In the past few weeks, I’ve spent a lot of time thinking about how spatial heterogeneity and spatially structured host populations affect parasite transmission. Consider this post my brain dump regarding this fascinating line of inquiry.
Modeling parasite transmission – well-mixed or spatially structured?
When we model parasite transmission, we usually assume that the parasite is moving through a population of hosts that is homogeneous and well-mixed. This is the “mass-action” type model. The assumption (for a directly transmitted parasite) is that every infected host is equally likely to interact with every susceptible host. How realistic is this assumption? Uhhh… probably not realistic at all, actually.
Instead of being well-mixed, interactions within the host population might occur at a local scale, where hosts only interact with their nearest neighbors. What if we were to model parasite transmission in two different ways: first under the assumption that the host population is spatially structured with local interactions, and then under the assumption that the host population is homogeneous and well-mixed. Would the outcomes of the two models be different?
Enter a recent, freaking awesome Am Nat paper by Wodarz et al. (2013), who did just that. When they used spatially structured vs. mixed populations in an agent based model, they found that host (and thus parasite) extinction was more likely in the spatially structured population. They saw the same outcome using ODE metapopulation models. Why should restricting interactions to the local scale increase the risk of extinction? Wodarz et al. (2013) argue that it is because the carrying capacity at the local scale is smaller than the carrying capacity in the well-mixed model. (See the self-shading idea, below.) Basically, a giant chunk of the “population persistence” parameter space in well-mixed models is lost when we switch to spatially structured models.
You ought to go take a look at the Wodarz et al. (2013) paper, because it is packed with cool stuff. Like, what if we change the scale of the local interactions? What if introduce migration among local neighborhoods (=patches)? Also, it’s open access. GO LOOK.
(EDIT: Begon et al. (2002) argue that you can also have what they call “homogeneous contact experience” without having homogeneous mixing – that is, even when interactions are spatially structured. If the rates of contact at a local, nearest-neighbor scale are the same as those at the global scale, you still get a homogeneous contact experience. Wodartz et al. considered both types of spatial structuring – the kind where local interactions scale with global interactions, and the kind where they don’t.)
How do spatially structured host populations affect parasite evolution?
Evolutionarily speaking, parasites don’t “want” their host population to go extinct. So, we should expect that there is some evolutionary pressure to maximize parasite transmission while minimizing the probability of host extinction. (I’ve talked about the tradeoff between transmission and virulence in a previous post.) In spatially-structured populations, where host (and thus parasite) extinction is more likely, we might therefore expect strong pressures for the evolution of less virulent parasites and/or lower transmission rates.
Boots and Mealor (2007) did an interesting experiment to test the hypothesis that parasites will evolve to have lower transmission rates in more spatially structured host populations. By interesting, I mean that they put moth larvae (the hosts) in three concentrations of jello – soft, intermediate, and hard. In the hard jello, moth larvae had the most restricted movement, and thus the most spatially structured populations. Then they introduced a virus into the moth-jello environment, and tracked the evolution of the virus’ infectivity (which is part of the transmission rate). As predicted, they found evolution to reduced infectivity/transmission in the hard jello.
When I first read Boots and Mealor (2007), I could not wrap my head around this idea that parasites with high transmission rates would “self-shade” themselves into extinction in highly structured host populations. The idea is that in spatially structured populations, every infected host individual will be surrounded by other infected individuals if transmission rates are high, so the parasite’s offspring will have no new territory to conquer. At first, that sounds pretty good for the parasite – it was so successful that it spread to all available hosts! But if no new susceptible hosts turn up to be infected – either from birth processes or immigration – then the parasite will go extinct. Enter a cool modeling paper by Lion and Boots (2010). They show that yes, evolution can select for parasites that are “less harmful” (=lower virulence) and “slower transmitting” (e.g., lower infectivity), but this depends on the rate of demographic turnover in the population. So. Cool.
Boots, M., and M. Mealor. 2007. Local Interactions Select for Lower Pathogen Infectivity. Science 315: 1284-1286.
Lion, S., and M. Boots. 2010. Are parasites prudent in space? Ecology Letters 13: 1245–1255. (Open access link to paper)
Wodarz, D., Z. Sun, J.W. Lau, and N.L. Komrova. 2013. Nearest-Neighbor Interactions, Habitat Fragmentation, and the Persistence of Host-Pathogen Systems. American Naturalist 182(3): E94-E11. (Link to paper)