Fig. 4.

Disease-introgression dynamics between two species with asymmetric initial conditions. The dynamics of the two-time-scales model are described by Eqs. (1)–(15), with parameters identical to those in Fig. 3 except that species 1 (orange) is initially exposed to a smaller pathogen package than species 2 (blue), i.e. species 2 experiences more novel pathogens at the time of contact; $P_1\left(0\right)=60$, $P_2\left(0\right)=100$. a Between-species contact rates (${\beta }_{ij}$, $i\ne j$) appear as dashed curves, and within-species contact rates (${\beta }_{ii}$) appear as continuous curves (Eqs. (10)–(13)). b Pathogen package size, $P_i$. c Disease burden, $D_i$. Species 1 experiences a lower disease burden at the initial phase, and therefore responds less strongly and maintains higher contact rates (in a). This higher contact rate leads to faster rates of adaptive introgression into species 1 (in b). Finally, species 1 is released from disease burden sooner than species 2 (in c), while still carrying many pathogens to which species 2 is vulnerable (in b)