Response to Comment on “Habitat Split and the Global Decline of Amphibians”

Becker et al. (1) showed a strong effect of habitat split on the richness of species with aquatic larvae but no effect on the richness of species with terrestrial development, both when habitat split was analyzed alone in linear regressions and when it was analyzed together with habitat loss and fragmentation in more complex path analyses. Cannatella (2) argues that if species with aquatic larvae are indeedmore affected by habitat split than species with terrestrial development, we would verify a negative relationship between the proportion of species with aquatic larvae (a binomial variable) and habitat split. By using a simple logistic regression, he did not find this effect. The answer to this question, however, requires more complex approaches. One important point is that the total number of species is not a fixed factor, as assumed by Cannatella (2), but a random variable that is affected by habitat split (3–5). We built two alternative linear models to test whether habitat split affects species with distinct developmental modes equally (model 1) or differently (model 2). Both models combine the effect of habitat split on the total species richness and on the proportion of this total that is represented by species with aquatic larvae. In model 1, the expected number of aquatic species is a fixed proportion of the expected total species richness. Model 2 is similar, except that the proportion of total species richness is a linear function of habitat split. Total species richness is a Poisson variate whose expected value is a linear function of habitat split. The number of aquatic species is a binomial variable, with parameter N as the expected total number of species and the parameter p (probability of a single success) as a constant for model 1 or a linear function of habitat split for model 2. We obtained maximum likelihood estimates of the parameters of each model with optimization routines (6, 7). The models were compared with deviance tests (4). Bothmodels predict a decrease in the richness of species with aquatic larvae with increasing habitat split (Fig. 1) due to the negative effect of habitat split on total richness [model 1, intercept a = 21.2 ± 3.0 (SEM), slope b = –0.099 ± 0.048; model 2, a = 21.2 ± 2.9, b = –0.095 ± 0.052]. In model 1, the proportion of species with aquatic larvae was estimated as 0.647 (± 0.062). Inmodel 2, this proportion decreases with habitat split (a = 0.841 ± 0.109, b = –0.005 ± 0.002). Only model 2 provides a significant fit in relation to the null model (model 1, deviance D = 2.92, df = 2, P = 0.23; model 2, D = 9.36, df = 3, P = 0.025). Model 1 underestimates the expected number of species with aquatic larvae in sites where habitat split is lower and overestimates it where habitat split is higher. Model 2 provides a better fit in comparison to model 1 (D = 6.44, df = 1, P = 0.011) and estimates that an increase in habitat split from 10% to 80% decreases the proportion of aquatic species from 0.80 to 0.45 across the studied sites. Cannatella (2) performed three independent logistic regressions to estimate the effect of habitat split, habitat loss, and fragmentation on the proportion of species with aquatic larvae, failing to consider them in a single analytical framework. We performed a path analysis (8), with the same structure used in Becker et al. (1), using the residuals of a regression between the number of species with aquatic larvae and the total number of species (both in log scale) as a continuous index of the prevalence of species with aquatic larvae in the community (Fig. 2). It shows a strong and negative effect of habitat split [standardized path coefficient = –2.187 ± 0.783 (SEM), P < 0.01] and a positive effect of habitat loss (standardized path coefficient = 1.807 ± 0.892, P < 0.05). Similar results emerged when we used a Poisson multiple regression model with a robust error variance (9–12). The positive influence of habitat loss can be explained by its negative influence on the richness of species with terrestrial development, as reported in (1). The question raised by Cannatella can also be answered at the species level. It can be rephrased as: “Are species with distinct developmental modes occurring in the same position along the habitat split gradient?” To test this hypothesis, we built a null model (13) based on the site records of all 58 closed-forest species reported in Becker et al. (1). The 12 sites were ranked according to their level of habitat split (1 to 12, from lower to higher levels of habitat split). Each species record in the matrix was replaced by the rank value of that site. For each species i, its location along the habitat split gradient was represented by the median rank ri, calculated based on the number of records of that species (Ni). The median location of species with aquatic larvae (ma, n = 34 species) and species with terrestrial development (mt, n = 24 species) along the habitat split gradient were determined by the median ri values for each developmental mode. The difference between the location of aquatic and terrestrial developing species along the habitat split gradient (d) was estimated as d = ma – mt. The significance of d was tested by a Monte Carlo simulation (10,000 trials), where the occurrences of each species i were randomly allocated among sites, considering the observed number of records for each species (Ni). Observed d was –2.5, this being significantly lower than one could expect by chance (P= 0.008). TECHNICALCOMMENT