Inferring moth emergence from abundance data: A novel mathematical approach using birth-death contingency tables

Background/Question/Methods

An important question in contemporary ecology is how the timing of key life history stages, such as insect emergence, may be responding to climate change. This question is difficult to answer because many existing ecological datasets only contain observations of insect abundance over time, but the timing of emergence of individuals is unknown. In this work, we develop a novel machine learning methodology for constructing models of the behavior (e.g., emergence) of individual organisms from data measured over collections of organisms. We analyzed abundance data for moth species collected in UV light traps deployed at two-week intervals over the course of five summers (May-October, 2004-2008) at the H. J. Andrews Experimental Forest. Our questions are the following: How well can we infer the distribution of emergence times from these data? How precisely can we test hypotheses about the factors that influence emergence times? Our method begins by defining a probabilistic model for the emergence date and lifespan of an individual moth. By assuming that moths are independent, we then derive the induced model for the birth-death contingency table of an entire population. The table is created by dividing time into intervals between trapping dates and then classifying each moth by its birth and death intervals. The table entries are the number of moths in each class. Trap counts are then modeled as noisy and incomplete measurements of the birth-death contingency table.  We present a Gaussian approximation that permits computationally efficient inference over the table given the trap counts to recover parameters of the individual model.

Results/Conclusions

The fitted model produces estimates of the parameters of the individual-based model such as the mean and variance in the number of degree days that drives emergence of moths. When applied to the observed (or predicted) degree day curve for a given site, the model generates a distribution of moth emergence dates. Using simulation experiments, we demonstrate how the birth-death contingency table model can recover the parameters of an individual moth emergence model from aggregate moth trapping data. We present fitted models of several moth species and apply these model results to test hypotheses about how the timing of moth emergence responds to climate variability.