In my second post for Quantitative Dynamics I’m going to discuss a topic that I have studied since my graduate work at the University of Nebraska. In 2010 Brigitte Tenhumberg, Richard Rebarber, Diana Pilson and I embarked on a journey studying the long-term, stochastic dynamics of wild sunflower, a disturbance specialist plant population that uses a seed bank to buffer against the randomness of disturbances.
Because the seeds of disturbance specialist plants cannot germinate without a soil disturbance, there are many periods of time for which these populations will have zero or few above-ground plants, and hence no new members of the population from one season to the next. As such, much like a freelance worker with uncertain pay, a seed bank (account) is necessary for long-term viability.
In our work (which you can find here, here and here) we created an integral projection model with stochasticity modeling 1) the presence of a disturbance and 2) the depth of a disturbance. We found through mathematical analyses and simulations that the presence of disturbances increased population viability (as you would expect), but the intensity, depth and autocorrelation of disturbances had a different effect on populations depending on their viability. For populations that were viable, increasingly intense and positively-autocorrelated disturbances enhanced long-term population sizes, whereas when populations were near extinction levels both dynamics were actually harmful to population viability. These results were novel and surprising. You can find my blog post on the topic in The American Naturalist as well.
In subsequent work we would like to study transient dynamics of such systems. Transient dynamics, to this point, have not garnered the attention of long-term dynamics in stochastic systems. However, my friend Iain Stott and colleagues have gotten the ball rolling in that direction, and it’s only a matter of time.