Chance Establishment for Sexual, Semelparous Species: Overcoming the Allee Effect

Abstract

We formalize the establishment process for a sexual, semelparous organism through the use of hierarchical probability modeling from parameters of survival, probability of being female, probability of being fertilized, and expected fecundity. We show how to calculate the expected per capita growth rate and probability of extinction. An Allee effect is observed if the expected population growth rate decreases as the initial population size decreases. The model can be further extended as a stochastic process to evaluate the probability of extinction in subsequent generations. One of the novel results is the formulation of an analytical probability distribution for the next generation population size. As case studies, we use the Chinese mitten crab (Eriocheir sinensis) and the apple snail (Pomacea canaliculata), both of which appear on the World Conservation Union's list of 100 worst invaders. We evaluate the strength of the Allee effect and conclude that apple snails experience a weak Allee effect and Chinese mitten crabs experience a strong Allee effect. We emphasize one scenario where the stochastic process reveals that invasion risk can be estimated by the probability of the survival of one fertilized female, because the expected fecundity for one surviving female overwhelms the system such that population persistence is almost certain.

Effects of food availability on reproductive output, offspring quality and reproductive efficiency in the apple snail Pomacea canaliculata

“…Recent theoretical models of P. canaliculata invasions indicate that the survival probability of a fertilized female is a key factor to invasion success (Jerde et al 2009). In this species, males can mate with several females (Burela and Martín 2009), the age at which males mature is not affected by food availability (Estoy et al 2002a;Tamburi and Martín 2009a) nor are the fecundity and the quality of the offspring of their mates.…”

“…Pomacea canaliculata females deposit egg masses above the water line, each containing 100-300 eggs (Estebenet and Cazzaniga 1993;Albrecht et al 1996;Estoy et al 2002b;Martín and Estebenet 2002). The high fecundity of P. canaliculata females coupled with their sperm storage capabilities Burela and Martín 2011) may enable colonizers to overcome low density or Allee effects, considered a cause for invasion failure (Jerde et al 2009). In this context, we investigated the reproductive response to food availability in P. canaliculata, specifically its effects on reproductive output, offspring quality and efficiency of food conversion to reproductive products, to identify the key factors of its life history strategy that contribute to its invasiveness.…”

Building the bridge between animal movement and population dynamics

“…At low densities, dispersers might struggle to find mates and establish new breeding units. Recent model developments have attempted to include this effect in spatial population dynamics (Hurford et al 2006;Tinker et al 2008;Jerde et al 2009), but they still make some of the assumptions of the perfect mixing model. We expect animals to be more efficient at finding each other than are randomly moving particles, but it might be a conservative feature of invasion models.…”

Temperature-dependent Allee effects in a stage-structured model for Bythotrephes establishment

“…It does not model the biological processes explicitly that lead to a reduction in per capita growth rate at low densities. In contrast to these phenomenological models, there are more mechanistic models, where the existence and magnitude of the Allee effect is allowed to emerge from the biologically motivated model structure (Veit and Lewis 1996;McCarthy 1997;Drake 2004;Molnar et al 2008;Jerde et al 2009). In this study, we take this mechanistic approach and demonstrate that an Allee effect emerges from a model based on the life cycle of Bythotrephes.…”