Discussion facilitator -- Dr. Helen Wearing
Here is the link to the paper selected by Helen: Eskola and Parvinen 2007. On the mechanistic underpinning of discrete-time population models with Allee effect. Theoretical Population Biology 72: 41-51.
Hope to see you all there!
Post-meeting note: Thanks for people who showed up today! The authors improved an existing model to mechanistically incorporate Allee effects. As opposed to phenomenologically modeling Allee effects, mechanistic parameters have physical meanings and can be measured in the field. They concluded that some sort of mating is necessary to have an Allee effect in their models. Another interesting part of this paper was that the model is a hybrid of continuous and discrete equations (although this paper is not the first one). We had mixed opinions about this paper; the math was not so interesting, and the biology is too simplified?! But the paper was good in the sense that it motivated an interesting discussion!
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2 comments:
Something else came up and I won't be able to make the meeting, but I did have a couple of questions I was hoping someone might be able to answer.
Does traditional theory predict that cannibalism can lead to the Allee effect?
What's a quasi-equilibrium?
Can someone explain time-scale separation?
Does traditional theory predict that cannibalism can lead to the Allee effect?
Short answer: I don't know. I can see how it may exasperate the plight of populations at low densities but it's hard to see how it could lead to a declining growth rate with smaller population densities in very simple models.
What's a quasi-equilibrium?
Can someone explain time-scale separation?
These questions are related. Time-scale separation can be used when the dynamics of a variable or variables occur on a much faster time-scale than the dynamics of all others in the system. This makes some assumptions about the relative magnitude of the parameters in the dynamical system, although the Eskola & Parvinen paper does not address this explicitly. The authors assume that the resource equilibriates on a much faster time-scale than the consumer population, so that R is at quasi-equilibrium: solve dR/dt=0 and obtain R(t) as a function of x_n(t) and substitute this expression for R(t) into the other differential equations. In other words, as the adult population changes over time, the resource adjusts to its "steady-state value" almost instantaneously. Of course, this value changes as a function of the adult population (hence the use of the term quasi-equilibrium).
Helen
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