Trait-Dependent Extinction Leads to Greater Expected Biodiversity Loss

Abstract

We use a classical combinatorial inequality to establish a Markov inequality for multivariate binary Markov processes on trees. We then apply this result, alongside with the FKG inequality, to compare the expected loss of biodiversity under two models of species extinction. One of these models is the generalized version of an earlier model in which extinction is influenced by some trait that can be classified into two states and which evolves on a tree according to a Markov process. Since more than one trait can affect the rates of species extinction, it is reasonable to allow, in the generalized model, k binary states that influence extinction rates. We compare this model to one that has matching marginal extinction probabilities for each species but for which the species extinction events are stochastically independent.1991 Mathematics Subject Classification. 05C05; 92D15.

Detecting patterns of species diversification in the presence of both rate shifts and mass extinctions

“…Recent studies have used Markov processes to account for the effect of specific traits upon the probability of extinction of a species, thus extending models of mass extinction beyond the field of bullets [ 21 ]. Such models can be used for instance to estimate the loss of phylogenetic diversity after a mass extinction event [ 39 ].…”

“…Second, in the “fair game” scenario, some form of lineage selection would occur, where the most successful species — in our case, the most diversifying species — before the event would be the most likely to survive. This could, for instance, happen if the probability of survival depends on a specific trait varying across the lineages of the phylogeny [ 21 ]. Finally, in the “wanton destruction” scenario [ 22 ], the event could induce such changes in the environmental conditions that the probability of extinction of the species and their post-event diversification rate would be uncorrelated to their initial speciation and extinction rates.…”

Predicting the loss of phylogenetic diversity under non-stationary diversification models

“…In the real world, phylogenetic trees are much more likely to have a small d and a high b, just because they have survived, so is it more likely to get a The fact that π is always concave as a function of p (including if we condition on the underlying tree) means that if the present mass extinctions are more or less painless (slow and sublinear), they will go faster than expected below p * when the dependence becomes super-linear. Moreover, the field of bullets model represents a conservative estimate: in reality, the extinction of a contemporary species will be likely to be correlated with the extinction of closely related species (due to shared traits (Faller and Steel, 2012) or niche proximity), which would yield an even worse portrait than the one we depict.…”

Detecting patterns of species diversification in the presence of both rate shifts and mass extinctions

“…Second, in the “fair game” scenario, some form of lineage selection would occur, where the most successful species — in our case, the most diversifying species — before the event would be the most likely to survive. This could, for instance, happen if the probability of survival depends on a specific trait varying across the lineages of the phylogeny(Faller and Steel 2012). Finally, in the “wanton destruction” scenario (Eble 1999), the event could induce such changes in the environmental conditions that the probability of extinction of the species and their post-event diversification rate would be uncorrelated to their initial speciation and extinction rates.…”