Following my answer to this question, a debate ensued on whether the loss in population of one species (namely red squirrels) due to its lesser resistance to a pathogen brought by a competing species (namely squirrel parapoxvirus and grey squirrel) should be labelled as a result of interspecies competition or not. Here I will try to state it as a question with in a more general setting. I'll give my own answer to it, and would welcome other views on the issue.
Assume the following: Species $A$ lives in a closed ecosytem and has reached carrying capacity $A=M_A$. At time $0$, a new species $B$ is introduced which is in competition with $A$, and additionally bears a pathogen to which it is resistant but which causes a high lethality rate in $A$.
It is observed that $A$ dimishes while $B$ thrives. Can we necessarily ascribe it to interspecific competition?
Answer
No, you cannot for certain ascribe it to competition, without further information. The mediation by a pathogen is similar to the effects on prey species that are indirectly caused by shared predators (e.g. Prey B increase -> Predator X increase -> more predation on Prey A). Such effects, which can be tricky to separate from direct competition, are usually called apparent competition (see e.g. the classic paper Holt. 1977. Predation, apparent competition, and the structure of prey communities. Theor Popul Biol 12).
However, to some extent, the terminology used may depend on what you view as "the environmental background". All species have lots of adaptations to certain aspects of their living environment, and these naturally differ between species. Some might be more resistant to a certain pathogen (of to drought or other abiotic factors), but this might trade-off against other traits. I that respect, you might view species B as outcompeting species A in a certain environment (e.g. in the presence of the pathogen). However, since you specifically know about the pathogen (which is the focal point of the question), and that species B will probably function as a host/source population of the pathogen, I think it is more useful and informative to label the effect as apparent competition. To partition the direct and indirect effects you will however need moe information.
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