Competitive coexistence of seasonal breeders

• Published in: Journal of mathematical biology Vol. 83; no. 4; p. 38
• Main Authors: Geng, Yunfeng, Lutscher, Frithjof
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Bistability; Coexistence; Consumers; Equilibrium; Growth rate; Life cycles; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Reproduction; Resource consumption; Competitive exclusion; 34A37; Semi-discrete model; Competitive coexistence; Seasonal population dynamics; Consumer-resource model; Stability analysis; 92D40
• ISSN: 0303-6812; 1432-1416
• DOI: 10.1007/s00285-021-01665-4

Many species are annual breeders who, between reproductive events, consume resources and may die. Their resource often reproduces continuously or has short, overlapping generations. An accurate model for such life cycles needs to represent both, the discrete- and the continuous-time processes in the community. The dynamics of a single discrete breeder and its resource can differ significantly from that of a fully continuous consumer–resource community (e.g., Lotka-Volterra) and that of a fully discrete one (e.g., Nicholson-Bailey). We study the dynamics of multiple discrete breeders on a single resource and identify a number of coexistence mechanisms and complex dynamics. The resource grows logistically, resource consumption is linear and consumer reproduction can be linear or nonlinear. We derive explicit conditions for the positive equilibrium state to exist and for mutual invasion to occur at that equilibrium. Stable equilibrium coexistence of more than one consumer is possible only when reproduction is nonlinear. Higher resource growth rate generally allows more consumers to stably coexist. Our explicit formulas allow us to generate communities of many coexisting consumers. Total biomass in the system seems to increase with the number of coexisting consumers. Complex patterns of coexistence arise, including bistability of equilibrium and non-equilibrium coexistence. The mixed continuous-discrete modeling approach can easily be adapted to study how certain aspects of global change affect discrete breeder communities.