Biologists often need to make predictions about how quickly animal or plant populations will grow or decline. For example, predictions of insect populations in agriculture are needed for pest management, and predictions of small fish and plankton species that are vital for marine food webs are important for marine conservation and management. Predicting population change is notoriously difficult because biologists know relatively little about the life cycle of most organisms and because they are subject to many influences of weather, predators, food resources, and habitat conditions. One important approach is to use past records of populations to estimate how quickly organisms develop, reproduce, and die. Accomplishing this is particularly difficult for the many kinds of organisms that can be counted only by their life stages, such as the eggs, larvae, or adults of insects. This project will improve methodology for estimating patterns of population change when only data on organism stages is available. The approach will be to adapt state-of-the-art computer algorithms to the context of such data. These algorithms will determine the range of plausible population growth patterns from the kind of rough data that can typically be collected. An important step in validating new algorithms for data analysis is to evaluate their performance in a controlled setting. Laboratory experiments with Pacific spider mites, an important agricultural pest, will be used for this purpose.
The new analytical methodology to be developed in this project will be made available to the public as open-source software. In addition, training workshops will be conducted at major national conferences to facilitate the broad dissemination and application of this software. This project will result in the training of undergraduate and graduate students and a post-doctoral researcher in mathematical and statistical methods for population ecology.
This project addressed the problem of analyzing data about changes in population size when the data are collected as counts of different life stages. For example, insects and other arthropods progress through a series of distinct life stages. When arthropod populations are studied in laboratories or in nature, researchers sample the abundance of each stage at multiple times through the duration of a study. Studies with this type of stage-structured data are important in research on such diverse systems as agricultural pests and marine plankton species. In this project we developed new mathematical and computational methods for estimating population models from such data. To do so, we first needed to adapt a computational approach known as "Particle Filtering" from other research domains involving time-series data to ecology. The first product was a paper published in the journal Ecology on such methods. Subsequently the ideas were extended to use the recently developed methods of Approximate Bayesian Computation, and another paper has been accepted to Ecology on such methods. In another branch of the project, simple versions of analysis methods for stage-structured data were used for a field study of life history variation. The result was a demonstration that Pacific spider mites, a common agricultural pest, appear to display distinct sub-groups on different grape cultivars, each with slightly different life schedules. A paper presenting those results was published in PLoS ONE. Much additional research from this project remains in preparation for journal publication. For the specific case of arthropod populations monitored in a laboratory, special analysis methods were developed. In this case, the same individuals are counted repeatedly, as opposed to random field samples of different individuals, necessitating special considerations. A customized Markov chain Monte Carlo algorithm was developed for such data and demonstrated for existing data of mealybug populations. For the alternative case where data are randomly sampled from a large population of individuals at each time, another Monte Carlo computational method was developed and demonstrated for existing data on grasshoppers. Additional research was initiated to analyze further field data sets and to develop mathematical theory about evolutionary variation in stage-structured life schedules. Finally, research was conducted to synthesize this ecological modeling problem with the goal of facilitating future advances. This project included research training for one graduate student, two undergraduates, and two post-doctoral researchers.
