Trait-dependent extinction leads to greater expected biodiversity loss

TL;DR

This paper demonstrates that trait-dependent extinction models, where multiple traits influence species extinction rates, predict greater biodiversity loss than models assuming independent extinction, using combinatorial and probabilistic inequalities.

Contribution

It introduces a generalized trait-dependent extinction model with multiple binary traits and compares it to independent models, establishing greater expected biodiversity loss.

Findings

Trait-dependent models lead to higher expected biodiversity loss.

Multiple traits influence extinction rates and increase extinction risk.

Mathematical inequalities support the comparison of models.

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.