A Mathematical Note on the Evolutionary Competitiveness of the Trisexual Nematode Auanema Rhodensis
A Mathematical Note on the Evolutionary Competitiveness of the Trisexual Nematode Auanema Rhodensis
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,
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- [1] J. Chaudhuri, V. Kache, A. Pires-daSilva, Regulation of sexual plasticity in a nematode that produces males, females, and hermaphrodites, Current Biology, 21 (2011), 1548-1551,
- [2] T. Hale, This Trisexual Worm Bends the Rules of Typical Genetics, IFL Science, 19/ 01/ 2018 (2018), http://www.iflscience.com/ plants-and-animals/a-trisexual-worm-bends-the-rules-of-typical-genetics/.
- [3] D.C. Shakes, B.J. Neva, H. Huynh, J. Chaudhuri, A. Pires-daSilva, Asymmetric spermatocyte division as a mechanism for controlling sex ratios, Nature Communications, 2(157) (2011).
- [4] S. Tandonnet, M.C. Farrell, G.D. Koutsovoulos, M.L. Blaxter, M. Parihar, P.L. Sadler, D.C. Shakes, A. Pires-daSilva, Sex- and gamete-specific patterns of X chromosome segregation in a trioecious nematode, Current Biology, 28 (2018), 93-99.
- [5] N. Kanzaki, K. Kiontke, R. Tanaka, Y. Hirooka, A. Schwarz, T. M¨uller-Reichert, J. Chaudhuri, A. Pires-daSilva, Description of two three-gendered nematode species in the new genus Auanema (Rhabditina) that are models for reproductive mode evolution, Scientific Reports, 7 (2017), 11135.
- [6] E. Garibaldi, M. Sobottka, A nonsmooth two-sex population model, Mathematical Biosciences, 253 (2014), 1-10.
- [7] K.P. Hadeler, R. Waldst¨atter, A. W¨orz-Busekros, Models for pair formation in bisexual populations, J. Math. Biol., 26 (1988), 635-649.
- [8] D.G. Kendall, Stochastic processes and population growth, J. R. Stat. Soc. Ser. B Stat. Methodol., 11 (1949), 230-264.
- [9] D.J. Rankin, H. Kokko, Do males matter? The role of males in population dynamics, Oikos, 116 (2007), 335-348.
- [10] J.D. Murray, Mathematical Biology I. An Introduction, 3rd ed., Springer, 2002.
- [11] J.D. Murray, Mathematical Biology II. Spatial Models and Biomedical Applications, 3rd ed., Springer, 2003.
- [12] F. Rupp, J. Scheurle, Analysis of a Mathematical Model for Jellyfish Blooms and the Cambric Fish Invasion, Dynamical Systems and Differential Equations, DCDS Supplement 2013 Proceedings of the 9th AIMS International Conference (Orlando, USA) (2013), 663-672.
- [13] F. Rupp, J. Scheurle, The dynamics of the jellyfish Joyride: Mathematical discussion of the causes to blooming, Math. Methods Appl. Sci., 38(16) (2015), 3408-3420.
- [14] E.C. Buehler, S. Das, J.F. Cully Jr., Equilibrium and extinction in a trisexual diploid mating system: An investigation, K. Deb (editor), Genetic and Evolutionary Computation – GECCO 2004, Lecture Notes in Computer Science, vol 3102, Springer, Berlin, Heidelberg, 2004.
- [15] E.C. Buehler, S. Das, J.F. Cully Jr., Equilibrium and Extinction in a Trisexual Diploid Mating System, 2004.
- [16] K. Jaffe, The dynamics of the evolution of sex: Why the sexes are, in fact, always two?, Interciencia, 21(6) (1996), 259-267.
- ISSN: 2636-8692
- Yayın Aralığı: Yılda 3 Sayı
- Başlangıç: 2018
- Yayıncı: Mahmut AKYİĞİT
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