A recent simulation study (Svensson et al. 2011) proposed the use of changes in age-structure as an indicator of density dependent effects on the growth of the Baltic grey seal (Halichoerus grypus) population. That approach provides a clever alternative to the direct examination of abundance estimates, and sidesteps the well-known difficulty of detecting trends in marine mammal populations from survey data (Taylor et al. 2007). However, there are three features of Svensson et al.'s analysis that limit its utility as a demonstration of the practicality of their methodology as a tool for investigating real-world problems.
ARTEFACTSThe first issue is that the results, as presented, seem to contain artefacts, patterns produced by the analysis rather than arising from the data. Simulations where the environmental carrying capacity was quite stable and density dependence only acted on populations close to their carrying capacity contained multiple periods when density dependence was detectable (Svensson et al. 2011, Figs. 3c, 4c). The initial periods were the intuitively obvious ones: late on in the growth of the population while it was decelerating towards the carrying capacity. The others seem to be associated with an overcompensatory response in the model (Svensson et al. 2011, Fig. 2b), a feature those authors noted. Such effects are sensitive to many factors including: the pattern of density dependent mortality; whether it exclusively affects pups; and the distribution of ages of first reproduction of females. Changes in any of these could alter the timing, duration and number of periods in which density dependent effects are detectable. None of them are easy to investigate, and the prevalence of overcompensatory effects in actual pinniped population trajectories seems an unexplored area. The examples in Svensson's paper suggest that density dependence is detectable for longer periods when abundance, rather than age-structure, is used as the indicator (Svensson et al. 2011, Figs. 3, 4), but it is difficult to anticipate how the relative durations would be affected by modifications to the model's structure.
METHOD FOR DETECTING DENSITY DEPENDENCEA second difficulty arises out of a mismatch between the population model and the regression used to identify density dependence. The population model appears almost deterministic, with stochasticity only occurring in the environmental carrying capacity. No uncertainty was described in the assessment of abundance. A significant quadratic term in a regression of log(abundance) against time was used to indicate the occurrence of density dependent effects. Regression assumes that each datapoint is independently drawn from a distribution centred on the appropriate point on an overall trendline (Gerrodette 1987), but these data are not independent: each year the abundance lies below the The online version of the article commented upon can be found at