The Theory of Ecological Communities—Vellend Equilibrium

I've been in an online reading group for a recent Princeton Monograph by Mark Vellend, The Theory of Ecological Communities. It was organized by Margaret Kosmala, our discussion group includes Diogo Provete, Beth Pringle, Giulio Valentino Dalla Riva, and Terry McGlynn.

This past week we finished chapter 5 of 12. The first three chapters concerned introductory material, including definitions, big ideas, and the history of community ecology. The subsequent three chapters describe Vellend's theory, which he describes as a synthesis of high-level processes borrowed from evolutionary biology. Specifically, Vellend argues that community ecology can be understood in terms of:

  1. Ecological drift
  2. Selection
  3. Dispersal
  4. Speciation
As Vellend argues that these processes could be insightful and potentially unify the multiplicity of theories of community ecology. And as Vellend has been developing these arguments, I have been extending it to other closely-related evolutionary concepts. One of which is the Hardy-Weinberg equilibrium, which I briefly describe below and later call the "Vellend Equilibrium."

So to begin, let me describe how I interpret of each of the above processes. One thing to notice is that for each process, I relax an assumption. In evolutionary biology, these assumptions are relaxed from a model called the Hardy-Weinberg equilibrium. This equilibrium describes a state of the (population genetic) system when no evolutionary change is occurring. Similarly, I think that we can use the same sort equilibrial model in ecology in concert with Vellend's ideas to describe a state of the (ecological) system when no ecological change is occurring. This is what I'd call the Vellend Equilibrium. Below, here's how it fits with the four processes mentioned above:

  1. Ecological drift is the result of relaxing an assumption of infinite population sizes. In evolutionary biology this process is called genetic drift when the same assumption is relaxed. In this universe all populations are finite, so genetic and ecological drift always occur in all real-world populations. The strength of drift is inversely related to the size of the population size; i.e., genetic drift is the strongest in small populations and vice versa.
  2. Selection is the result of relaxing the assumption of equal fitness (survival and reproduction) between groups. In evolutionary biology in the Hardy-Weidberg equilibrial state would mean that there is no differential fitness between genotypes. In ecology, we could understand the Vellend equilibrial as a state where there is no differential fitness between species.
  3. Dispersal is the result of relaxing the assumption of mass action through spatial structure. Mass action that is assumed means that all individuals interact with each other with the same probability and that changes in density (say, due to a predation event in a prey-predator model) occur instantaneously. When we assume that there is more than one population, we assume that within a population mass action still holds but that between population, interaction is limited through a process that we call dispersal.
  4. Speciation is the result of relaxing the assumption that the types of individuals never change between generations. In evolutionary biology, this is the assumption that mutations happen. In ecology, this is the assumption that there is no speciation.

There are many other assumptions of Hardy-Weinberg, which include (a) organisms are diploid, (b) only sexual reproduction occurs, (c) generations are non overlapping, (d) mating is random, and (e) allele frequencies are equal in the sexes. These don't all necessarily seem applicable, which begs the question of the applicability of the analogy. My response would be that the equilibrial models need not be the same every way, but that an equilibrial model---the Vellend Equilibrium---is useful for understanding the way that ecological communities change.

The last thought I had on this brief post (I could expound on this, but not here or now) is that Hardy-Weinberg is quantitative and the Vellend Equilibrium is not . . . yet. What if we were to simplify our ecological community to two species, just like we simplified population genetics to a diploid, di-allelic system to understand the Hardy-Weinberg equilibrium? Can we create a similar quantitative model against we can empirically compare to understand changes in ecological communities with just two species?