  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.
