Consequences of violating the recapture duration assumption of mark–recapture models: a test using simulated and empirical data from an endangered tortoise population

Authors


Present address and correspondence: Susan O’Brien, Macaulay Institute, Craigiebuckler, Aberdeen AB15 8QH (fax +1224 311556; e-mail sue.obrien@jncc.gov.uk).

Summary

  • 1Mark–recapture methods are frequently used to estimate survival rates, which inform wildlife management policies. Mark–recapture models assume zero mortality of marked animals during the period of recapture and therefore that this period is of negligible duration relative to the interval between recapture events. This ‘recapture duration assumption’ is frequently violated yet is rarely tested for its potential to bias survival estimates. We investigated whether violating the recapture duration assumption increased precision at the cost of increased bias in estimates of survival.
  • 2Using both simulation and empirical approaches, annual survival and recapture rates were estimated under recapture period durations that either conformed to, or violated, the recapture duration assumption. Empirical data were derived from a population of endangered Madagascar ploughshare tortoises Geochelone yniphora.
  • 3Estimates of ploughshare tortoise survival were higher and had smaller standard errors when the recapture duration assumption was violated. As the ‘true’ ploughshare tortoise survivorship was unknown, a simulation approach was used to assess whether short or long recapture periods gave the most reliable estimates.
  • 4The simulation study showed that violating the recapture duration assumption increased precision but did not increase bias in parameter estimates, even if up to 50% of the annual mortality occurred during the recapture period. The most precise and least biased survival estimates were obtained when sample size (number of marked individuals) was greatest, i.e. when both survival and recapture rates were high. Bias in survival estimates was negligible unless the recapture rate during the recapture period was < 0·2. We conclude that the most precise ploughshare tortoise parameter estimates were generated by using lengthy recapture occasions that violated the recapture duration assumption.
  • 5Synthesis and applications. To achieve the most precise and least biased survival estimates we recommend violating the recapture duration assumption and using a recapture period that maximizes sample size and achieves a recapture rate of > 0·2 during the recapture period. If both survival and recapture rates are relatively constant during the recapture period, survival estimates will then have negligible bias. If a recapture rate of > 0·2 during the recapture period cannot be achieved, methods other than mark–recapture should be used to quantify demographics. These recommendations apply to any species with an annual survival rate > 0·05.

Introduction

Across the globe, wild populations are managed for a diversity of reasons. Decisions on how best to manage a wild population to achieve the desired objectives depend upon a good understanding of that population's demography (Coulson et al. 2001; Boyce, Irwin & Barker 2005). Biased estimates of demography can lead to inaccurate predictions of the future status of a population, which may result in implementation of inappropriate management policies and a failure to achieve the management goals (Brook et al. 1997). One widely used method for estimating demographic rates is mark–recapture (Lebreton et al. 1992). Mark–recapture methods estimate demographic parameters using a probabilistic framework to interpret the rate at which marked individuals are re-encountered in a population. One assumption of mark–recapture models is that recapture occasions are of negligible length relative to the interval between them and therefore that no mortality occurs during the recapture occasion (the recapture duration assumption).

Mark–recapture studies violate the recapture duration assumption by using recapture occasions of long duration relative to the interval between recapture occasions for several reasons, to: (i) allow recapture of more marked individuals thereby obtaining sufficiently large sample sizes; (ii) reduce variance around a parameter estimate; (iii) reduce the number of parameters to be estimated, thereby increasing efficiency and precision of parameter estimation; (iv) cope with sparse data; and (v) mediate the effects of ‘trap happiness’ and ‘trap shyness’ (Smith & Anderson 1987; Hargrove & Borland 1994; Pradel et al. 1997; Viallefont, Kanyamibwa & Asselain 1999; White & Burnham 1999; Peach, Hanmer & Oatley 2001; Schaub & Jenni 2001; Schaub et al. 2001). However, most studies that report the use of lengthy recapture occasions do not consider the consequences of violating the recapture duration assumption. For example, of 31 studies published in the peer-reviewed literature that used mark–recapture models to estimate annual survival, 13 used lengthy (> 2 months) recapture occasions. However, only four mentioned the potential for bias in parameter estimates as a result of violating this assumption and only one tested empirically for potential bias (Anderson et al. 2001; Frederiksen & Bregnballe 2001; Chaloupka & Limpus 2001; Clausen et al. 2001; Forero, Tella & Oro 2001; Gauthier et al. 2001; Hall, McConnell & Baker 2001; Hoyle, Pople & Toop 2001; Murphy 2001; Peach, Hanmer & Oatley 2001; Seamans et al. 2001; Tavecchia et al. 2001; Willemsen & Hailey 2001). This is surprising given the frequency with which mark–recapture data are tested for violating other model assumptions (Anderson & Burnham 1980; Pollock et al. 1990; Choquet et al. 2003; McCarthy & Parris 2004).

If bias does increase with length of recapture occasion, a trade-off would exist between lengthy recapture occasions, which would maximize precision, and short recapture occasions, which would minimize bias. To our knowledge there have been just two previous studies that have used a simulation approach in order to explore the consequences of violating the recapture duration assumption, and neither of these studies explicitly compared short- and long-recapture occasions (Smith & Anderson 1987; Hargrove & Borland 1994). In this present study, we tested these consequences using simulated mark–recapture data and empirical data from a population of tortoises.

The rare ploughshare tortoise Geochelone yniphora Vaillant, 1885 is threatened with extinction (Smith et al. 1999; Hilton-Taylor 2000). This species is now reduced to approximately 600 individuals in five isolated populations in north-west Madagascar, as a result of commercial exploitation and habitat loss from bush fires (Smith et al. 1999). To conserve the tortoise it would be advantageous to take some juveniles into captivity as an insurance against extirpation of the remaining wild tortoises. However, if the population is found to be declining this policy could be detrimental and, instead, it would be more useful to identify which life stages of the wild populations would benefit most from action to reduce mortality rates (Pedrono & Sarovy 2000; Pedrono et al. 2004). Reliable estimates of tortoise survival rates are therefore needed to ensure the most appropriate conservation management policies are implemented. A long-term mark–recapture study was carried out on the largest ploughshare tortoise population to obtain an understanding of this population's demographics. However, there is the question of whether it is appropriate to use lengthy recapture occasions to maximize the number of tortoises recaptured, to lead to the most precise estimates of survival. This approach could introduce significant bias into estimates of survival, potentially misleading conservation managers.

The aim of this study was to assess the degree of bias and precision of parameter estimates generated under short and lengthy recapture occasions. Using simulation and empirical data, we provided the first published estimates of ploughshare tortoise survival and assessed whether a trade-off exists between precision and bias in parameter estimates from lengthy recapture occasions.

Materials and methods

empirical study

Study area and study species

The ploughshare tortoise is a large [45 cm carapace length (CL)] herbivorous terrestrial reptile, endemic to Madagascar in the Indian Ocean (Smith et al. 1999). The largest population is at Cap Sada, north-west Madagascar (16°02′S, 45°20′E), found in 150 ha of bamboo scrub habitat (Smith et al. 1999). The area is semi-arid, with seasonal precipitation, predominantly October–March, during which the tortoises become active. Ploughshare tortoises lay an average of 3·2 eggs clutch−1 and an average of 2·45 clutches year−1, during January to May (Pedrono, Smith & Sarovy 2001). Eggs hatch at the end of October, after an average 237-day incubation (Pedrono, Smith & Sarovy 2001). The average hatch rate is reported to be 54·6% (Pedrono, Smith & Sarovy 2001).

Mark–recapture methods

Three-hundred and twenty-nine ploughshare tortoises at Cap Sada were captured, marked and released during several days of most months from October 1993 to February 2000 (for further details see Smith et al. 1999). Survival and recapture rates for ploughshare tortoises were estimated using the computer program mark (White & Burnham 1999). Recapture histories were generated using recapture occasions of three durations: 1 month (December only), 3 months (October–December) and 6 months (October–March). These periods were selected as the greatest numbers of tortoises are encountered in these months. Annual survival, recapture and transition probabilities were estimated using a multistrata model, an extension of the Cormack-Jolly–Seber (CJS) model, in MARK (Hestbeck, Nichols & Malecki 1991; Brownie et al. 1993; White & Burnham 1999). Four size classes (strata) were used in the mark–recapture models: hatchling class, CL ≤ 52 mm; small juvenile class, 52·1 mm < CL ≤ 86 mm; large juvenile class, 86·1 mm < CL ≤ 300 mm; adult class, CL > 300 mm. These size classes correspond approximately with age 0, age 1–3, age 4–16 and age 17+, respectively (Pedrono et al. 2004). This grouping was selected to generate sufficient sample sizes and achieve homogeneity in survival and recapture rates within classes, as determined by a satisfactory goodness-of-fit to the CJS model (White & Burnham 1999).

A candidate model set of nine multistrata models was fitted to each of the three sets of recapture histories. Survival (S) was allowed to vary with size class (g) or vary with time as an additive effect (g + t). Survival was not permitted to be constant or vary only through time as it would not be biologically feasible for a long-lived species such as tortoises to have similar hatchling and adult survival rates. Survival was also not allowed to vary through time as an interactive effect (g × t) as this model required too many parameters to be estimated for the available data. Recapture (p) was allowed to vary with group (g), time (t), group and time as an interactive (g × t) and additive effect (g + t), and remain constant (.). However, the recapture probability for hatchling tortoises was fixed at 0·00 as individuals marked in their first year of life, as hatchlings, that were recaptured in the next recapture occasion a year later were 1 year old and therefore in the small juvenile size class. Transition parameters (ψ) were set to vary among size classes (g) only. All but three transition parameters were fixed to 0·00 in all models, as an individual could not move to a smaller size class nor jump to a much larger size class (e.g. from hatchling to large juvenile). The transition parameter for individuals moving from the hatchling to the small juvenile size class was set to 1·00 because all individuals that were marked as hatchlings could only be recaptured as small juveniles. The model with the lowest Akaike's information criterion (AIC) in the candidate model set was selected to estimate survival, recapture and transition parameters (Akaike 1973; Burnham & Anderson 1998).

Population model

A deterministic size-structured post-breeding census matrix population model was used to predict the rate of growth of the ploughshare tortoise population when parameterized by each of the three sets of survival and transition probability estimates derived from 1 month, 3 months and 6 months duration mark–recapture occasions (Caswell 2001). A deterministic model was used to give an impression of the overall trend in tortoise population dynamics, under each set of parameter estimates, rather than using a more complex stochastic model that would provide estimates of the potential variance in population growth. The population model comprised four stages, which corresponded with the same four size classes used in the mark–recapture analysis. At each time step an individual either remains in stage i or, if sufficiently large, moves to the next size class, stage i + 1, conditional on surviving through the current time step:

image(eqn 1 )

where Si is annual survival probability, ψi is annual transition probability, i = H, SJ, LJ or A, which corresponds with the hatchling size class, small juvenile size class, large juvenile size class and adult size class, respectively. F, the annual fecundity rate per adult female, is assumed to be the product of mean clutch size, mean number of clutches per year and mean hatch rate (Pedrono, Smith & Sarovy 2001). Only female population dynamics were modelled, as the polygynous mating system of tortoises means that a shortage of males is unlikely to limit population growth unless numbers are very low (Wilbur & Morin 1988; Kokko, Lindström & Ranta 2001). Fecundity was therefore divided by two, under the assumption that hatchling tortoises exhibit an equal sex ratio. The finite rate of population increase, λ, was the dominant eigenvalue of matrix A (Caswell 2001; equation 1).

simulation study

Recapture histories were simulated for each month over 7 years, resulting in the same data structure as the empirical mark–recapture study. At the start of the simulation, a simulated population of 1000 individuals was alive and unmarked. Through each month of the simulated study, individuals died at a rate determined by the known monthly survival rate, inline image, which was derived from an annual survival rate, inline image, by inline image, where inline image, 0·1, 0·2, 0·4, 0·6, 0·8 or 0·98. In each month, individuals could potentially be captured and marked at a rate determined by the known monthly recapture rate, inline image, where inline image = 0·02, 0·05, 0·1, 0·2, 0·3, 0·5, 0·7 or 0·9. Simulated individuals, once marked, were then recaptured in subsequent recapture occasions at a rate determined by the known recapture rate,inline image. The number of months of each year in which mark–recapture occurred (i.e. the length of the recapture occasion) was described by the parameter Rj, where R= 1 month or 6 months, corresponding with a recapture occasion of December only and October–March, and j was the year of the simulation study (j = 1, 2 … , 7). The simulation model was built in Microsoft Excel and random numbers were used to allocate a fate (survived/died, captured/not captured) to each individual, each month. For each combination of the possible values of S*, p* and R, a set of recapture histories was generated (n = 112).

A standard CJS mark–recapture model of survival and recapture varying through time, {inline image(t),inline image(t)}, was fitted to each set of simulated recapture histories, where inline image is the estimate of annual survival probability dependent on recapture occasion duration, R, and inline image is the estimate of annual recapture probability dependent on recapture occasion duration, R. Models with survival and recapture constrained to be constant were also fitted to each set of recapture histories. The most parsimonious model was selected by AIC, as described above. A random subset of models was tested for goodness-of-fit, using the bootstrap method in mark, and were found to have a consistently good fit to the mark–recapture data.

Bias in estimates of survival and recapture rates were quantified by subtracting known parameter values from the corresponding parameter estimates, generated by the recapture histories simulated from the known parameters. Bias in survival rates, Bs, was found by inline image and inline image. To calculate bias in recapture rates, it was necessary to adjust the monthly recapture rate, inline image, to a recapture rate for a 6-month period, inline image, by inline image. Bias in recapture rates, Bp, was therefore inline image and inline image.

Results

empirical study

The most parsimonious multistrata model was {S(g),p(g + t),ψ(g)} (survival rate varying with size class, recapture rate varying with size class + time and the rate of transition between size class varying with size class; Table 1). Varying the length of recapture occasion did not result in a different most parsimonious model. The number of tortoises that were marked during mark–recapture was higher under lengthy recapture occasions (6 months; n = 329), compared with short recapture occasions (1 month; n = 177) and intermediate length recapture occasions (3 months; n = 239).

Table 1.  Selection of multistrata mark–recapture models fitted to the empirical ploughshare tortoise recapture histories, generated by (a) 1-month, (b) 3-month and (c) 6-month duration recapture occasions. Survival (S), recapture (p) and transition parameters (ψ) were held constant (.) or were allowed to vary with tortoise body size class (g) and through time (t). Not all parameters could be estimated for all models, resulting in different numbers of parameters for the same model
 ModelAICΔAICNo. parametersModel deviance
(a) 1-month long recapture occasion
1{S(g),p(g + t),ψ(g)}394·37 0·0014141·95
2{S(g),p(t),ψ(g)}394·60 0·2312146·72
3{S(g + t),p(t),ψ(g)}395·93 1·5615141·20
4{S(g + t),p(g + t),ψ(g)}397·39 3·0217137·98
5{S(g + t),p(g),ψ(g)}402·03 7·6611156·38
6{S(g),p(g),ψ(g)}402·49 8·12 9161·26
7{S(g),p(g × t),ψ(g)}404·8610·4923130·85
8{S(g),p(.),ψ(g)}406·5812·21 7169·68
9{S(g + t),p(.),ψ(g)}411·1016·7310167·68
(b) 3-month long recapture occasion
1{S(g),p(g + t),ψ(g)}546·14 0·0014191·08
2{S(g + t),p(g + t),ψ(g)}555·10 8·9619189·10
3{S(g),p(g × t),ψ(g)}555·22 9·0923180·25
4{S(g),p(t),ψ(g)}565·9419·8012215·18
5{S(g + t),p(t),ψ(g)}572·2026·0712215·62
6{S(g),p(g),ψ(g)}573·1226·98 9228·72
7{S(g + t),p(g),ψ(g)}579·7433·6114224·69
8{S(g),p(.),ψ(g)}590·3444·20 7250·12
9{S(g + t),p(.),ψ(g)}594·1147·9812243·36
(c) 6-month long recapture occasion
1{S(g),p(g + t),ψ(g)}919·45 0·0014303·03
2{S(g),p(g × t),ψ(g)}925·21 5·7624287·19
3{S(g + t),p(g + t),ψ(g)}927·82 8·3618302·86
4{S(g),p(g),ψ(g)}936·4216·97 9330·48
5{S(g + t),p(g),ψ(g)}945·5326·0814329·11
6{S(g),p(t),ψ(g)}962·9743·5212350·77
7{S(g + t),p(t),ψ(g)}970·6551·1917347·84
8{S(g),p(.),ψ(g)}977·6458·18 7375·83
{S(g + t),p(.),ψ(g)}985·2365·7812373·03

Ploughshare tortoise annual survival, generated under 6-month duration recapture occasions, was low in the early life stages (hatchling annual survival mean = 0·500, SE = 0·091; small juvenile annual survival mean = 0·749, SE = 0·062) but was very high for tortoises in the large juvenile (mean = 0·911, SE = 0·037) and adult (mean = 0·971, SE = 0·016) life stages (Fig. 1). Survival estimates derived from longer (6 month) recapture occasions were consistently higher than estimates derived from short (one month) recapture occasions, although this increase was not statistically significant because of the larger errors associated with survival estimates generated under short recapture occasions (Fig. 1). As expected, the annual recapture probability increased with both body size and recapture occasion duration in ploughshare tortoises (small juvenile = 0·228, 0·202 and 0·274, large juvenile = 0·336, 0·711 and 0·688, adult = 0·517, 0·699 and 0·772, for recapture occasion durations of 1, 3 and 6 months, respectively). No standard error is presented with mean recapture rates, as this would show the variance in recapture rates among years rather than act as a measure of confidence in each of the parameter estimates generated by mark. Unlike survival and recapture parameter estimates, the mean annual transition probability estimates did not show any increase with either body size or length of recapture occasion. The rate of transition between size classes was low but had large standard errors associated with these estimates because of the relatively low number of transitions among size classes in the tortoise mark–recapture data [mean and standard error of small juvenile to large juvenile transition = 0·064 (0·017), 0·017 (0·018), 0·082 (0·027), mean and standard error of large juvenile to adult transition = 0·121 (0·070), 0·074 (0·036), 0·074 (0·029), for recapture durations of 1, 3 and 6 months, respectively].

Figure 1.

Ploughshare tortoise mean annual survival probability for the four tortoise size classes, generated from recapture histories derived from mark–recapture occasions of 1-month, 3-month and 6-month duration. Estimates were generated by fitting the model {S(g),p(g + t),ψ(g)} to the recapture histories. Error bars represent standard errors.

Population model

The deterministic matrix population model predicted the ploughshare tortoise population to be increasing (+3·5% per annum, λ= 1·035) when parameterized with survival rates generated by 6-month duration recapture occasions, but to be declining (−3·5% per annum, λ= 0·965) when survival rates generated by 1-month recapture occasions were used. Estimates derived from intermediate length (3-month) recapture occasions suggested the tortoise population was slowly declining, at a rate of −1·6% per annum (λ = 0·984).

simulation study

In all cases, the most parsimonious model was {inline image(.), inline image(.)}, i.e. survival and recapture probabilities were constant through time. Model selection results are not presented as they were numerous, but the reduced model was consistently the most parsimonious.

Bias in parameter estimates did not increase with recapture occasion duration, as the mean bias in parameter estimates for 1- and 6-month duration recapture occasions was consistently close to zero [mean and standard error in survival estimates generated under short −0·007 (0·023) and long 0·005 (0·005) recapture occasions; mean and standard error in recapture estimates generated under short −0·018 (0·013) and long −0·004 (0·006) recapture occasions]. The likelihood of generating an estimate of survival that was very different to the true parameter value was very small under lengthy recapture occasions but was greater under short recapture occasions, as illustrated by the size of the standard error around the mean bias. However, if confidence in a parameter estimate is low, i.e. the standard error is large, the estimate is unlikely to be significantly different to the true value.

Sample size, defined as the number of individuals marked in the simulation study of a possible 1000 individuals in the simulated population, strongly influenced the degree of bias in survival and recapture estimates (Fig. 2a,b). At small sample sizes (n < 100), parameters frequently could not be estimated or were wrongly estimated. For sample sizes of n= 100–200, survival estimates differed from the true parameter value by up to 0·200 but were generally not significantly different from the true parameter value because of the large error associated with these estimates (Fig. 2a,b). With increasing sample size, the magnitude of bias in survival estimates declined rapidly, as did standard error, i.e. the largest sample sizes gave the most precise and least biased estimates. Generally, estimates of recapture rate followed a similar pattern to survival estimates, although both bias and standard error were occasionally large at larger sample sizes. Some recapture rates could not be estimated, even at very large sample sizes, but all of these points were simulated using a low survival rate of 0·05 (Fig. 2b). The even distribution of points above and below the x-axis further illustrates the absence of systematic bias in data generated by lengthy recapture occasions (Fig. 2a,b).

Figure 2.

Bias (estimated rate – known rate) in (a) survival estimates and (b) recapture estimates from simulated recapture histories generated by 1- and 6-month duration recapture occasions. At low sample sizes mark–recapture models were unable to estimate some parameters, which are allocated a bias value = 1·00 on these plots. Sample size is the total number of individuals that were ‘encountered’ during the six marking sessions from the simulated population of 1000 individuals. Error bars represent standard errors around the estimated rates.

Bias in parameter estimates was generally low (< 0·1) but did increase when the recapture rate was low (< 0·2) and the recapture occasion was short (Fig. 3a,b). Bias in recapture estimates was the same as for survival estimates under both short and long recapture occasions, apart from when survival rate was < 0·2. A survival rate of < 0·2 consistently resulted in biased recapture estimates, irrespective of the recapture rate. If the true survival and recapture rates for ploughshare tortoises were presumed to be those values obtained from using a 6-month recapture occasion, then the simulation results suggested that estimates of ploughshare tortoise survival and recapture rates would carry negligible bias under 6-month duration recapture occasions (Fig. 3a). However, the simulation results suggested hatchling and small juvenile survival and recapture rates could be biased under 1-month duration recapture occasions because of the lower recapture rate of tortoises in the two smaller size classes (Fig. 3b). This agreed with the results of the empirical study (Fig. 1).

Figure 3.

Bias in survival estimates from simulated recapture histories generated under (a) 6-month and (b) 1-month recapture occasions. Bias for values of survival for which no simulation was run has been interpolated from known bias. Light colours represent a negligible degree of bias (< 0·08), dark colours a high degree of bias. At low sample sizes mark–recapture models were unable to estimate some parameters, which appear as the darkest colour on these plots. Ploughshare tortoise survival and recapture estimates, generated under 6-month recapture occasions, are marked on the plots as H (hatchling), SJ (small juvenile), LJ (large juvenile) and A (adult). Tortoise recapture rates presented in the 1-month plot (b) are the 6-month rates scaled for a recapture occasion duration of 1 month only. Hatchling recapture rate was always 0·00 as hatchlings were only recaptured as small juveniles, so hatchling survival is represented by a line on the plots.

Discussion

Bias in survival and recapture estimates, derived from simulated encounter histories, was generally small. Contrary to expectations, violating the recapture duration assumption actually improved parameter estimates, by increasing precision, without incurring any additional bias, despite up to 50% of annual mortality occurring during the recapture occasion. Bias in survival estimates was < 0·1 when recapture rate during the recapture occasion was > 0·2, for any value of survival, although bias was reduced as survival rate increased. Survival rates were least biased and most precise when sample sizes were largest. Sample size is determined by both survival and recapture rates and, because the likelihood of recapturing an individual increases with the length of time spent searching for it, the least biased and most precise estimates of survival were obtained under longer recapture occasions. Low survival rates can be successfully estimated by mark–recapture models when recapture rate is reasonably high, but when survival rate becomes very low recapture rate inevitably becomes very low, as individuals die before they are recaptured, and estimating recapture rates becomes difficult.

Smith & Anderson (1987) found negligible bias in survival estimates when survival was high but, when survival was low and variable among or within recapture occasions, bias could be large. Hargrove & Borland (1994) found bias to be < 5% when survival rates were > 0·500 during the recapture occasion. This agrees with the results of our study, although we found a larger degree of bias in survival estimates than Hargrove & Borland (1994) when the recapture rate was low.

Estimates of ploughshare tortoise survival and recapture rates increased proportionately with length of recapture occasion. As the simulation study found lengthy recapture occasions yielded unbiased and more precise estimates, it is reasonable to assume that the empirical tortoise survival estimates derived under 6-month recapture occasions are closest to the true tortoise survival rate. These are the first published estimates of ploughshare tortoise survival. Estimates from 1-month duration recapture occasions are considered to be underestimates of the true tortoise survival rate, possibly because marked tortoises are not being recaptured during the short recapture occasion and the mark–recapture models assume these individuals have died rather than not being recaptured.

Adult ploughshare tortoise annual survival, generated by 6-month duration recapture occasions, was consistently very high, while hatchling survival was low but increased through the juvenile life stages. These estimates are as expected for a species that follows a ‘slow’ life-history strategy of a very long reproductive life span during which many offspring are produced, only a few of which will survive to maturity (Stearns 1992). A larger body size has been demonstrated to offer lower mortality risks for many tortoise and turtle populations through reduced predation risk, greater mobility and an increased ability to withstand physiologically stressful periods (Morafka 1994; Bodie & Semlitsch 2000; Janzen, Tucker & Paukstis 2000). Broadly similar rates and patterns of survival have been reported for 30 species of turtle and tortoise (Iverson 1991).

The deterministic population model, parameterized with survival rates generated under 6-month duration recapture occasions, predicted a slow growth rate of +3·5% per annum for the Cap Sada ploughshare tortoise population. This is similar to the growth rate of approximately 1% per annum found by Pedrono et al. (2004) for the same population. As the ploughshare tortoise population was at a low density, relative to other Madagascar tortoises, it is unlikely any intrinsic population process was limiting population growth (O’Brien et al. 2003; Pedrono et al. 2004). This growth rate suggests the population should sustain the removal of a few juveniles to supplement a captive breeding programme. The deterministic population model gave very different predictions for the status of the Cap Sada ploughshare tortoise population, depending on recapture occasion duration. This illustrates the importance of basing wildlife management policies on reliable unbiased demographic rates to avoid implementing ineffective and potentially detrimental management policies (Brook et al. 1997; Coulson et al. 2001). However, when used correctly, mark–recapture provides applied ecologists with a valuable tool for gaining insight into the demographics of wild populations (Frederiksen et al. 2004).

conclusions and recommendations

We suggested a trade-off may exist when estimating mark–recapture parameters, between maximizing precision by maximizing sample size and minimizing bias by conforming to the recapture duration assumption. We conclude that this trade-off does not exist as there is no cost, in terms of the degree of bias, to violating the recapture duration assumption, when survival is constant through time. To minimize bias and maximize precision in mark–recapture parameter estimates, we therefore recommend maximizing sample size (the number of individuals marked and the number of times marked individuals are recaptured). When the recapture rate during the recapture occasion is low (< 0·2), we recommend lengthening recapture occasions to increase sample size and thereby to increase the recapture rate to > 0·2. If the recapture rate during the recapture occasion cannot be raised above 0·2, for example if animals are very hard to recapture or the logistics of staying at a site prohibit lengthening recapture occasion duration, then we suggest using an alternative method to mark–recapture as it will not give reliable results and associated errors could be very large. It is always worthwhile creating several sets of recapture histories using different length recapture occasions and observing how sample size, parameter estimates and variance around these estimates change, to detect any inherent bias in the data. We also recommend using a concurrent independent measure of demography, such as distance sampling (Buckland et al. 1993), as an insurance against undetected biases in mark–recapture estimates. These recommendations apply equally to any population or species that has an annual survival rate of > 0·05. Finally, it is the responsibility of those advising wildlife management policy makers to ensure they have a thorough understanding of the methods they use to address applied scientific questions (Mills et al. 1996; Reed et al. 2002).

Acknowledgements

We are grateful to Morten Frederiksen for advice on developing the simulation study. We also wish to thank Morten Frederiksen, David Cope, Alison Hester, Robin Pakeman, Joanna Durbin, Pete Goddard and two anonymous referees for their insightful and constructive comments on earlier drafts of this paper. Thanks also to Giacomo Tavecchia for advice on mark–recapture methods, and Tim Coulson and Marcus Rowcliffe for useful discussion. We are grateful to David Cope for producing some of the figures and to all those who collected the empirical data, including Lora Smith and Miguel Pedrono. The Durrell Wildlife Conservation Trust and the Natural Environment Research Council funded this research.

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