We formalize the establishment process for a sexual, semelparous organism using hierarchical probability modeling from life history parameters of survival, probability of being female, probability of a female being fertilized by a male, and the expected fecundity. From this probability model, we show how to calculate the expected per capita growth rate and probability of extinction, as a function of the initial population size. An Allee effect is observed if the expected population growth rate decreases as the initial population size decreases. A weak Allee effect is observed when expected growth is decreasing but remains greater than one, and a strong Allee effect is observed when the expected growth rate decreases less than one. The model can be further extended as a stochastic process to evaluate the probability of extinction in subsequent generations. We use two semelparous, sexual organisms that appear on the IUCN's list of 100 world's worst invaders as case studies, the Chinese mitten crab (E. sinensis) and the apple snail (P. canaliculata).
Results/Conclusions
The modeling formulation results in a compound Poisson process and has a non-linear mating function. Consequently the population dynamics have an emerging Allee effect. Using point estimates from the literature, we evaluate the strength of the Allee effect and conclude that apple snails experience a weak Allee effect and the Chinese mitten crab experiences a strong Allee effect. The stochastic process reveals that invasion risk can be estimated by the probability of one fertilized female surviving, because the expected fecundity for one surviving female overwhelms the system such that population persistence is almost certain.
