Fig. 10

Comparison of the three parametrically heterogeneous Allee growth models. The initial distribution is truncated exponential on the interval [0, 1] for all three models. Parameters are c = 1, l = 1, m=.1 for each respective model; the initial population size is N(0) = 0.2. a The total population size N(t) for all three models, with c-distributed Allee model increasing most gradually, l-distributed Allee model remaining at a steady size before increasing, and m-distributed Allee model predicting a decrease in population size to near-zero until the escape phase. b Expected value of each of the parameters for their respective models and (c) variance of each of the parameters for their respective models. In every case, escape phase is accompanied by increase in both the expected value and variance. The c-distributed model maintains heterogeneity at a steady state; l-distributed model rapidly becomes more homogeneous at the steady state; m-distributed model slowly gradually loses heterogeneity over time after the escape phase