TY - JOUR

T1 - Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data

AU - Matis, J.H.

AU - Kiffe, T.R.

AU - van der Werf, W.

AU - Costamagna, A.C.

AU - Matis, T.I.

AU - Grant, W.E.

PY - 2009

Y1 - 2009

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 - fluctuations

KW - size

U2 - 10.1016/j.ecolmodel.2009.04.026

DO - 10.1016/j.ecolmodel.2009.04.026

M3 - Article

VL - 220

SP - 1745

EP - 1751

JO - Ecological Modelling

JF - Ecological Modelling

SN - 0304-3800

IS - 15

ER -