Applied Mathematics Seminar

The coexistence of annual life histories and those with delayed reproduction (biennial and perennial) within natural populations is puzzling because, all else being equal, earlier reproduction will lead to increased population growth rates. Solving this, and similar problems in life history evolution, requires a range of mathematical tools. Data on individual survivorship and reproduction were collected over multiple times for each life history type. From these data a demographic matrix model was used to determine the population growth rate. Elasticities were calculated to compare the contribution of each transition in the life cycle to increasing the population growth rate, but an important question then remains; do transitions through the annual life history pathways contribute more or less than transitions through the delayed life history pathways? The answer to this part of the problem required a fresh approach. I used results from graph theory to construct loops in the life cycle graph that partitioned the shared elasticities to each of the life history pathways. Finally, numerical simulations of the seed bank dynamics were conducted to extend the analysis because there is limited empirical information available for this part of the life cycle.