Using Mark-recapture to provide population census data for use in Red Listing of invertebrates: the rare terrestrial snail Prestonella bowkeri as a case study

Abstract

Invertebrates in general, and terrestrial molluscs in particular, are greatly affected by the current biodiversity extinction crisis, and accurate assessment of these organisms for inclusion in Red Lists is essential for the conservation of these taxa. However, obtaining accurate population counts of molluscs for this purpose can be challenging. Using Prestonella bowkeri, a terrestrial snail up to 23 mm in length and 14 mm in width found in mesic rocky cliff face habitats on the Great Escarpment of southern Africa as an example, we show that the use of Mark-recapture techniques to obtain population census data is appropriate to terrestrial molluscs of this size and larger. While currently listed as vulnerable, our results indicate that there are as many as 4,108 individuals of this species in one population, which suggests that the population size (sensu the IUCN definition) is probably >20,000, and the species could be down-listed and classified as near threatened. However, when considering the problems associated with applying the IUCN Red List criteria to invertebrates, and the very small number of populations and hence area of occupancy of this species, down-listing would be premature.

Appendix

Mark-recapture equations

Y = The difference between the survival of animals newly exposed to marking and others

N = Estimate of number of individuals in the population

z = Standard normal deviate

a = Total number of marked individuals in the first sample

n = Total number of individuals in the second sample

r = Total recaptures (individuals marked at time 1 and recaught at time 2)

n _i  = Total number of individuals in sample i

r _i  = Total recaptures in sampe i

r _i ’ = The number of marked animals in the ith sample that are recaptured again

u _i  = The total unmarked animals in the ith sample

R _i  = The total animals marked on the ith occasion and subsequently recaptured

N’ = Prior estimate of population size

CV = Coefficient of variation

s² = Variance

M _i  = Total no. of captured animals at time

The Petersen–Lincoln estimator

$$N = \frac{an}{r}$$

The Gaskell and George Formula

$$N = \frac{an = 2N'}{r + 2}$$

Schnabel census method (S = 3)

$$N^{2} \left( {r_{2} + r_{3} } \right) - N\left( {n_{1} n_{2} + n_{1} n_{3} + n_{2} n_{3} } \right) + n_{1} n_{2} n_{3} = 0$$

Schnabel census method (S > 3)

$$N_{i} = \frac{{(M_{i} + 1)\,(n_{i} + 1) }}{{r_{i} + 1}}-{1}$$

$$N = \frac{{\mathop \sum \nolimits N_{i} }}{(s - 1)}$$

Manly’s test of the effect of marking

$$y = { \ln }\left( {\frac{{ri^{'} }}{ri} \times \frac{ui}{Ri}} \right)$$

$$g = \frac{y}{{\left( {\frac{1}{ri'} + \frac{1}{Ri} - \frac{1}{ri} - \frac{1}{ui}} \right)^{\frac{1}{2}} }}$$

Cormack’s test of equal catchability (method 2)

$${\hat{C}}{V} = \frac{{\left( {r_{{123}} r_{{10}} } \right) - \left( {r_{{12}} r_{{13}} } \right)}}{{\left( {r_{{12}} + r_{{123}} } \right)\left( {r_{{13}} + r_{{123}} } \right)}}$$

$${\hat{s}}^{2} = \frac{{r_{{123}}^{2} n_{{12}} }}{{\left( {r_{{12}} + r_{{123}} } \right)^{2} (r_{{13}} + r_{{123}} )^{2} }}\left[ {\frac{1}{{r_{{123}} }} - \frac{1}{{n_{1} }} - \frac{{r_{{12}} + r_{{13}} }}{{(r_{{12}} + r_{{123}} )(r_{{13}} + r_{{123}} )}}} \right]$$

$$CV = \frac{{1 - 2{\hat{C}}{V} - \sqrt {1 - 8{\hat{C}}{V} } }}{{2\left( {1 + {\hat{C}}{V} } \right)}}$$

$$s^{2} = {\text{ }}\frac{{\left( {3 - \sqrt {1 - 8{\hat{C}}{V} } } \right)^{4} \left( {{\hat{S}}^{2} } \right)}}{{16\left( {1 - 8{\hat{C}}{V} } \right)\left( {1 + {\hat{C}}{V} } \right)^4}}$$

$$z = \frac{CV}{{s^{2} }}$$