TY - JOUR

T1 - Population age and initial density in a patchy environment affect the occurrence of abrupt transitions in a birth-and-death model of Taylor's law

AU - Jiang, Jiang

AU - DeAngelis, Donald L.

AU - Zhang, Bo

AU - Cohen, Joel E.

N1 - Funding Information:
J.J. was supported as Postdoctoral Fellow at the National Institute for Mathematical and Biological Synthesis (NSF Award #EF-0832858). D.L.D. was partially supported by the FISCHS Project (Future Impacts of Sea Level Rise on Coastal Habitats and Species) at the USGS Southeast Ecological Science Center, funded by USGS Ecosystems Mapping and the USGS Greater Everglades Priority Ecosystems Science . J.E.C. was partially supported by U.S. National Science Foundation grants EF-1038337 and DMS-1225529 and thanks Priscilla K. Rogerson for assistance. Any use of trade, product, or firm names in this article is for descriptive purposes only and does not imply endorsement by the U.S. Government

PY - 2014/10/10

Y1 - 2014/10/10

N2 - Taylor's power law describes an empirical relationship between the mean and variance of population densities in field data, in which the variance varies as a power, b, of the mean. Most studies report values of b varying between 1 and 2. However, Cohen (2014a) showed recently that smooth changes in environmental conditions in a model can lead to an abrupt, infinite change in b. To understand what factors can influence the occurrence of an abrupt change in b, we used both mathematical analysis and Monte Carlo samples from a model in which populations of the same species settled on patches, and each population followed independently a stochastic linear birth-and-death process. We investigated how the power relationship responds to a smooth change of population growth rate, under different sampling strategies, initial population density, and population age. We showed analytically that, if the initial populations differ only in density, and samples are taken from all patches after the same time period following a major invasion event, Taylor's law holds with exponent b=1, regardless of the population growth rate. If samples are taken at different times from patches that have the same initial population densities, we calculate an abrupt shift of b, as predicted by Cohen (2014a). The loss of linearity between log variance and log mean is a leading indicator of the abrupt shift. If both initial population densities and population ages vary among patches, estimates of b lie between 1 and 2, as in most empirical studies. But the value of b declines to ~1 as the system approaches a critical point. Our results can inform empirical studies that might be designed to demonstrate an abrupt shift in Taylor's law.

AB - Taylor's power law describes an empirical relationship between the mean and variance of population densities in field data, in which the variance varies as a power, b, of the mean. Most studies report values of b varying between 1 and 2. However, Cohen (2014a) showed recently that smooth changes in environmental conditions in a model can lead to an abrupt, infinite change in b. To understand what factors can influence the occurrence of an abrupt change in b, we used both mathematical analysis and Monte Carlo samples from a model in which populations of the same species settled on patches, and each population followed independently a stochastic linear birth-and-death process. We investigated how the power relationship responds to a smooth change of population growth rate, under different sampling strategies, initial population density, and population age. We showed analytically that, if the initial populations differ only in density, and samples are taken from all patches after the same time period following a major invasion event, Taylor's law holds with exponent b=1, regardless of the population growth rate. If samples are taken at different times from patches that have the same initial population densities, we calculate an abrupt shift of b, as predicted by Cohen (2014a). The loss of linearity between log variance and log mean is a leading indicator of the abrupt shift. If both initial population densities and population ages vary among patches, estimates of b lie between 1 and 2, as in most empirical studies. But the value of b declines to ~1 as the system approaches a critical point. Our results can inform empirical studies that might be designed to demonstrate an abrupt shift in Taylor's law.

KW - Demography stochastic

KW - Fluctuation scaling

KW - Leading indicators

KW - Power law

KW - Regime shift

KW - Taylor's law

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U2 - 10.1016/j.ecolmodel.2014.06.022

DO - 10.1016/j.ecolmodel.2014.06.022

M3 - Article

AN - SCOPUS:84904554456

VL - 289

SP - 59

EP - 65

JO - Ecological Modelling

JF - Ecological Modelling

SN - 0304-3800

ER -