title: Heterogeneous 'proportionality constants' - A challenge to Taylor's Power Law for temporal fluctuations in abundance.
abstract: Taylor's Power Law for the temporal fluctuation in population size (TL) posits that the variance in abundance scales according to aM(b); where M is the mean abundance and a and b are the 'proportionality' and 'scaling' coefficients. As one of the few empirical rules in population ecology, TL has attracted substantial theoretical and empirical attention. Much of this attention focused on the scaling coefficient; particularly its ubiquitous deviation from the null value of 2. Here we present a line of reasoning that challenges the power-law interpretation of the empirical log-linear relationship between the mean and variance of population size. At the core of our reasoning is the proposition that populations vary not only with respect to M but also with respect to a; which leaves the log-linear relationship intact but forfeits its power-law interpretation. Using the stochastic logistic-growth model as an example, we show that ignoring among-population variation in a is akin to ignoring the variation in the intrinsic rate of growth (r). Accordingly, we show that the slope of the log-linear relationship (b) is a function of the among-population (co)variation in r and the carrying-capacity. We further demonstrate that local environmental stochasticity is sufficient to generate the full range of observed values of b, and that b can in fact be insensitive to substantial differences in the balance between variance-generating and stabilizing processes.
authors.affiliation: Department of Life-Sciences, Ben-Gurion University of the Negev, POB 653, 84105 Beer-Sheva, Israel; The Interuniversity Institute for Marine Sciences, POB 469, Eilat, Israel. Electronic address: mkiflawi@bgu.ac.il.
authors.forename: Moshe
authors.initials: M
authors.lastname: Kiflawi
authors.affiliation: Department of Life-Sciences, Ben-Gurion University of the Negev, POB 653, 84105 Beer-Sheva, Israel; The Interuniversity Institute for Marine Sciences, POB 469, Eilat, Israel. Electronic address: ofrimann@gmail.com.
authors.forename: Ofri
authors.initials: O
authors.lastname: Mann
authors.affiliation: Australian Institute of Marine Science, UWA Ocean Sciences Institute (MO96), 35 Stirling Highway, Crawley, Western Australia 6009 Australia. Electronic address: M.Meekan@aims.gov.au.
authors.forename: Mark G
authors.initials: MG
authors.lastname: Meekan
mesh_terms: D017753:Ecosystem; D008954:Models, Biological; D011156:Population Density; D013997:Time Factors
keywords: Carrying-capacity; Population growth; Temporal changes