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I want to analyse the effects of percentage mortality from two sources (a predator and a disease) on the population abundance of a host measured at 12 sites for 8 years, with the main aim being to look for any delayed density-dependent effects of the predator or disease on the host population. I plan to use GLMMs/GAMMs.

The population abundance and % mortality due to predation/disease are all measured from samples of the host (a moth larva) at each site/time period, but about 45% of samples failed to collect any hosts. Assuming these are genuine zeros, clearly there is no corresponding explanatory data (% predation/disease mortality) for these zero-abundance cases.

Therefore, are there any methods to deal with this problem? Clearly, these cases could just be discarded, but would this bias the analysis etc? Indeed, prevalence estimates are also obviously very variable/unreliable when the sample size is very small, so it may also be best to discard all cases below a threshold sample size, but again does this have serious implications for biasing the analysis etc?

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