Premium
Analysis of Steady‐State Populations With the Gamma Abundance Model: Application to Tribolium
Author(s) -
Dennis Brian,
Costantino Robert F.
Publication year - 1988
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.2307/1941275
Subject(s) - abundance (ecology) , goodness of fit , gamma distribution , stationary distribution , stochastic differential equation , mathematics , statistics , population , multiplicative function , stochastic modelling , logistic function , ordinary differential equation , statistical physics , population model , probability distribution , generalized gamma distribution , econometrics , differential equation , ecology , biology , physics , mathematical analysis , markov chain , demography , sociology
We develop a stochastic model for the abundance of adult populations of the four beetle Tribolium. The model is in the form of a stochastic differential equation containing adult recruitment and mortality rates perturbed by multiplicative noise. A deterministic version of the model (an ordinary differential equation) predicts a fixed, stable equilibrium; by contrast, the stochastic model predicts a stationary probability distribution for population size. The model can be approximated closely by a stochastic logistic equation having a gamma distribution as a stationary solution. We develop or clarify various practical aspects of making statistical inferences for the resulting gamma abundance model, including estimation of parameters, testing goodness of fit, obtaining confidence intervals for functions of parameters, and testing to compare two gamma distributions. Analyses of 11 data sets on Tribolium suggest that the gamma model deserves more widespread consideration as an equilibrium abundance model for other species.