Coupled populations subject to control (and what we can learn from pure theory)
Some ecologists, and indeed scientists, evaluate models models based on their ability to predict data. I will not dispute that a strong connection to data is important for certain applications, but I think there is much we can learn from exploring the behaviour of models even in the absence of data.
Case in point: our recent publication in Theoretical Ecology (yup, I'm a theoretician now) investigating the dynamics of coupled populations subject to control. The modelling study was motivated by sea louse parasites on salmon farms, which are connected via the dispersal of free-living larvae and subject to treatment with chemotherapeutants. How should managers treat farmed salmon for lice to minimize resurgence of parasite populations within the area? Should they coordinate? How does the optimal management strategy depend on the level of connectivity between adjacent farms? What if connectivity is not reciprocal? These seem like pretty applied questions, right?
A complex meta-population model accounting for time-lags in the sea louse lifecycle and dependence on environmental conditions has been attempted by some, but such models inevitably display pretty complicated dynamics, and sometimes it's hard to know the root cause of what you're seeing. We found ourselves in that boat (or on that farm?), and decided to simplify, and simplify, and simplify the model until we arrived at something we could understand. And we arrived at this:
Basically, the simplest model you could imagine that describes two populations, u and v, that grow exponentially according to an internal growth rate (diagonal elements) and dispersal from the other population (off-diagonal). However, even this model showed some pretty cool stuff.
We found that treatments were most efficient if they happened together, so that the parasites on one farm couldn't go and infect the other farm. Makes sense - people have known this for a long time in the context of rescue effects. However, if the two populations were unbalanced, i.e., one grew faster than the other, it was very hard to synchronize their dynamics to achieve maximum treatment efficiency. The dynamics appeared somewhat chaotic when connectivity was added into the mix (although not actually chaotic - we calculated the Lyapunov exponent ;-)). However, if populations were strongly connected by dispersal, they tended to synchronize themselves!
What does this mean for sea lice on salmon farms? Well, in some ways it's just supporting what we already knew: coordinated area management is key to successful management of sea lice. However, contrary to what we might have expected, strong connectivity among farms can actually help achieve this. I think the interesting part is that we arrived at this result with even the most basic model, and as such, it might have broader implications than just sea lice on salmon farms.
Next step? Start to add in some of that biological complexity again...
