A differential equation model for the impact of data centers on bird population dynamics

Abstract

Anthropogenic noise pollution has been shown to decrease bird clutch size and nest survival by masking bird mating calls and delaying clutch initiation. In the past few years, there has been a massive increase in demand for data centers and the concerns around constant noise produced by servers and cooling systems, which overlap with and mask low frequency mating calls. Anthropogenic noise affects different species in different ways, so any modeling of its impact on bird populations must take into account how different species react to noise. To address this, we modify the traditional Fisher-KPP model for logistic population growth and diffusion by adding interspecific competition and noise-induced decreases in reproduction. We solve the system numerically for two competing bird populations and a constant noise source over a 10 year period and a 10 kilometer space using a combination of implicit Crank-Nicolson methods and forward Euler methods. Sobol sensitivity analysis identified noise strength, bird vocal intensity, carrying capacity, birth rate, death rate, and diffusion rate as the most sensitive parameters (Si > 0.1)  with respect to the final bird population distribution. Furthermore, when compared to a population with no sensitivity to noise, sensitive populations had significantly decreased population distributions across the space, and almost no population within 1 km of the data center. These results suggest that data centers will likely have a large impact on nearby bird populations and that work should be done to mitigate the impacts of the produced noise.