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To examine the co-evolution of quantitative traits in hosts and parasites, wepresent and study a co-evolutionary model of a social parasite-host system thatincorporates (1) ecological dynamics that feed back into their co-evolutionaryoutcomes; (2) variation in whether the parasite is obligate or facultative; and(3) Holling Type II functional responses between host and parasite, which areparticularly suitable for social parasites that face time costs for hostlocation and its social manipulation. We perform local and global analyses forthe co-evolutionary model and the corresponding ecological model. In theabsence of evolution, the facultative parasite system can have one, two, orthree interior equilibria, while the obligate parasite system can have eitherone or three interior equilibria. Multiple interior equilibria result in richdynamics with multiple attractors. The ecological system, in particular, canexhibit bi-stability between the facultative-parasite-only equilibrium and theinterior coexistence equilibrium when it has two interior equilibria. Ourfindings suggest that: (a) The host and parasite can select differentstrategies that may result in local extinction of one species. These strategiescan have convergence stability (CS), but may not be evolutionary stablestrategies (ESS); (b) The host and its facultative (or obligate) parasite canhave ESS that drive the host (or the obligate parasite) extinct locally; (c)Trait functions play an important role in the CS of both boundary and interiorequilibria, as well as their ESS; and (d) A small variance in the traitdifference that measures parasitism efficiency can destabilize theco-evolutionary system, and generate evolutionary arms-race dynamics withdifferent host-parasite fluctuating patterns.

Co-evolutionary dynamics of a host-parasite interaction model: obligate versus facultative social parasitism