Evolutionary Branching

Individual-based simulations in Example 2 show population splitting into smaller trait groups near the singularity. Numerical TSS simulations in Example 2 remain near an evolutionary singularity at approximately 3.2 rather than converging. Derivative criteria identify the singularity at x=3.2 as a branching point in adaptive-dynamics terminology. The branching phenomenon is biologically strained under the TSS assumptions because the TSS assumes no coexistence. Example 2 uses trait-dependent birth, no natural death, and separable age-trait competition with the Kisdi kernel.