EEB319H1 Study Guide - Final Guide: Ricker Model, Flour Beetle, Nonlinear System
9 Dec 2016
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Get population size fluctuations without randomness (no stochasticity) = non-linear patterns that have to do with the chaos theory. The ricker model: discrete time, density dependent model, 1:1 line shows nt+1 = nt. Abundance in current time step equals abundance in next time step. Cobwebbing: intersection of model line and 1:1 is unstable. Increasing r and plotting ricker model on time-series: at first have single point equilibrium, then damped oscillations (overshoot/undershoot, then stable 2-cycle oscillation, then stable 4-cycle oscillation, then stable 8-cycle oscillation, then chaos (no pattern) Is shown by numerical bifurcation plot: notice period doubling equilibrium. Lecture 14 chaos theory & stage-structured populations. Ricker model: overcompensation model, density-dependent, discrete-time, deterministic (if you don"t add the stochasticity component) Chaotic attractors: all points on time series fall onto particular shape in state space, if was stochasticity, would see shotgun blast of points, attractor not a point. Stage structure: construct lifecycle graphs, arrows represent transitions (survival, assumptions:
