Article:
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F. Rupp (2020): A Mathematical Note on the Evolutionary Competitiveness of the Trisexual Nematode
Auanema Rhodensis, Journal of Mathematical Sciences and Modelling, 3 (1), pp. 10-24.


Abstarct:
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Trisexual species with female, male and self-fertilizing hermaphrodite sub-populations
are rather exceptions in nature. Though, certain nematode/ worm species, like Auanema
Rhodensis, have evolved that way. Applying Kendall-like non-logistic mating functions, we
provide a series of reproduction models to holistically study the iterations between the sexes
and shed light on the increased population stability/ survival strength compared to bisexual
species or trisexual species with non-self-fertilizing hermaphrodites. Besides the increased
survival strength, the survival of such trisexual species populations is, in contrast to usually
known (bisexual) species populations, entirely linked to the relation between birth and death
proportionality factors, and no population thresholds are required for survival. In that sense,
while mathematically studying the complete equilibria and bifurcation landscape in terms
of existence and (non-linear) stability, as well as the global dynamics of these models, we
provide a comprehensive analysis of the reproduction dynamics of trisexual species.

Keywords:
Auanema Rhodensis, bifurcation, Global dynamics, Mathematical biology, Population dynamics,
Reproduction dynamics, Stability, Trisexual species.

2010 AMS: 37C70, 37G10, 37N25, 92D25.