How emergence and death assumptions affect count-based estimates of butterfly abundance and lifespan

Transect count data form the basis of many butterfly and other insect monitoring programs worldwide. A clear understanding of the limitations of such datasets, including the potential for biases in the statistical methods used to analyze them, is therefore crucial. The classical Zonneveld model (CZ) can extract estimates of a suite of demographic parameters from transect count datasets, and has also been used in theoretical analyses of protandry and reproductive asynchrony. The CZ relies on strong assumptions about the emergence and death processes underlying observed transect count datasets. Though reasonable as a starting place, a growing body of empirical evidence suggests these assumptions will, in many cases, not hold. Here, I explore how violations of these assumptions bias CZ-based estimates of two key population parameters: total population size and mean individual lifespan. To do this, I generalize the Zonneveld model by relaxing the symmetrical emergence distribution and constant death rate assumptions such that the generalized models contain the CZ as a special case. Using the generalized models as data generating processes, I then show that the CZ is able to closely mimic the shape of the abundance time course produced by either variant of the generalized model under a wide range of conditions, but produces highly biased estimates of population size and mean lifespan in doing so. My analysis therefore demonstrates both that the CZ is not robust to violations of its emergence and death assumptions, and that a good observed fit to transect count data does not mean these assumptions are satisfied.