The impact of environmental change on host-parasite coevolutionary dynamics

Abstract

Environmental factors are known to affect the strength and the specificity of interactions between hosts and parasites. However, how this shapes patterns of coevolutionary dynamics is not clear. Here, we construct a simple mathematical model to study the effect of environmental change on host-parasite coevolutionary outcome when interactions are of the matching-alleles or the gene-for-gene type. Environmental changes may effectively alter the selective pressure and the level of specialism in the population. Our results suggest that environmental change altering the specificity of selection in antagonistic interactions can produce alternating time windows of cyclical allele-frequency dynamics and cessation thereof. This type of environmental impact can also explain the maintenance of polymorphism in gene-for-gene interactions without costs. Overall, our study points to the potential consequences of environmental variation in coevolution, and thus the importance of characterizing genotype-by-genotype-by-environment interactions in natural host-parasite systems, especially those that change the direction of selection acting between the two species.

Figure 1.

Impact of environment on host–parasite coevolutionary dynamics with MA interactions. (a) Theoretical predictions for the persistence of RQ dynamics. The horizontal axis shows environmental parameter E and the vertical axis shows effective selection coefficients. The blue and the purple curves show the effective selection coefficient of the host and the parasite, respectively. The horizontal bar shows the parameter areas of E where the interaction is antagonistic (ξ_Hξ_P>0; hatched areas), and where it is synergistic (ξ_H ξ_P<0; white area). Blue line, ξ_H; purple line, ξ_P. (b) The coevolutionary dynamics for the situation in (a) when the environment changes slowly. RQ dynamics occur only for the values of E where ξ_H ξ_P>0. Black lines, host A; green lines, parasite A; brown line, environment. Values used in (a) and (b) are s_H^E1 = 0.3, s_P^E1 = 0.35, s_H^E2 = 0.1, s_P^E2 = 0.5. Panel (b) further assumes T = 4000.

Figure 2.

Impact of the rapidly changing environment on host–parasite coevolutionary dynamics with MA interactions. Both panels show the simulation results of the model. (a) Rapid RQ dynamics in spite of comparatively weak selection. (b) Slow RQ dynamics in spite of comparatively strong selection. Allele-frequency changes proceed faster in (a) than in (b) because the long term, average selection acting on the population (effective selection) in (a) is stronger than such long-term selection in (b). In both panels, subplots show rapid allele fluctuations from one generation to another caused by rapidly altering direction of selection. Importantly, in both panels, the condition is fulfilled; its violation would lead to a permanent synergistic interaction, and hence allele fixation. Values used in (a) are s_H^E1 = 0.4, s_P^E1 = 0.6, s_H^E2 = 0.01, s_P^E2 = 0.1, and values used in (b) are s_H^E1 = 0.71, s_P^E1 = 0.95, s_H^E2 = 0.7, s_P^E2 = 0.94. All simulations use T = 2 (environment not shown). Black lines, host A; green lines, parasite A.

Figure 3.

Impact of slowly and rapidly changing environment on host–parasite coevolutionary dynamics with GFG interactions. (a) Impact of a slowly changing environment. Coevolutionary cycles emerge for E ∈ (0,1). As E changes between E1 and E2, the interaction model changes from the GFG into the MA-like interaction. (b) Impact of rapidly changing environment. The impact of environment is again subdivided into a long-term and a short-term effect. The long-term effect is determined by the geometric mean effective selection coefficient. The short-term effect yields step-like allele fluctuations owing to an inherent asymmetry of the GFG model (selection acting on an allele in one environment is much stronger than the selection acting in the other environment). Values used in (a) and (b), are s_H^E1 = 0.35, s_P^E1 = 0.48, s_H^E2 = 0.3, s_P^E2 = 0.45, and furthermore T = 4000 in (a) and T = 2 in (b). Black lines, host A; green lines, parasite A; brown lines, environment (for sake of clarity, not shown in panel b).