种群与进化
A consensus tree is a phylogenetic tree that synthesizes a given collection of phylogenetic trees, all of which share the same leaf labels but may have different topologies, typically obtained through bootstrapping. Our research focuses on…
There is a growing need to integrate sustainability into tertiary mathematics education given the urgency of addressing global environmental challenges. This paper presents four case studies from Australian university courses that…
Studies that predict species extinction have focused on a range of flora and fauna but in regard to Homo sapiens there are, with one notable exception, no predictive studies, only considerations of possible ways this may occur. The…
Modelling disease outbreak models remains challenging due to incomplete surveillance data, noise, and limited access to standardized datasets. We have created BIGBOY1.2, an open synthetic dataset generator that creates configurable epidemic…
Phylogenetic trees are ubiquitous and central to biology, but most published trees are available only as visual diagrams and not in the machine-readable newick format. There are thus thousands of published trees in the scientific literature…
Phylogenetic trees summarize evolutionary relationships. The Billera-Holmes-Vogtmann (BHV) space for comparing phylogenetic trees has many elegant mathematical properties, but it does not encompass trees with differing leaf sets. To…
We develop a linear one-sex dynamical model of human population reproduction through marriage. In our model, a woman may marry and divorce multiple times; however, only women who are currently married are assumed to bear children. The…
This work provides a geometric version of the next-generation matrix method for obtaining the basic reproduction number of an epidemiological model. We exhibit a certain correspondence between any system of ODEs and Petri nets. We observe…
The rich and varied ways that genetic material can be passed between species has motivated extensive research into the theory of phylogenetic networks. Features that align with biological processes, or with desirable mathematical…
Trap cropping is a pest management strategy where a grower plants an attractive "trap crop" alongside the primary crop to divert pests away from it. We propose a simple framework for optimizing the proportion of a grower's field or…
Identifiability of phylogenetic models is a necessary condition to ensure that the model parameters can be uniquely determined from data. Mixture models are phylogenetic models where the probability distributions in the model are convex…
Numerous living systems are hierarchically organised, whereby replicating components are grouped into reproducing collectives -- e.g., organelles are grouped into cells, and cells are grouped into multicellular organisms. In such systems,…
Although the descriptive epidemiology of primary breast cancer is well characterized in the US, breast cancer recurrence rates have not been measured in an unselected population. The number of breast cancer survivors at risk for recurrence…
The Central Dogma of molecular biology, as originally proposed by Crick, asserts that information passed into protein cannot flow back out. This principle has been interpreted as underpinning modern understandings of heredity and evolution,…
Summary: Ancestral recombination graphs (ARGs) are a complete representation of the genetic relationships between recombining lineages and are of central importance in population genetics. Recent breakthroughs in simulation and inference…
The depiction of populations - of humans or animals - as "population pyramids" is a useful tool for the assessment of various characteristics of populations at a glance. Although these visualisations are well-known objects in various…
Ecosystems frequently display the coexistence of diverse species under resource competition, typically resulting in skewed distributions of rarity and abundance. A potential driver of such coexistence is environmental fluctuations that…
We present a mathematical model to study the transmission dynamics of soil-transmitted helminth (STH) infections and to assess the impact of community-based water, sanitation, and hygiene (WASH) program interventions. STH infections are a…
A common assumption in evolutionary thought is that adaptation drives an increase in biological complexity. However, the rules governing evolution of complexity appear more nuanced. Evolution is deeply connected to learning, where…
The aim of this paper is to present an, admittedly somewhat subjective, bird's eye view of the mathematical theory concerning the spread of an infectious disease in a susceptible host population with static structure, culminating in a…