Density dependence hypotheses and the distribution of fecundity

Abstract

1. Beja & Palma (2008, Journal of Animal Ecology, 77, doi: 10.1111/j.1365-2656.2007.01312.x) attempt to provide a critical analysis of the effectiveness and limitations of a previously published method (Ferrer et al. 2006, Journal of Animal Ecology, 75, 111-117.) to discriminate between Habitat Heterogeneity Hypothesis and the Individual Adjustment Hypothesis using real data from a Bonelli's eagle Hieraaetus fasciatus population. 2. They conclude that significant and strong correlations between mean and CV or skewness are expected under a biologically plausible assumption about brood size distribution, and that the two hypotheses cannot therefore be distinguished. 3. A major concern we have with their paper centres on this biologically plausible brood-size distribution. They used the same quasi-Poisson distribution of brood sizes (typical for a saturate population under Habitat Heterogeneity Hypothesis) for both families of simulations. So, is not surprising that both groups gave similar results. 4. They argued that this approach was 'empirical', free of theoretical assumptions. But in testing between hypotheses, what we are looking for is precisely the differences among theoretical brood-size distributions predicted under the two hypotheses. 5. Summarizing, with the same mean fecundity at high densities, both hypotheses must have different brood-size distributions. So the use of a single left-skewed distribution, typical of a real saturated population (most likely under Habitat Heterogeneity Hypothesis) in attempts to distinguish between the two hypotheses by re-sampling several times on the same left-skewed distribution, as done by Beja & Palma, is clearly inappropriate.