide abundance estimates, and contrast results with estimates of abundance derived from beachside nesting counts. We additionally test whether turtle survival is associated with changes in longline fishing effort to evaluate the hypothesis that differences in abundance trends could be caused by this fishery mortality. This model framework is generally applicable to sea turtles and birds using data that are often collected (Kendall et al. 2009) and could be used in other systems to provide support for competing hypotheses regarding population recovery and anthropogenic impacts on sea turtles (Bjorndal et al. 2011).

Materials and methods

Data

Leatherback sea turtles are a large-bodied sea turtle with relatively high reproductive output (measured as number of eggs per female per year), while loggerhead sea turtles have lower reproductive output (Van Buskirk & Crowder 1994). After maturity, both species practise skip-nesting periodically due to the high energetic demands of reproduction (Rivalan et al. 2005). They return to the nesting beach multiple times during a nesting season, although the pattern of skip-nesting and clutch frequency (the number of nests per nesting year) varies among species and populations (Van Buskirk & Crowder 1994). Loggerhead sea turtles have strong site fidelity (measured as variability in location of nests within a given season) relative to leatherback sea turtles (R. Nel, A. Punt & G.R. Hughes unpublished data; Rivalan et al. 2006; Tucker 2010), perhaps arising from different evolutionary histories and sensory cues (Mrosovsky 1983; Kamel & Mrosovsky 2004).

Tag-resighting data are available from 1965 to 2009 from approximately 53 km of nesting beach in the KwaZulu-Natal region of South Africa, ranging from 3·2 to 56 km south of the South Africa-Mozambique border. Effort was relatively sparse from 1965 to 1972 and has changed slightly over time, for example, with the use of contracted ecotourism operators for sampling starting in the 1996/1997 sampling season. Sampling is conducted from mid-October to mid-March each season, and sampling effort within the existing design is greater in the northern than the southern region of the beach. During sampling, technicians count the number of nests that are observed in each season, and this count has been treated as a relative index of abundance (R. Nel, A. Punt & G.R. Hughes unpublished data). However, this nest count survey cannot account for changes in detectability over time, whether due to changes in sampling effort or availability (Mazerolle et al. 2007). Analysis of the location of observed nests suggests that loggerhead sea turtles are more geographically specific in the location of their nesting returns and prefer the northern part of the survey beach, while leatherback sea turtles range more evenly across the entire survey beach (R. Nel, A. Punt & G.R. Hughes unpublished data). This observation leads to a hypothesis that leatherback sea turtles are more likely to exhibit changes in availability than loggerhead sea turtles, because they are more likely to expand out of the surveyed beach over time (Eckert et al. 1989).

Upon encountering a turtle on the surveyed beach, sampling technicians attach tags to the proximal end of a front flipper for loggerhead sea turtles or a back flipper for leatherback sea turtles. Flipper tags have ranged from plastic (cattle or fish) tags to Monel/Titanium tags since 1965. Since the 1992/1993 season, a random subset of turtles has also received additional microchip tags, which are believed to be permanent for these turtle species and allows estimation of flipper tag loss.

Model overview

The model explicitly approximates transitions between different possible stages for each turtle over time (Fig. 1). The modelled stages for individuals at sea include (1a) at the beginning of a feeding season, (1b) after surviving a feeding season, (1c) retaining the flipper tag throughout the feeding season and (1d) having either died or lost the flipper tag. Transitions while between at sea stages include survival or mortality, tag loss or tag retention and either skip-nesting or returning to a nesting beach in a given year. Modelled stages for individuals during a nesting season include: (2a) preparing for a nesting season, (2b) returning to the surveyed beach, (2c) returning to a different or unmonitored part of the beach and (2d) each nesting event on the surveyed beach. Transitions during a nesting season include returning either to the surveyed beach or to a different beach and the number of nests laid in that nesting season. Each year, turtles are assumed to either return to the at-sea stage (i.e. state 1a), either by way of nesting or skip-nesting or to have left the tagged population by mortality or tag loss (i.e. state 1d). Additionally, turtles are assumed to either remain at the surveyed beach or an alternative beach for all nesting events in a nesting season.

Figure 1.

 Schematic for the model showing states (circles; 1: at sea; 2: at a nesting beach) and transitions (arrows and boxes; S: Survival; T: Tag loss; R: Skip-nesting behaviour; inline image: availability, that is the probability of returning to the monitored nesting beach in a nesting season; inline image: detection probability for each nesting event; inline image: number of nesting events in each nesting season; variables with a subscript t can vary annually) where the ‘Detection probability’ box (inline image) shows where each detection event occurs.

Parameters are estimated for each modelled transition probability. Specifically, survival (inline image), availability (i.e. the probability of returning to the nesting beach, inline image), detection probability for each nesting event (inline image), and skip-nesting parameters (inline image) can be estimated as varying over time, while parameters governing tag loss (inline image) and clutch frequency (i.e. the number of nests per season for each nesting individual, inline image) are assumed to be constant over time (Table 1). The model was implemented in the Automatic Differentiation Model Builder software (Fournier et al. 2011) and the source code is available online (https://sites.google.com/site/thorsonresearch/code/turtles/). Further details regarding model implementation are given in Appendices S1 and S2, Tables S1 and S2 in the Supporting Information. We approximated skip-nesting as being constant over time in all base model configurations, similarly to past multistate sea turtle modelling (Rivalan et al. 2005; Monk, Berkson & Rivalan 2010) and as is frequently reported for sea turtles (Van Buskirk & Crowder 1994), while providing a sensitivity analysis of model estimates to this assumption (Appendix S3 Supporting Information).

Table 1.   Parameters used in the multistate robust design model, including parameter name, symbol, whether it is annually varying or constant over time, the number of possible parameterizations to be searched across during model building and the range in the number of parameters for each.
Parameter nameSymbolAnnually varying?Number of parameterizationsNumber of parameters
  1. *The sensitivity of selected model estimates is evaluated in Supplementary Appendix S3 and Supplementary Figs S4 and S5.

Survivalinline imageYes431–43
Detection probabilityinline imageYes431–43
Probability of returning to the surveyed beach in a nesting seasoninline imageYes431–43
Skip-nesting behaviourinline imageNo*41–4
Expected value for individual-level variability in number of nesting events in a nesting seasoninline imageNo10 (value is fixed)
Overdispersion for individual-level variability in number of nesting events in nesting seasoninline imageNo11
Tag lossinline imageNo14

Detectability

The detectability parameter in conventional CJS models is decomposed in this study into three components: skip-nesting (the probability of skipping nesting in a given year and hence being unavailable for beachside sampling); availability (the probability of returning to the surveyed beach rather than a different beach in a nesting season); and detection probability (the probability of detection for each nest laid). To represent skip-nesting, we model the probability that a turtle will return to a nesting beach as being dependent upon the number of years since last nesting. Availability can be estimated separately by utilizing ‘robust design’ data (Pollock 1982; Kendall, Nichols & Hines 1997), for example, the number of times a given nesting turtle is observed in a single nesting season. These multiple observations occur because each nesting turtle will lay several clutches of eggs and thus each turtle is susceptible to detection several times during any season that they return to the surveyed beach. Thus, changes between years in the average number of observations for each turtle can be informative about changes in detection probability separately from the other factors affecting the CJS detectability parameter.

Specifically, we model detectability as (equation 1):

image(eqn 1)

where inline image is the probability of h nesting events given that a turtle is nesting in year t, inline image represents the probability of each nesting turtle returning to the sampled nesting beach during a nesting season t, and inline image represents the detection probability during each of h nesting visits that a turtle performs during a nesting season. Skip-nesting was approximated using first-, second-, third- and fourth-order Markov models for temporary emigration (Rivalan et al. 2005; Monk, Berkson & Rivalan 2010; Appendix S1 and Table S2 Supporting Information).

The distribution of likely clutch frequencies for each species (inline image, equation 1) is modelled as a truncated negative binomial distribution, which can account for variability among individuals in the expected number of nesting events per nesting season (Lindén & Mäntyniemi 2011). In this application, we assume that clutch frequency is constant over time, as is frequently reported (Van Buskirk & Crowder 1994) and has been assumed previously (Rivalan et al. 2005; Monk, Berkson & Rivalan 2010). Time-varying clutch frequency would be perfectly confounded with varying detection probabilities without using additional time-indexed data for each nesting return (Rivalan et al. 2006). We have additionally fixed the expected clutch frequency (inline image) at its median value from Van Buskirk & Crowder (1994); leatherback: 5·39 per year; loggerhead: 3·5 per year). Values of inline image from Van Buskirk & Crowder (1994) may be underestimates because of unobserved nesting returns (Rivalan et al. 2006; Tucker 2010). However, we confirmed that changing these inline image values had little impact on relative trends of any model output over time.

Tag loss

Microtags have been implanted in addition to flipper tags for a randomly chosen subset of tagged individuals for both leatherback and loggerhead sea turtles since the early 1990s, and there are 168 instances for leatherback and 1864 for loggerhead of microchip recaptures. These data are used to calculate the rate of flipper tag loss, given the assumption that microchips are not subject to tag loss and that all flipper tag loss is constant over time. Specifically, we estimate four parameters, representing the probability of immediate flipper tag loss because of improper application, tag loss within a given nesting season, tag loss between nesting seasons and an annual increase in the probability of tag loss between nesting seasons representing age-dependent tag loss (Appendix S1). Time-varying tag loss was not considered because no information was available regarding tag loss rates prior to the 1990s.

Time-varying effects

In this model, survival (inline image), detection probability for each nesting event (inline image), availability (inline image) and skip-nesting parameters (inline image) could all vary over time. In conventional CJS models, time-varying effects are usually approximated using one of two extreme cases: constant for all years or estimated separately for each individual year. We instead use a general form for time-varying parameters that includes these two extreme cases as well as various stages in-between. Specifically, survival, detection probability and availability are approximated by a piecewise form where the number of knots (i.e. where piecewise lines join) is selected using the Akaike Information Criterion (AIC, Akaike 1974) and knots are evenly positioned throughout the 43 year time series, and skip-nesting parameters are assumed to be time constant in base models. Model selection considered from 1 (i.e. constant for all years) to 43 (i.e. different for each year) degrees of freedom (d.f.) for each of survival, detection probability and return probability, plus four possible forms for skip-nesting behaviour (433 × 4 = 318 028 possible models). This number of models is infeasible for a full search across all possible combinations, and we instead use a stepwise model selection algorithm to select a parsimonious smoothness for each parameter. Details of the model selection algorithm are given in Appendix S2, and sensitivity of the selected model to time-varying skip-nesting parameters is demonstrated in Appendix S3.

Longline fishing effort and survival

We explore the hypothesis that increases in longline fishing effort in sea turtle habitats may explain decreases in survival, thus inhibiting recovery for leatherback sea turtles. To do this, we develop an annual index of longline fishing effort in areas that are likely to be inhabited by loggerhead and leatherback sea turtles that nest at the surveyed beach, and test whether this index is negatively correlated with survival (Veran et al. 2007). Effort data (in hooks per year) were available for South African fishery, 2006–2009, as well as from the Indian Ocean Tuna Commission (IOTC), 1954–2009. Data for the IOTC are primarily reported within 5° latitude/longitude cells, and we included longline effort for cells where the NW corner was between 6°19′S and 40°48′S, and 1°18′E and 61°36′E (Fig. 2). These boundaries were chosen based on movement of 20 satellite-tagged individuals from this nesting beach (R. Nel, unpublished data). This index will not capture many of the effects (i.e. depth, season) that will contribute to a standardized index of effective fishing effort, although it represents as much information as is available regarding longline fishing effort for these populations. Additionally, any departure from an ideal standardized index of fishing effort will cause an attenuated estimate of the impact of longline fishing effort, that is an estimated coefficient biased towards zero and a conservative test of statistical significance. The index was then divided by its maximum value to generate a relative index and was assumed to have a negative impact on the logit-link of survival, after accounting for decadal changes in average survival (e.g. caused by changes in nesting beach management, Appendix S2).

Figure 2.

 Region (dotted box) for which longline fishing effort is assumed to potentially influence leatherback and loggerhead survival (upper panel) and relative index of longline fishing effort per year within that region (lower panel).

We constructed models with and without longline effort and used AIC to evaluate the strength of evidence for an effect of longline fishing on survival. Specifically, we conducted stepwise model selection for the degrees of freedom for detection probability and return probability given a decadal model for survival, both with and without longline fishing effort.

Estimates of abundance

Abundance for all females above nesting-age was estimated for all models using the Horvitz-Thompson estimator (Horvitz & Thompson 1952, equation 2):

image(eqn 2)

where inline image is the resulting estimate of total nesting-age female abundance for year t, Ut is the number of unique turtle IDs observed during year t, and inline imageis the expected number of years between each nesting season conditional upon survival (calculated using the delta-method from estimated skip-nesting parameters inline image given time constant skip-nesting estimates). The standard error for log(inline image) was estimated using the delta-method. A relative index of abundance Ct was also estimated for comparison with the number of detected nests where species was identified using distinguishing characteristics from the track leading to each nest (R. Nel, A. Punt & G.R. Hughes unpublished data).

We present abundance estimates derived from tag-resighting and nesting count data along with a smoothed abundance trend for each, estimated using a generalized additive model (Hastie & Tibshirani 1990; Wood 2006). This is not intended as a formal estimate of population abundance, which would require further analysis using an integrated or state-space model (Buckland et al. 2004), but is instead presented to aid in the interpretation of annually varying estimates of abundance. This smoothed trend was estimated in log-space to reflect the fact that inline image is constrained to be positive, and errors in inline image are probably log-normally distributed. inline image was used as a weighting term for each inline image, while all nesting count estimates were given equal weighting.

Results

Tagging rates for both leatherback and loggerhead sea turtles (Fig. 3) increased from 1965 to the late 1990s, and both decreased in the early 2000s prior to a recovery by 2009. By contrast, the number of annual resightings for leatherback sea turtles decreased from the 1960s to 2009, which can be explained by either decreased survival or decreased detection probabilities. For loggerhead sea turtles, annual resightings parallel the number of new tags, that is, they increase from the 1960s to the 1990s, then dip and recover in the 2000s.

Figure 3.

 Number of new unique tags (solid line) and tag resightings (dotted line) for leatherback and loggerhead sea turtles each year.

Stepwise model selection using AIC estimates an almost saturated model for loggerhead sea turtles, and a more parsimonious model for leatherback sea turtles (Table 2). For loggerhead sea turtles, AIC selects an annually varying model for the detection probability for each nesting event (43/43 d.f.) and an almost saturated model for availability (42/43 d.f.) and differs substantially from the saturated model only for survival probability (34/43 d.f.). For the leatherback sea turtles, by contrast, AIC selects a relatively parsimonious model for survival (12/43 d.f.) and availability (21/43 d.f.), but again has an almost saturated model for detection probability (40/43 d.f.). In both cases, the high degrees of freedom estimated for detection probabilities implies that the ‘robust design’ data are highly informative about the annual changes in detection probability for each nesting event (see Appendix S3 and Figs S1–S3 in Supporting Information for model fits to the robust design data and estimated skip-nesting behaviours).

Table 2.   Selected degrees of freedom for first-order fixed-knot spline for survival (inline image), the detection probability for each nesting event (inline image), availability (inline image) and the estimated form for the skip-nesting behaviour
 SurvivalDetectionAvailabilitySkip-nesting
Leatherback1240213rd order Markov
Loggerhead3443424th order Markov

Estimated parameters and confidence intervals show that detectability has declined over time for leatherback sea turtles (Fig. 4a), but has no directional trend for loggerhead sea turtles (Fig. 4b). As expected given the consistent sampling design since the 1972/1973 season, detection probability is approximately constant over time for both loggerhead and leatherback sea turtles, although there is a slight decrease for both species since the 2000s. This pattern of slightly decreased detection probabilities after the 2000s is similar between species, and follows the start of sampling by concessioners in the 1996/1997 season. Changes in detectability for leatherback sea turtles are thus explained by a precipitous decrease in availability since approximately 1990. Survival is relatively high for both species, although it exhibits periodic drops that are easier to identify for leatherback sea turtles, for which AIC has selected a more smooth approximation for survival, than for loggerhead sea turtles. These trends are similar when allowing time-varying skip-nesting parameters (S4 and S5 in Supporting Information), although confidence interval width is somewhat increased in that case.

Figure 4.

 Detectability (inline image, equation 1), survival probability (inline image), detection probability for each nesting event (‘detection rate’, inline image) and availability (inline image) for (a) leatherback and (b) loggerhead sea turtles, with mean (points) and approximate 95% confidence intervals (lines).

There are large differences in estimated abundance trends from tag-resighting data and nesting count data (Fig. 5). For leatherback sea turtles, nest count data suggest that abundance increased rapidly from 1965 to 1975 and has been approximately steady since then, while the tag-resighting data implies that rebuilding occurred largely in the 1990s and has dropped somewhat in the 2000s. Additionally, the tag-resighting model estimates the abundance of nesting-age female leatherbacks to be approximately 1000 in 2010. For loggerhead sea turtles by contrast, the nest count data suggest that nesting-age female abundance has increased rapidly in the 2000s, while the tag-resighting data estimate that abundance increased rapidly from 1965 to 1980 and has fluctuated since then, with a nesting-age female abundance of approximately 3000 in 2010.

Figure 5.

 Estimated abundance (solid line) and a GAM estimate of survival (dotted line) using the Horvitz-Thompson estimator based on estimated detection probability (black) and observed nests (grey) for leatherback and loggerhead sea turtles, where the observed nest generates a relative index of abundance but is scaled for display with the tag-resighting index in numbers.

Between-model variability in survival and abundance estimates (Fig. 6) is greater for the leatherback sea turtles than for loggerhead sea turtles, as expected given that leatherback has fewer data. In general, loggerhead sea turtles show well-defined estimates of survival and abundance, while leatherback sea turtles have considerable uncertainty regarding abundance and survival in recent years (e.g. since 2005), where there is at least one model that depicts a rapid decrease in abundance from 2005 to 2008. This uncertainty in model estimates at the beginning and end of time series data is a common characteristic of multistate tag-resighting models.

Figure 6.

 Estimated abundance and survival for leatherback and loggerhead sea turtles for all models with ΔAIC (Akaike Information Criterion) < 10 that were encountered during the stepwise model selection process.

Finally, model selection (Table 3) shows that increased fishing effort has no explanatory power for decreased survival for either species (ΔAIC = 2, which arises when the fishing effort parameter inline image). In fact, examination of survival estimates on a decadal scale shows that survival for both species is likely to have increased rapidly during the 1960s–1970s and is approximately level or slightly increasing in recent decades. This steady or increasing trend in survival on a decadal scale is inconsistent with the hypothesis that historical increases in longline fishing effort has contributed to decreased survival.

Table 3.   ΔAIC (Akaike Information Criterion) between including or excluding a negative impact of longline fishing effort on survival for leatherback and loggerhead sea turtles, given AIC-selected degrees of freedom for spline approximation for the detection probability for each nesting event (inline image), availability (inline image) and the estimated form for the skip-nesting behaviour
ΔAICFishing effort included?Effect of fishing effort on survival (inline image)SurvivalDetectionAvailabilitySkip-nesting
Leatherback
0·0NoDecadal40373rd order Markov
2·0Yes0·000Decadal40373rd order Markov
Loggerhead
0·0NoDecadal43424th order Markov
2·0Yes0·000Decadal43424th order Markov

Discussion

Comparison with existing tag-resighting models

We develop a tag-resighting model that is appropriate for sea turtles, sea birds and other animals that are only easily observable upon return to a nesting area and demonstrate its utility using data for leatherback and loggerhead sea turtles in South Africa. This model is designed to disaggregate detectability into three components: skip-nesting behaviours, availability and detection probability for each nesting event.

For the species in this study, nesting is energetically costly and thus is rarely performed in consecutive years. Periodic detectability could also be caused by a semelparous life history, for example, salmons, as well as some marine mammals, lizards and sea birds (Kendall et al. 2009). Skip-nesting behaviour has previously been modelled using first- or higher-order Markovian transitions (Rivalan et al. 2006; Converse et al. 2009; Monk, Berkson & Rivalan 2010). We have instead opted to model all possible return patterns that could result in a given resighting history, and this allows our model to potentially include non-Markovian transitions (e.g. a Poisson distribution for years between nesting returns). Although for simplicity we have restricted our attention to Markovian transition models, future studies could explore other transition models that may be more parsimonious (e.g. a Poisson rate parameter being environmentally driven), particularly when estimating time- or environmentally varying remigration probabilities.

In tag-resighting software such as MARK (White & Burnham 1999), time-varying parameters such as detectability are conventionally approximated in one of two ways: constant for all years or estimated separately for each year. In this study, we use an approximation that includes the constant or annual models as extreme cases and use AIC to select a parsimonious smoothness for time-varying parameters. This spline approximation could be applied generally in other tag-resighting or population dynamics models (Gimenez et al. 2006) and is likely to be parsimonious in many instances with limited data availability.

This model can be improved by future research in several ways. Time-indexed data regarding each nesting return would provide additional information and could allow estimation of time-varying clutch frequencies and/or changes in detection probability within a nesting season (Kendall & Bjorkland 2001). Skip-nesting behaviours may also be modelled as environmentally variable, as has been estimated for green sea turtles Chelonia mydas (Limpus & Nicholls 1988), and possible environmental covariates could be screened and tested. However, time-varying skip-nesting behaviours have not been thoroughly explored in sea turtle or bird mark-resighting models (Rivalan et al. 2005; Monk, Berkson & Rivalan 2010), and will require analytic or simulation testing to explore the possible biases arising from model misspecification.

Implications for sea turtle research and conservation

The KwaZulu-Natal sea turtle populations have tag-resighting data over an extremely long time period relative to other sea turtles and provide an excellent case study for examining conservation impacts of beach protection and fishery bycatch. Nesting beaches for these populations have received increasing protection (R. Nel, A. Punt & G.R. Hughes unpublished data), which has helped restore other leatherback sea turtle populations (Dutton et al. 2005). However, a relative index of abundance derived from nest counts had shown apparent population rebuilding for loggerhead but not leatherback sea turtles.

We have found no evidence that either loggerhead or leatherback sea turtle survival has declined during the period when longline fishing effort has increased. Although this null result could also be caused by using an imprecise index of longline fishing effort, the observed increase in longline fishing effort over time was robust to changes in the area used to calculate this index. Nevertheless, we cannot discount the hypothesis that small-scale fisher targeting or seasonal turtle behaviours could cause effective fishing effort to diverge from the index we calculated. Additionally, the bycatch rates reported by the South African longline fishery (Petersen et al. 2009) would result in large (>100) annual catches of each species if extrapolated in recent years to all longline effort (Bourjea et al. 2008), and several thousand leatherback and loggerhead individuals are estimated to be taken as bycatch by longline fisheries in the Indian Ocean each year (Lewison, Freeman & Crowder 2004). This difficulty in distinguishing between competing hypotheses is common when using observational data to assess anthropogenic impacts on sea turtles (Bjorndal et al. 2011), although we believe our effort represents the best available science regarding the impact of longline fishing on historical survival rates for these populations.

As an alternative explanation of the leatherback nest count data, we find that nesting count data can be explained by declining detectability caused by a decreased probability of returning to the monitored portion of the KwaZulu-Natal nesting beach. One explanation for this decreased availability is range expansion, in which nesting beach protection at nearby beaches has increased survival, causing an increase in the proportion of the nesting population that nests at unmonitored beaches. Range expansion could also be caused by increased interspecific or intraspecific competition for nesting space, although evidence for social or behavioural cues for leatherback nest site selection is generally inconclusive (Owens, Grassman & Hendrickson 1982; Dutton et al. 1999). Either way, range expansion would imply that count studies (e.g. of nests or nesting individuals) within fixed sampling areas can result in a biased index of abundance. The possibility of interspecific and intraspecific competition could be evaluated by modelling the probability of nesting in a given beach-kilometre as being affected by the location of past nesting and the density of nesting individuals in that area. This spatial model would also allow spatially explicit estimates of detection probability and is a possible topic for future research.

The hypothesis of range expansion causing declining detectability should be addressed within future sea turtle and bird surveys designs, including that at the KwaZulu-Natal nesting beach. Specifically, infrequent sampling (e.g. nesting beach counts every couple of years) could be extended southwards and northwards to search for turtles with tags from the monitored nesting beach. Informal sampling could not be included in future tag-resighting models because of spatial variability in detection rates, but would still address the question of whether individuals tagged at the KwaZulu-Natal nesting beach are returning to distant beaches. This proposal of intermittent and possibly informal count sampling beyond the historical nesting area is consistent with the call by Bjorndal et al. (2011) for improved data collection to distinguish between alternative hypotheses regarding managed species. However, additional sampling will never answer the question of historical changes in range. We thus believe that robust design data and its ability to distinguish changes in availability and sampling design is likely to remain the primary method to make inference about historical range expansion or contraction and, hence, population recovery.

Acknowledgements

The authors would like to thank Ezemvelo KZN Wildlife, which is responsible for collecting the data reported in this article, and EcoAdvice (Santosh Bachoo). Funding for data collection was provided by NMMU and NRF, while support for model development and analysis was provided by the University of Washington, a National Marine Fisheries Service (NMFS) groundfish project grant to the University of Washington, the NMFS-Sea Grant Population Dynamics Fellowship (NA09OAR4170120), and the Joint Institute for the Study of the 353 Atmosphere and Ocean (JISAO) under NOAA Cooperative Agreement No. 354 NA17RJ1232. We also thank L. Clarke, T. Essington, S. Heppell, S. Hilber, R. Hilborn, I. Stewart and one anonymous reviewer.

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