Size structure, age-size dynamics and life history variation
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Here we present a new technique to study life history variation when only length distributions of populations are known. Shape of length distribution in a population is to a significant extent determined by the degree to which an average individual approaches its asymptotic maximum size. Statistically, the shape of a length can be characterised by its skewness, measuring the degree of symmetry in the distribution. Positive skew (long right tail) in a length distribution suggests that relative few individuals survive long enough to approach asymptotic size in a population, whereas the opposite is true for negative skew (long left tail). With a simple model of age-size dynamics in a population showing indeterminate growth, we show that skewness is strongly correlated with the ratio between mortality rate and the growth parameter k in the von Bertalanffy growth model; this ratio is a dimensionless number that is one of Beverton’s ‘life history statics’. We demonstrate the new technique with data from deep-pelagic fishes collected during the 2004 Mar-Eco expedition along the northern Mid- Atlantic Ridge. Keywords: Dimensionless numbers, growth trajectory, life-history invariants, mortality