Table 2.
Model overview
| Model | description | features | stochastic dynamics (small N) × | deterministic dynamics (large N) ∗ | stochastic dynamics (medium N) † | population size change |
|---|---|---|---|---|---|---|
| evolution. game theory | ||||||
| Evo + | Birth-death process. Which individual reproduces depends on the current fitness effect by the antagonist, normalised by the population average fitness effects (+) | intraspecific competition (+) | slow extinction | stasis | NFDS | no |
| Evo | Like Evo + but fitness effects are compared between two individuals not with the population average | pairwise competition | slow extinction | NFDS | extinction | no |
| Hybrid | Hybrid model with reactions between two genotypes of different populations, single birth of parasite and death of host by dynamically adjusted rates. | no competition | extinction | NFDS | extinction | yes, but dynamically constrained |
| theoret. ecology | ||||||
| EcoEvo + | Independent reactions between individual hosts and parasites, single birth and death events or competition in hosts | intra-host competition (+) | fast extinction | stasis | NFDS | yes, but carrying capacity |
| EcoEvo | Like EcoEvo + but without competition within hosts. For infinite population size this is the Lotka-Volterra dynamics | no competition | fast extinction | NFDS | extinction | yes, uncon-strained |
Model names and their main differences. The Evo + and Evo model are derived from evolutionary game theory while the EcoEvo + and EcoEvo model stem from theoretical ecology. The Hybrid model combines elements from both. Models are ordered by population size constraint. The deterministic dynamics apply to the two types matching alleles interaction matrix. Details on the models and analysis are available in the Additional file 1.
×population size change speeds up the extinction of genotypes (Fig. 1)
∗for large population sizes N the deterministic dynamics dominate (Fig. 2). Damped oscillations lead to an attractive equilibrium (‘stasis’). When the equilibirum is neutral genotype abundances oscillate induced by negative frequency-dependent selection (‘NFDS’).
†when population size is intermediate dynamics are strongly influenced by their deterministic characteristics but with stochastic noise. Stochastic dynamics with oscillations are stabilised by the attractive deterministic fixed point which can countervail the stochastic outward pull, postponing extinction (‘NFDS’). Without the attractive pull the time to the first extinction of a genotype is much shorter (‘extinction’).