TY - JOUR

T1 - Population dynamics models based on cumulative density dependent feedback

T2 - A link to the logistic growth curve and a test for symmetry using aphid data

AU - Matis, James H.

AU - Kiffe, Thomas R.

AU - van der Werf, Wopke

AU - Costamagna, Alejandro C.

AU - Matis, Timothy I.

AU - Grant, William E.

N1 - Funding Information:
We thank Philip Dixon of Iowa State University and Lia Hemerik of Wageningen University for helpful comments on a previous draft of this paper. Funding for field research was provided by USDA-CSREES (Grant 2004-35302-14811), a North Central Regional IPM grant, NSF-LTER program at KBS (NSF DEB 0423627), and the Michigan Agricultural Experiment Station.

PY - 2009/8/10

Y1 - 2009/8/10

N2 - Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize "boom and bust" population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl-Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.

AB - Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize "boom and bust" population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl-Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.

KW - Cumulative size dependency

KW - Density dependent feedback

KW - Logistic growth model

KW - Logistic probability density

KW - Minimal mechanistic model

KW - Population eruption and decline

KW - Population growth laws

KW - Skew

UR - http://www.scopus.com/inward/record.url?scp=66149181770&partnerID=8YFLogxK

U2 - 10.1016/j.ecolmodel.2009.04.026

DO - 10.1016/j.ecolmodel.2009.04.026

M3 - Article

AN - SCOPUS:66149181770

SN - 0304-3800

VL - 220

SP - 1745

EP - 1751

JO - Ecological Modelling

JF - Ecological Modelling

IS - 15

ER -