TRANSITIONS IN POPULATION-DYNAMICS - EQUILIBRIA TO PERIODIC CYCLES TOAPERIODIC CYCLES

1. We experimentally set adult mortality rates, mu(a), in laboratory c ultures of the flour beetle Tribolium at values predicted by a biologi cally based, nonlinear mathematical model to place the cultures in reg ions of different asymptotic dynamics, 2, Analyses of time-series resi duals indicated that the stochastic stale-structured model described t he data quite well. Using the model and maximum-likelihood parameter e stimates, stability boundaries and bifurcation diagrams were calculate d for two genetic strains, 3, The predicted transitions in dynamics we re observed in the experimental cultures. The parameter estimates plac ed the control and mu(d)=0.04 treatments in the region of stable equil ibria, As adult mortality was increased, there was a transition in the dynamics. At mu(a)=0.27 and 0.50 the populations were located in the two-cycle region. With mu(a)=0.73 one genetic strain was close to a tw o-cycle boundary while the other strain underwent another transition a nd was in a region of equilibrium, In the mu(a)=0.96 treatment both st rains were close to the boundary at which a bifurcation to aperiodicit ies occurs: one strain was just outside this boundary. the other just inside the boundary. 4, The rigorous statistical verification of the p redicted shifts in dynamical behaviour provides convincing evidence fo r the relevance of nonlinear mathematics in population biology.