Abstract

Laboratory data show that populations of flour beetles (Tribolium), when grown in a periodically fluctuating volume of flour, can exhibit increases in numbers above those attained when grown in a constant volume (of the same average). A discete stage-structured model of Tribolium dynamics with periodic environmental forcing is presented and analyzed. This model is an appropriately modified version of a validated model for Tribolium growing in a constant volume of flour. Theorems implying the existence and stability of periodic solutions are proved. The time avertages of periodic solutions of the forced model are compared with equilibrium levels of the unforced model (with the same average flour volume). Parameter constraints are determined for which the average population numbers in the periodic environment are greater than (or less than) the equilibrium population numbers in the associated environment. Sample sets of parameters taken from the literature are given for which these parameter constraints are fulfilled.