PARENT SESSION
Oral Session # 13: Statistical Ecology.
Presiding: R Stevens
Monday, August 4. 8:00 AM to 11:30 AM, SITCC Meeting Room 205.

Deconvolving avian nesting data using Fourier transforms to recover the distribution of nest initiation times.

Stanley, Thomas^*,1, ¹ USGS Fort Collins Science Center, Fort Collins, Colorado, USA

ABSTRACT- Nest initiation in birds is thought to be influenced by factors like temperature, precipitation, predation, and even global warming, and there is much ecological interest in the influence of nest initiation times on factors like clutch size, nesting success, and nestling growth and survival. The most common method for reconstructing distributions of nest initiation times involves aging the eggs or young in an active nest, then backdating to determine when the nest was initiated. However, when nests are not found on the day they are initiated and nest survival rates are less than one, this method is biased and can lead to erroneous conclusions or inferences. Nest initiation in a population can be conceptualized as a temporal signal that passes through a filter, in this case a survival process, to yield an observable signal n(t) that is the number of active nests in the population at time t. In this talk, I show mathematically that this filtering process is the convolution of the distribution of nest initiation times and the survival function for nests. Because n(t) is observable, and because the survival function can be modeled and parameterized (e.g., using the Mayfield estimator), it is therefore possible to deconvolve n(t) to recover the unobserved distribution of nest initiation times. I demonstrate deconvolution of n(t) using the Convolution Theorem and Fourier transforms when n(t) is sampled at regular or irregular intervals.

Key words: Fourier transform, convolution/deconvolution, nest initiation, nest survival