That is important destination but maybe too subtle a starting point.

Start with ecological models for inter-species interactions (predation, competition, mutualism, etc.) where there are more examples and the patterns are simpler, starker, and more intuitive. Roughly, death processes may depend on all involved populations but birth processes depend on each species separately. Then move to natural selection and evolution, intra-species interactions, where the birth processes for each genotype may depend on populations of all the different genotypes, and death processes depend on the phenotypes of all the different populations.