Fig 1.
Coevolutionary dynamics between hosts and transmissible cancers, and evolution of sex.
(A) Sensitivity of the population genetic models to the selection coefficients (shost,scancer) and to the proportion of transmissible neocancers that are recently derived from the original host (α). Red lines delimit the parameter spaces leading to non-steady and steady coevolutionary dynamics in the three-locus model (plain line; found numerically) and in the simplified one-locus model (dashed line; found analytically in S1 Appendix). In the three-locus model, the dynamic is defined as ‘steady’ when the variance in genotypic frequencies over 500 time steps is below 10−10. Dark purple indicates conditions under which a modifier allele associated with sexual reproduction (and with recombination, at least for one of the recombination rates tested) can invade in the three-locus model in at least one of the 100 simulation runs. The code used to perform this sensitivity analysis can be found in S1 Source Code. (B-C) Examples of non-steady and steady coevolutionary dynamics in the three-locus model. The linkage disequilibrium in the host is calculated as , i.e., a positive linkage disequilibrium here represents a non-random excess of allele combinations ab and AB. In (B) and (C), parameter values are: shost = 0.5, scancer= 0.8, and α = 0 (B) or α = 0.1 (C).
Fig 2.
Flowchart of the epidemiological model.
Fig 3.
Sensitivity to epidemiological parameters, based on the signs of partial derivatives.
Each epidemiological parameter can affect the proportion of neocancers (; in blue) and the strength of selection caused by transmissible cancer (
; in red) at equilibrium, either directly or via its effect on prevalence of transmissible cancers (cf. Eqs 6 and 7; and see S3 Appendix). The right panel under the column ‘equilibrium state’ denotes the overall effect of a change in parameter value on
or
. From these sensitivity analyses, we infer whether changes in the epidemiological settings can favour the evolution of sex or not (as predicted in the previous population genetic model; in purple). Note that
and
do not depend on parameters b, K, and θ.
Fig 4.
Sensitivity to epidemiological parameters, and conditions favouring sex.
(A, B) Effects of epidemiological parameters on at equilibrium. (C) Conditions under which sex should be favoured (inferred from the three-locus population genetic model; Fig 1A). In grey, we represent the conditions under which the host population gets extinct, assuming that the baseline birth rate b equals to one (condition leading to extinction: μ+νP*(λ0,β,μ,ν)>b; see S3 Appendix). The code used to perform this sensitivity analysis can be found in S1 Source Code.