Hierarchical models for describing space-for-time variationsin insect population size and sex-ratio along a primary succession

Chronosequences of glacier retreat are useful for investigating primary successions over time periods that are longer than direct observation would permit. In this context, space-for-time substitution studies have been applied to assess the effects of climate change on invertebrate assemblages. However, population dynamics of insect species following retreating glaciers has been under-investigated until now due to difficulty in applying capture-recapture methods and correctly identifying species in the field. Removal sampling methods are commonly used, but imperfect detectability is rarely accounted for in the analytical framework. In this paper we study the effects of environmental drivers of spatial, and indirectly temporal, variation in population size and sex-ratio of cold-adapted insects through a hierarchical framework for abundance. We show the importance of a metapopulation design, where samples are replicated in space and time, to model data from small and scattered populations, typically present in habitats with climate-mediated selective pressure like those along glacier forelands. This scattered distribution can influence the observation or sampling process and thus species detectability. Our results show that glacier retreat differently affects species-specific changes of population size and sex ratio along the chronosequence, even if the species are taxonomically related. Small-sized populations occur on the glacier surface, near the glacier front, and in sites deglaciated for at least 100 yrs. On the contrary, larger populations occupy sites deglaciated for more than 20 yrs, but less than 100 yrs. This pattern is described by the concave relationship of abundance with both species richness of other arthropods (proxy of habitat complexity) and soil organic matter (proxy of soil maturity). Sex-ratio showed opposite patterns in relation to time since deglaciation. Hierarchical models that estimate abundance of spatially distinct subpopulations represent useful tools for accurately assessing changes in species abundance following climate change while accounting for possible bias associated with imperfect detectability, an issue which is often neglected in space-for-time substitution studies on invertebrates and, more generally, in studies involving pitfall trapping.