The previous post introduced the concept of long-term ecological persistence in the fossil record. Very often in the geological past, once a clade (group of organisms descended from a common ancestor) became established, it would persist for a long time. And often some of those clades would become diverse, consisting of many species, and dominant, i.e. being very abundant members of their ecological communities. E.g., think trilobites or dinosaurs. As a result, we also have had communities and ecosystems in the past that have long-lasting characteristics because of the geologically persistent clades within them. Thus, the history of life can be divided and sub-divided into a set of nested types of communities. This is a surprising observation, because that history is embedded in processes of change, notably evolution and the dynamic geology of our planet. Many explanatory hypotheses have been put forward. Most of these assert that it is some particular feature of the clades themselves that make them persistent, such as greater rates of speciation (they evolve new species faster than less persistent clades), or competitive superiority (they muscle out other clades, making them less persistent). Others have pointed to ecological interactions among the species, suggesting that the possibility for the interactions to be altered by evolutionary change is constrained by the heavy dependence of survival on the interactions themselves, a sort of “ecological locking”. We instead suggest a new hypothesis, and it goes like this.
Our hypothesis centers on biotic interactions, i.e. the interactions among species, such as predation. Those interactions exist within an organizational framework above the level of species, namely the functional groups into which a community’s species can be categorized, that is, the “jobs” that species perform. These functional groups may be further resolved based on habitat (where species live), foraging habitat (where they feed), and so on, yielding guilds of species. Examples of guilds from our study system include things such as “carnivorous insects”, “very large carnivorous amphibians”, and “small amniote insectivores/carnivores”. Finally, the interactions among species can also be grouped into interactions among guilds. Our hypothesis claims that the patterns of interactions among guilds affect (1) the persistence of a species in the community, i.e. the probability that the species will not become locally extinct after a period of time, and (2) the stable coexistence of species for an indefinite period of time. The second point hinges on my opinion that one of Nature’s nasty little secrets is that, in general, species do not like each other. I think that many species would be most happy if they could get by with a stable supply of sustenance and shelter, and not have to deal with species that don’t wish to be eaten, species that want to eat you, species that compete with you for sustenance and shelter, species that sponge off you (parasites), and so on. The hypothesis further predicts that once such a pattern becomes established, the likelihood of it changing will be low, both because of the persistence of its species, and because that persistence is superior to that conferred by other patterns. There is nothing preventing either the development or establishment of inferior patterns, but we should expect them to be geologically short-lived because their species will be less persistent, and the coexistences less stable.
The hypothesis maybe summarized as follows. When groups of interacting evolutionary lineages co-evolve, the patterns of interactions that result among them:
- Promote the persistence of species within the community, i.e. probabilities of local extinction are low.
- Promote the indefinite stable co-existence of the species.
Once attained, the likelihood that these patterns will be altered in any significant way (evolution of dramatically novel species or ecologies) is very low. If such a pattern or community type is altered, it is likely due to extreme perturbation of the external environment, accompanied by widespread extinctions.
In the next post I will explain how we went about testing the hypothesis using the Permian-Triassic mass extinction, and fossils of the Karoo Basin in South Africa.
indicate whether species i preys on species j. The question is, what is the interaction between two consumer species, i and m. My first step is to simply count the number of prey shared between i and m, measured as the 
and 
rows; let’s designate that 
(
). We can refine our view a bit by asking what fraction of a species’ prey is represented by that overlap, which is simply
is the in-degree, or number of prey for species i in the food web network. You can think of this as the potential impact of species m on i. This is not quite satisfactory though, because 
may be vastly different. For example, in our 
. Then weight the interaction strength between m and its prey uniformly according to 
in keeping with a conventional symbol for competitive interaction, but again point out that this is a very unparameterized measure compared to what is normally considered for use in Lotka-Volterra-type models or as measured empirically. You’ll notice that the values increase as the specialization of the interactors increases. It would be nice to scale these to a unit maximum to facilitate comparison, but I haven’t done that yet.
, then that probability is a hypergeometric solution
. But the formula gives![p(s\geq 1\vert E=1) = \left [ 1 - \frac{2!(3-1)!}{3!(2-1)!}\right ] \left [ 1 - \frac{2!(3-2)!}{3!(2-2)!}\right ]^{2} = \frac{4}{27}](https://s0.wp.com/latex.php?latex=p%28s%5Cgeq+1%5Cvert+E%3D1%29+%3D+%5Cleft+%5B+1+-+%5Cfrac%7B2%21%283-1%29%21%7D%7B3%21%282-1%29%21%7D%5Cright+%5D+%5Cleft+%5B+1+-+%5Cfrac%7B2%21%283-2%29%21%7D%7B3%21%282-2%29%21%7D%5Cright+%5D%5E%7B2%7D+%3D+%5Cfrac%7B4%7D%7B27%7D&bg=ffffff&fg=000&s=0 "p(s\geq 1\vert E=1) = \left [ 1 - \frac{2!(3-1)!}{3!(2-1)!}\right ] \left [ 1 - \frac{2!(3-2)!}{3!(2-2)!}\right ]^{2} = \frac{4}{27}")
