Extinction thresholds in host-parasite dynamics

In this paper, we review the main thresholds that can influence the population dynamics of host-parasite relationships. We start by considering the thresholds that have influ enced the conceptualisation of theoretical epidemiology. The most common threshold involving parasites is the host population invasion threshold, but persistence and infec tion thresholds are also important. We recap how the existence of the invasion threshold is linked to the nature of the transmission term in theoretical studies. We examine some of the main thresholds that can affect host population dynamics including the Allee effect and then relate these to parasite thresholds, as a way to assess the dynamic consequences of the interplay between host and parasite thresholds on the final out come of the system. We propose that overlooking the existence of parasite and host thresholds can have important detrimental consequences in major domains of applied ecology, including in epidemiology, conservation biology and biological control.