title: Evolution, the loss of diversity and the role of trade-offs.
abstract: We investigate how the loss of previously evolved diversity in host resistance to disease is dependent on the complexity of the underlying evolutionary trade-off. Working within the adaptive dynamics framework, using graphical tools (pairwise invasion plots, PIPs; trait evolution plots, TEPs) and algebraic analysis we consider polynomial trade-offs of increasing degree. Our focus is on the evolutionary trajectory of the dimorphic population after it has been attracted to an evolutionary branching point. We show that for sufficiently complex trade-offs (here, polynomials of degree three or higher) the resulting invasion boundaries can form closed 'oval' areas of invadability and strategy coexistence. If no attracting singular strategies exist within this region, then the population is destined to evolve outside of the region of coexistence, resulting in the loss of one strain. In particular, the loss of diversity in this model always occurs in such a way that the remaining strain is not attracted back to the branching point but to an extreme of the trade-off, meaning the diversity is lost forever. We also show similar results for a non-polynomial but complex trade-off, and for a different eco-evolutionary model. Our work further highlights the importance of trade-offs to evolutionary behaviour.
authors.affiliation: School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, S3 7RH, Sheffield, UK . Electronic address: a.best@shef.ac.uk.
authors.forename: Alex
authors.initials: A
authors.lastname: Best
authors.affiliation: Department of Mathematical Sciences, Mathematical Sciences Building, The University of Liverpool, L69 7ZL, Liverpool, UK.
authors.forename: Roger
authors.initials: R
authors.lastname: Bowers
authors.affiliation: Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, Scotland, UK.
authors.forename: Andy
authors.initials: A
authors.lastname: White
mesh_terms: D000818:Animals; D044822:Biodiversity; D005075:Biological Evolution; D008962:Models, Theoretical; D009154:Mutation / Q000235:genetics*
keywords: Adaptive dynamics; Host resistance; Life-history evolution; Trade-offs; Trait extinction