I am trying to model the relationship between a continuous response variable (sample-corrected species-diversity estimates) and a continuous predictor variable (geographic spread). I have log-transformed both variables to make the relationship linear.
However, discussions about how to address heteroscedasticity in GLMs all seem to concern cases where variance in the response increases as the predictor variable increases. My problem is the reverse — high variance in species diversity at low values of geographic spread, decreasing as geographic spread increases.
Is there a GLM link function that can cope with this type of heteroscedasticity?