Fig. 2

Example of population dynamics based on the Lotka-Volterra equations (left) and the Replicator Dynamics (right). While the dynamics on the right side resembles the common Red Queen pattern, the left side is more complex. In a pure matching-allele model (top), the plot on the left shows two independent sets of Lotka-Volterra dynamics, one for \(\mathcal {H}_{1}\) and \(\mathcal {P}_{1}\) (blue and red solid lines, correspondingly) and a second one for \(\mathcal {H}_{2}\) and \(\mathcal {P}_{2}\) (blue and red dotted lines). As the model deviates from MA model with increasing α (rows 2–4) more complicated dynamics arise, since the four population densities of \(\mathcal {H}_{1}\), \(\mathcal {H}_{2}\), \(\mathcal {P}_{1}\), and \(\mathcal {P}_{2}\) are coupled (parameters γ=0.005, κ=0.5, and σ=0.01 for both Lotka-Volterra and Replicator Dynamics. Host birth rate b _h =1.5 and parasite death rate d _p =1.0 in the Lotka-Volterra case. Initial population densities h ₁=p ₁=150, h ₂=p ₂=50)