Applying allometric scaling to predator-prey systems

In population dynamics, mathematical models often contain too many parameters to be easily testable. A way to reliably estimate parameters for a broad range of systems would help us obtain clearer predictions from theory. In this paper, we examine how the allometric scaling of a number of biological quantities with animal mass may be useful to parameterise population dynamical models. Using this allometric scaling, we make predictions about the ratio of prey to predators in real ecosystems, and we attempt to estimate the length of animal population cycles as a function of mass. Our analytical and numerical results turn out to compare reasonably to data from a number of ecosystems. This paves the way for a wider usage of allometric scaling to simplify mathematical models in population dynamics and make testable predictions.Comment: 9 pages, 3 figure

Analytical derivation of the radial distribution function in spherical dark matter halos

The velocity distribution of dark matter near the Earth is important for an accurate analysis of the signals in terrestrial detectors. This distribution is typically extracted from numerical simulations. Here we address the possibility of deriving the velocity distribution function analytically. We derive a differential equation which is a function of radius and the radial component of the velocity. Under various assumptions this can be solved, and we compare the solution with the results from controlled numerical simulations. Our findings complement the previously derived tangential velocity distribution. We hereby demonstrate that the entire distribution function, below 0.7 v_esc, can be derived analytically for spherical and equilibrated dark matter structures.Comment: 6 pages, 5 figures, submitted to MNRA

The uneasy coexistence of predators and pathogens

Disease and predation are both highly important in ecology, and pathogens with multiple host species have turned out to be common. Nonetheless, the interplay between multi-host epidemics and predation has received relatively little attention. Here, we analyse a model of a predator-prey system with disease in both prey and predator populations and determine reasonable parameter values using allometric mass scaling relations. Our analysis focuses on the possibility of extinction events rather than the linear stability of the model equations, and we derive approximate relations for the parameter values at which we expect these events to occur. We find that if the predator is a specialist, epidemics frequently drive the predator species to extinction. If the predator has an additional, immune prey species, predators will usually survive. Coexistence of predator and disease is impossible in the single-prey model. We conclude that for the prey species, carrying a pathogen can be an effective weapon against predators, and that being a generalist is a major advantage for a predator in the event of an epidemic affecting the prey or both species

Lockdowns exert selection pressure on overdispersion of SARS-CoV-2 variants

The SARS-CoV-2 ancestral strain has caused pronounced superspreading events, reflecting a disease characterized by overdispersion, where about 10% of infected people cause 80% of infections. New variants of the disease have different person-to-person variability in viral load, suggesting for example that the Alpha (B.1.1.7) variant is more infectious but relatively less prone to superspreading. Meanwhile, non-pharmaceutical mitigation of the pandemic has focused on limiting social contacts (lockdowns, regulations on gatherings) and decreasing transmission risk through mask wearing and social distancing. Using a mathematical model, we show that the competitive advantage of disease variants may heavily depend on the restrictions imposed. In particular, we find that lockdowns exert an evolutionary pressure which favours variants with lower levels of overdispersion. Our results suggest that overdispersion is an evolutionarily unstable trait, with a tendency for more homogeneously spreading variants to eventually dominate

Numerical smallpox model used for Epidemics 9 presentation

The script used to generate the numerical results presented on Andreas Eilersen's poster at the 2023 Epidemics 9 conference.</p