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
VL - 220
SP - 1745
EP - 1751
JO - Ecological Modelling
JF - Ecological Modelling
SN - 0304-3800
IS - 15
ER -