  Mitochondrial function relies on the coordinated expression of mitochondrial
and nuclear genes, exhibiting remarkable resilience regardless the
susceptibility of mitochondrial DNA (mtDNA) to accumulate harmful mutations. A
suggested mechanism for preserving this mito-nuclear compatibility is the
nuclear compensation, where deleterious mitochondrial alleles drive
compensatory changes in nuclear genes. However, prevalence and conditioning
factors for this phenomenon remain debated, with empirical evidence supporting
and refuting its existence. Here, we investigate how mito-nuclear
incompatibilities impact nuclear and mitochondrial substitutions in a model for
species radiation under selection for mito-nuclear compatibility, similar to
the process of mtDNA introgression. Mating eligibility relies on genetic
(nuclear DNA) and spatial proximity, with populations evolving from partially
compatible mito-nuclear states. Mutations do not confer advantages nor
disadvantages, with no optimal nuclear or mitochondrial types, but individual
fitness decreases with increasing incompatibilities, driving the demand for
mito-nuclear genetic coordination. We find that selection consistently promotes
compensation on incompatible nuclear genes, resulting in more substitutions
than compatible or non-interacting genes. Surprisingly, low mitochondrial
mutation rates favor compensation, as do increased selective pressure or a
higher number of mismatches. High mitochondrial mutation rates boost
substitutions in initially compatible nuclear genes, relaxing the selection
against mito-nuclear incompatibilities and mirroring the compensatory
evolution. Moreover, the presence of incompatibilities accelerates species
radiation, but richness at equilibrium is not directly correlated with
substitutions' response, revealing the complex dynamics triggered by
mitochondrial introgression and mito-nuclear co-evolution.
