Eldan Goldenberg's lab notebook

Benjamin Kerr - A Migratory Solution to a Tragedy of the Commons in a host-pathogen metapopulation

The last of the mini-symposium talks was by Benjamin Kerr, who presented a study that combined modelling and 'wet-lab' experiments to understand how a pathogen's population is regulated.

The issue is that a maximally short-term-efficient pathogen will have quick success but then die out because the host has been driven to extinction. So in reality all lethal pathogens have some limiting factor to the speed of their spread, but it's not clear why there isn't a regular cycle of pathogens evolving to become more virulent and then dying out because their host is extinct. After all, the evolving population doesn't have any high-level information about the drawbacks of greater virulence, or the co-ordination to decide not to evolve greater virulence; there must be some systematic reason why it happens so rarely.

Kerr studied a particular pair of populations—a strain of E.Coli and T4 coliphage, which is a virus that uses E.Coli as a host—but the idea is applicable to all host-pathogen relationships. Actually it has at least some bearing on predatory-prey relationships in general, but many of these are complicated by the predator not being entirely dependent on one species for prey.

Kerr's experiments—using a cellular automaton model, and then testing with real organisms on a microtitre plate—involved manipulating the extent of mixing between subpopulations. In the computer model, this means that each cell was considered one subpopulation (with the relative prevalance of bacteria and phages as a variable that would change over time), and they could either all mix with each other, or only mix with neighbours. In the wet lab, the experiments were conducted on a plate with 96 wells, each of which was a separate unit, and the experimental variable was the way in which the contents of these were mixed with each other, ranging from only mixing with neighbours to complete promiscuous mixing across the whole plate.

What he found was that in a small population, such as an isolated cell/well, there was a predictable rock-paper-scissors type cycle, in which the empty site would be colonised by E.Coli, which would flourish for a while until one of the regular mixing events brought in some phage, which would then have its own population explosion, kill of the bacteria and then starve. Across the whole set of subpopulations, continual panmictia (which effectively turns the whole population into one big well) led to extinction as this cycle played itself out on a larger scale, but the results for other conditions were different between the computer model and the biological experiments.

In the computer model, intermittent unrestricted migration (panmictia) led to an oscillatory cycle of both phage and bacteria populations, which was the sum effect of that cycle taking place in each individual cell. Restrict migration, in which cells only mixed with their immediate neighbours, led to considerably greater population stability, as clumps of cells that were dominated by bacteria or phage moved slowly across the array.

The wet-lab experiments turned out differently: it was actually intermittent but geographically unrestricted migration that led to the somewhat more stable populations, and supported the highest density of phages. It turns out that a single mutation can switch the phage between more and less rapacious forms, and the driving force behind the results seems to be competition between the two phage forms. Locally and in the short term, the more rapacious phage has an advantage, because it outcompetes its less rapacious cousin for limited resources. However, over the long term any given well that gets dominated by the more rapacious phages is more likely to experience an extinction event, so the less rapacious phages actually get more chances to be propagated from one well to the next.

This effect seems to depend on the rate of mixing between the subpopulations, and therein lies a general lesson that applies to all simulation work: results can be quite sensitive to the particular set of parameter values in force.