caa a22 4500 477140564 CHVBK 20180405111731.0 cr unu---uuuuu 170330e19971101xx s 000 0 eng 10.1007/s002850050098 doi (NATIONALLICENCE)springer-10.1007/s002850050098 The effect of periodic habitat fluctuations on a nonlinear insect population model [Elektronische Daten] [Shandelle M. Henson, J. M. Cushing] Abstract.:  Laboratory data show that populations of flour beetles (Tribolium), when grown in a periodically fluctuating volume of flour, can exhibit significant increases in numbers above those attained when grown in a constant volume (of the same average). To analyze and explain this phenomenon a discrete stage-structured model of Tribolium dynamics with periodic environmental forcing is introduced and studied. This model is an appropriately modified version of an experimentally validated model for flour beetle populations growing in a constant volume of flour, in which cannibalism rates are assumed inversely proportional to flour volume. This modeling assumption has been confirmed by laboratory experiments. Theorems implying the existence and stability of periodic solutions of the periodically forced model are proved. The time averages of periodic solutions of the forced model are compared with the 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 constant environment. Sample parameter estimates taken from the literature show that these constraints are fulfilled. These theoretical results provide an explanation for the experimentally observed increase in flour beetle numbers as a result of periodically fluctuating flour volumes. More generally, these integrated theoretical and experimental results provide the first convincing example illustrating the possibility of increased population numbers in a periodically fluctuating environment. Springer-Verlag Berlin Heidelberg, 1997 Henson Shandelle M. Department of Mathematics, Building No. 89, Interdisciplinary Program on Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA, US aut Cushing J. M. Department of Mathematics, Building No. 89, Interdisciplinary Program on Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA, US aut https://doi.org/10.1007/s002850050098 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002850050098 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Henson Shandelle M. Department of Mathematics, Building No. 89, Interdisciplinary Program on Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA, US aut NATIONALLICENCE 700 1- Cushing J. M. Department of Mathematics, Building No. 89, Interdisciplinary Program on Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA, US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer