Speaker
Description
Natural populations exhibit complex class structures that shape evolutionary trajectories. While evolutionary demography provides a formal framework to predict adaptation using invasion fitness, the high mathematical dimensionality of these models often precludes interpretable analytical solutions. We introduce two complementary tools to simplify complex life cycles. First, we formulate the 'invasion determinant,' an algebraic method that yields a direct scalar condition for mutant invasion. Second, we develop the Projected Next-Generation Matrix (PNGM), which structurally compresses life-cycle graphs by eliminating secondary classes. We demonstrate that this reduction is mathematically equivalent to separating dynamical timescales, explicitly preserving Fisher's reproductive values for the retained focal classes. We will illustrate with diverse ecological examples.
Joint work with Ryosuke Iritani.
