Does discrete logic equation ignore death rate during off season?

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SUMMARY

The discussion centers on the limitations of the discrete logistic equation, specifically its inability to account for death rates during off-seasons in beetle populations. The equation, represented as Xn+1=Xn+rXn(1-(X2/K)), effectively models population growth only during breeding seasons. However, it fails to incorporate mortality rates that occur between these seasons, leading to inaccuracies in population predictions. This limitation is particularly significant when breeding seasons are short relative to the time between them, necessitating a more comprehensive model to reflect true population dynamics.

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Observation of the growth of some beetle population suggests that discrete logistic equation would be more appropriate since these animals have distinct breeding season.

discrete logistic equation: Xn+1=Xn+rXn(1-(X2/K))


the result of this equation accounts for population only season to season which means it neglects the death rate from off season (for birth rate it does make sense that the population will grow at some period of calendar but if the breeding seasons were very short compare to the lag time between next season the death rate from off season would have a high impact on the population and this model would not give an appropriate population in function of time.
 
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The model gives one step per breeding season - sure, it cannot include deaths between seasons. Depending on the factors used and the initial values, the model can describe the population directly before or directly after the breeding session (or somewhere in between, but that is more complicated). The population for other times can be estimated based on this value and the death rate.
 
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