Our #RacerScholars this week are Maeve L. McCarthy, Ph.D. and Howard H. Whiteman, Ph.D. Their article, “A model of inter-cohort cannibalism and paedomorphosis in Arizona Tiger Salamanders, Ambystoma tigrinum nebulosum,” appears in volume 9, issue 2, of the International Journal of Biomathematics.
Cannibalism is widespread in size-structured populations. If cannibals and victims are in different life stages, dominant cohorts of cannibals can regulate recruitment. Arizona Tiger Salamanders, Ambystoma tigrinum nebulosum, exhibit facultative paedomorphosis in which salamander larvae either metamorphose into terrestrial adults or become sexually mature while still in their larval form. Although many salamanders exhibit cannibalism of larvae, the Arizona Tiger Salamander also exhibits cannibalism of young by the aquatic adults. We formulate a differential equations model of this system under the assumption that the terrestrial adults do not impact the system beyond their contribution to the birth of young larvae. We establish non-negativity, boundedness and persistence of the salamander population under certain assumptions. We consider the equilibrium states of the system in the presence or absence of a birth contribution from the terrestrial or metamorph adults. Constant per capita paedomorphosis leads to asymptotically stable equilibria. The per capita paedomorphosis rate of the larvae must be density dependent in order for periodic solutions to exist. Furthermore, the stage transition rate must be sufficiently decreasing in order to guarantee the existence of an unstable equilibrium. Periodic solutions are only possible in the presence of a unique nontrivial unstable equilibrium. Our results conform to previous theory on paedomorphosis which suggests general applicability of our results to similar systems.
A model of inter-cohort cannibalism and paedomorphosis in Arizona Tiger Salamanders, Ambystoma tigrinum nebulosum
By Maeve L. McCarthy and Howard H. Whiteman
International Journal of Biomathematics: MAR 2016, vol. 9(2)