### Introduction

- Top of page
- Summary
- Introduction
- Methods
- Results
- Discussion
- Acknowledgements
- Supplementary material
- References
- Supporting Information

Many types of ecological studies require the unique identification of individuals, which is usually achieved by marking. Methods such as tattooing and banding are difficult to use on amphibians because of their particular anatomy and the nature of their skin (Halliday 1996). Perhaps the most common method of marking amphibians is toe clipping, in which a unique combination of digits (or part thereof) is removed from each individual (Hero 1989; Waichman 1992; Halliday 1996). For subsequent analysis, it is usual to assume that the method of marking does not influence the animal's survival or behaviour. A marking method that has adverse effects on the marked animals will violate this assumption and compromise the quality of the data, unless it is possible to account for these effects. In addition, there are ethical and conservation implications if animals are harmed.

The adverse impacts of toe clipping on amphibians, such as inflammation and infection of feet and limbs, and a reduction in the return rate of marked animals, have been reported in some cases (Clarke 1972; Humphries 1979; Golay & Durrer 1994; Lemckert 1996; Reaser & Dexter 1996; Williamson & Bull 1996) but not in others (Lemckert 1996; Williamson & Bull 1996). Parris & McCarthy (2001) helped to resolve this apparent inconsistency by demonstrating that absences of statistically significant effects in some previously published studies could be attributed to a lack of statistical power rather than absences of actual effects. Based on fitted regression lines, we estimated that return rates declined by 6–18% for each toe removed after the first (Parris & McCarthy 2001). However, this analysis did not provide meaningful confidence intervals for the estimate, or analysis of how the impact of toe clipping might change with the number of toes removed.

Here, we present a Bayesian reanalysis of the data used by Parris & McCarthy (2001). A Bayesian analysis uses a model to combine prior information with new data to produce updated estimates of the parameters (Hilborn & Mangel 1997; Wade 2000; Link *et al*. 2002). The model defines how the parameter of interest (in this case the effect of toe clipping) is related to the data. In the present study, we developed statistical models that define the relationship between the number of frogs that are recaptured and the effect of toe clipping as a function of the number of toes removed. We demonstrated the relatively simple implementation of our analysis using WinBUGS, a freely available program developed by researchers at the MRC Biostatistics Unit and Imperial College, London, UK (Spiegelhalter *et al*. 2003). We also extended the analysis by permitting the influence of toe clipping to increase or decrease with the number of toes removed. The results presented here illustrate one way that biologically reasonable models with a focus on parameter estimation can help to clarify the results obtained in ecological studies.

### Results

- Top of page
- Summary
- Introduction
- Methods
- Results
- Discussion
- Acknowledgements
- Supplementary material
- References
- Supporting Information

For the analysis assuming a constant effect of toe clipping for each toe removed (model A), the results were broadly consistent with those of Parris & McCarthy (2001), with return rates reduced by approximately 4–11% for each toe removed (Fig. 1). There was strong evidence for a negative effect of toe clipping in the studies of Williamson & Bull (1996), Lüddecke & Amézquita (1999) and Clarke (1972), because the 95% credibility intervals were less than zero. This was equivalent to the conclusion of Parris & McCarthy (2001), who determined that the observed decline (or a larger decline) was unlikely to have occurred if the number of toes removed did not affect the return rate. For the study of Lemckert (1996), the negative mean provided some evidence that toe clipping reduces return rates (Fig. 1), although it is possible that there is no effect or that toe clipping increases return rates (the credibility interval encompassed zero). The wide credibility interval for this study was consistent with its low statistical power (Parris & McCarthy 2001).

By using credibility intervals to present the results, the predicted impacts of toe clipping can be compared with values that might be considered biologically important, not just statistically significant (Fig. 1). For example, we can be confident that the reduction in return rate was greater than 0·02 (equivalent to one frog not returning due to toe clipping for every 50 toes removed) for three of the four studies. In the case of Lemckert (1996), the results were also consistent with an impact of at least 1 in 50.

The analysis in which the effects of toe clipping were permitted to change with each toe removed (model B) provided evidence for increasingly negative effects with each toe removed in the studies of Williamson & Bull (1996) and Lüddecke & Amézquita (1999) (Fig. 2). The study of Clarke (1972) suggested an increasing impact, although the possibilities of no impact or a declining impact could not be eliminated given the width of the credibility intervals. The data from Lemckert (1996) provided little insight into this particular question, with few data to indicate a trend and relatively wide credibility intervals.

The influence of toe clipping on return rates appeared to be relatively consistent across the different studies, because the credibility intervals for the different studies largely overlapped (Fig. 2). Thus, model C seemed to be appropriate for the data. Removing the second toe was estimated to reduce recapture rates by approximately 3·5% (*m*_{2} = −0·035), with the impact increasing to approximately 30% for the eighth toe (*m*_{8} = −0·3) (model C). These impacts were in addition to the effect of removing previous toes. Because the 95% credibility interval for toe number two had an upper bound of approximately zero, it is possible that removing a second toe could have a negligible effect on the return rate. There are no animals in the data sets without toes removed, so it is not possible to estimate the impact of removing the first toe. Extrapolation suggests this impact may be small (Fig. 3), although this should be regarded as speculative because we cannot be sure that the relationship is even approximately linear beyond the range of the data.

The results in Fig. 3 (which are on a per toe basis) were also expressed in terms of the cumulative effect of toe clipping by plotting *R*(*n*)/*R*(1) vs. *n* using the relationship in equation 3 (Fig. 4). This demonstrated how, relative to those with one toe removed, the return rate of animals with *n* toes removed decreases with toe clipping. Expressing the results in this form, rather than including the effect of removing the first toe, avoided extrapolation beyond the range of the data (Fig. 4). Thus, the return rate of frogs with two toes removed was estimated to be approximately 96% of those with one toe removed. This ratio decreased to 65% for frogs with five toes removed and 28% for those with eight toes removed. The precision of these estimates decreased as the number of toes clipped increased, with the range of the 95% credibility intervals being 7% for two toes and 18% for eight toes.

Models B and C, in which the effect of toe clipping increased with each toe removed, fit the data better than model A, based on the calculated DIC values (Table 1). Model A in turn provided a better fit than the original logistic regression model of Parris & McCarthy (2001).

Table 1. Deviance information criteria (DIC; Spiegelhalter *et al*. 2002) indicating the goodness-of-fit of the original logistic regression of Parris & McCarthy (2001) and the three new models (models A, B and C) Model | DIC |
---|

Logistic regression | 532·6 |

A, constant effect of toe clipping | 522·9 |

B, changing effect varying among studies | 506·2 |

C, changing effect consistent across studies | 507·2 |

### Discussion

- Top of page
- Summary
- Introduction
- Methods
- Results
- Discussion
- Acknowledgements
- Supplementary material
- References
- Supporting Information

The return rate following marking is the product of the probability of survival and the probability of recapturing an animal that is alive. Thus, the observed changes in return rate following removal of the second and subsequent toes are due to changes in the probability of survival, changes in the probability of recapture conditional on survival, or both. Reductions in the probability of survival (Clarke 1972; Humphries 1979; Williamson & Bull 1996) may result from infection, a reduction in the mobility or dexterity of marked animals, and a consequent increased susceptibility to predation or starvation. A number of studies have observed infection of feet and limbs following toe clipping (Clarke 1972; Humphries 1979; Golay & Durrer 1994; Lemckert 1996; Reaser & Dexter 1996; Williamson & Bull 1996). Reductions in the probability of recapturing living, marked animals may result from changes in their behaviour such as reduced activity or a propensity to leave the study area following toe removal (an anti-predator response; Lemckert 1996).

A change in the return rate of marked individuals following toe clipping invalidates one of the basic assumptions of mark–recapture studies, unless this effect is known and accounted for in subsequent analyses (Donnelly & Guyer 1994). Mark–recapture analyses that estimate recapture and survival probabilities could incorporate the effects of toe clipping by including the number of clipped toes as a covariate. The results of our analyses should be included in future studies that use population data based on toe clipping of frogs and toads. For example, the predicted change in return rate with each toe removed (Fig. 3) could be used as a model against which alternative models (e.g. with no change in return rate following toe clipping) could be compared.

The results of our reanalysis of published data on the effects of toe clipping on the return rate of frogs are consistent with those of Parris & McCarthy (2001). However, the present reanalysis also suggests that apparent differences among previous studies in the effect of toe clipping on return rates may be due to the different number of toes that were removed from individual animals. The model with a consistent, linear change in the effect of toe clipping with each toe removed (model C) demonstrated that the impact of clipping each toe increases as more toes are removed, corresponding to a rapidly compounding effect on the behaviour and/or survival of the marked frogs. Frogs have 18 toes in total, four on each of the fore feet and five on the hind feet. As well as assisting with balance and locomotion, the enlarged, adhesive disks on the toes of many tree frogs enable them to climb steep or vertical surfaces. It is perhaps not surprising that the fewer the toes a frog still possesses, the greater the effect of removing one more could have on its probability of return.

The observed changes in the survival and/or behaviour of frogs following toe clipping raises concerns about the ethics of using the technique for mark–recapture studies, particularly if the study species is endangered or a large number of toes is removed. These ethical concerns are magnified if possible biases in the data are ignored, thereby reducing their scientific value. The recommendations made by Parris & McCarthy (2001) for minimizing the impacts of toe clipping on individual animals remain relevant. Of particular importance will be the use of a planned marking scheme, such as those suggested by Hero (1989) and Waichman (1992), to minimize the number of toes that are removed.

In addition to providing data for estimating the survival rate and movement of individuals, toes clipped from frogs can provide material for genetic analysis and bone for skeletochronology for estimating age (Friedl & Klump 1997; Driscoll 1998; McGuigan *et al*. 1998). Usually only one toe is required for the latter two purposes, so the impact on individuals and the population is likely to be substantially less than that of studies that require the removal of multiple toes. While it is not possible to comment on specific situations, the scientific and conservation benefits of marking frogs with toe clipping need to be weighed against the likely impacts that we have identified in this study, and the possible impacts of alternative marking methods.

The statistical models we used are relatively simple representations of possible effects of toe clipping. More complex models could be developed, although we do not believe they are necessary for the purpose of exploring our particular questions. Despite their relative simplicity, most standard statistical packages cannot be used to analyse the statistical models in this study. By using the program WinBUGS, we were able to design specific models rather than relying on the statistical models that are available in standard software packages. WinBUGS is freely downloadable and relatively user-friendly. Some experience with computer programming is useful when using WinBUGS, although there is also a graphical user interface for constructing the models, reducing the need for programming skills. Further, the program includes examples for numerous different statistical models, making it relatively easy to learn the WinBUGS language.

Our results illustrate how the regression models and extensive power analyses of Parris & McCarthy (2001; which required 24 figure panels and several tables) can be represented simply within a single figure by using a relevant statistical model and focusing on parameter estimation rather than significance testing (Fig. 1). Bayesian methods are sometimes criticized because of the possibility of subjectivity in defining the prior distributions (Oakes 1986). We avoided this problem to some degree by using flat priors that did not constrain the width of the posterior distribution, making the results numerically similar to a likelihood-based analysis (Link *et al*. 2002). Likelihood-based methods could also be used to analyse the models in this study (Anderson, Burnham & Thompson 2000; Burnham & Anderson 2002). While we acknowledge there is debate about which statistical approach is the most appropriate for particular circumstances (Oakes 1986; Anderson, Burnham & Thompson 2000; Johnson 1999, 2002; Robinson & Wainer 2002), our results support calls for a greater emphasis on estimation rather than null hypothesis significance testing. As we found with our reanalysis, focusing on parameter estimation can clarify the representation and interpretation of the statistical analysis. We recommend this approach because of its relevance, robustness and relative simplicity.