“Generation time in structured populations”

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Stephen P. Ellner (July 2018)

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New analysis shows several measures of generation time in structured populations are unexpectedly equal in many cases


Generation time is an intuitively simple concept, but for structured populations there are multiple definitions, and no general understanding of how they relate to each other. François Bienvenu and Stéphane Legendre, in their note “A New Approach to the Generation Time in Matrix Population Models,” appearing in the June 2015 issue of The American Naturalist, introduced a new measure of generation time Ta, the average time between birth events in an ancestral lineage, and derived the remarkably simple formula Ta = λ (vT w)/(vT F w) for any matrix model, where F is the fecundity matrix and v,w are reproductive value and stable population structure. Here I generalize their formula and interpretations of Ta to continuous or continuous-discrete population structure, and derive similar formulas for three other established generation time measures: average parent age across all births at one time (Ā), and mean parent age at birth events for a cohort (μ1) or generation (Tc). The new formulas reveal that these differently-defined measures are unexpectedly often identical in value, and clarify when they differ.