![]() In the case where the numbers can increase, $\beta$ would be positive and would represent the log of the expected proportional increase in numbers. ![]() The second line could also be written as $\log(\mu) = \beta + \log(N)$ (which looks like the regression formula containing an offset) or $\mu/N = \exp(\beta)$, which shows that you're modeling $\beta$ as the log-proportion of survival. ![]() Note that the binomial model would be a binomial GLM, I don't know where you heard that a Poisson or negative binomial with an offset is preferable to a binomial model for a number of individuals surviving out of an initial number I would normally prefer a binomial as it is closer to the actual stochastic process we think is going on.
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