Abstract

Changes in the size of natural populations can often track changes in environmental variables like temperature, and looking at the frequency of these changes can give insight into population dynamics. Whether the changes in a population’s size is dominated more by longer-term trends (lower frequencies) or by short-term variation (higher frequencies) can have consequences for the long-term survival of that population. Multiple studies have found that variation in temperature is becoming more dominated by lower frequency variation, although mean temperature is increasing. It is unclear how the variability of the sizes of natural populations are responding to these changes, and how these changes to individual populations may impact communities as a whole. To investigate this, we used Fourier analysis to generate an index of weighted mean frequency for more than 30,000 time series of population abundance and biomass values and looked at how our index was changing over time. Then, to see how this may impact population longevity within a community, we used a Dynamic Allometric Trophic Network model to generate random food webs, and introduced seasonal variability at varying frequencies, with some changing over time. We found an increase in the short-term variability of population size in one dataset, representing a frequency change of around 0.06% annually. The other dataset had a decrease of around 0.01%, although many individual taxonomic groups saw increases. In our model results, we found likelihood of extinction was very small (4.031 × 10-6%) for all species, but that increasing frequencies resulted in a 17% decrease in extinction likelihood. This might suggest a slightly decreased likelihood of extinction for species whose population sizes are becoming more variable in the short term.

Advisor

Bush, Michael

Second Advisor

Ison, Jennifer

Department

Biology; Mathematics

Disciplines

Ordinary Differential Equations and Applied Dynamics | Other Applied Mathematics | Other Ecology and Evolutionary Biology | Population Biology

Keywords

Population Dynamics, Fourier Analysis, Community Stability, Ecological Modeling, Theoretical Ecology

Publication Date

2026

Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis

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Available for download on Thursday, May 15, 2031

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© Copyright 2026 Peter Rothstein