Weighting Individuals by Reproductive Value in Calculating Species Diversity

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Abstract
If the species in a community has zero intrinsic rate of natural increase (ri=O), its population will still undergo marked fluctuations until it achieves a stationary age distribution. If each individual is weighted by Fisher''s reproductive value and one then considers total reproduction value (Vi) rather than total numbers (Ni), the Vi for such a population will remain constant. If the various species in a community are in a state of equilibrium (all ri =0) but reproduce at different times of the year and oscillate around their equilibrium proportions owing to shifts in age distributions, then converting raw numbers into total reproductive values will enable one to perceive directly what these equilibrium proportions are. If the "equilibrium" proportions themselves are changing (some or all ri=0) then the same procedure will enable one to follow the genuine changes with time, independently of shifting age distributions. It is suggested that in using the Shannon-Wiener function (z Pilog2Pi) to measure species diversity, the Pi should ideally refer to the Vi/E Vi rather than Ni/s Ni, or, better yet, to Wi/z Wi, where Wi=kiVi and the ki are the metabolic rates for individuals of comparable age among the various species.