Related papers: Using genetic data to estimate diffusion rates in …
In this paper, we use a stochastic partial differential equation (SPDE) as a model for the density of a population under the influence of random external forces/stimuli given by the environment. We study statistical properties for two…
Phylogenetic comparative methods explore the relationships between quantitative traits adjusting for shared evolutionary history. This adjustment often occurs through a Brownian diffusion process along the branches of the phylogeny that…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…
This paper analyzes the stationary distributions of populations governed by the discrete stochastic logistic and Ricker difference equations at equilibrium examines with the gamma distribution. We identify mathematical relationships between…
Population synthesis is a critical task that involves generating synthetic yet realistic representations of populations. It is a fundamental problem in agent-based modeling (ABM), which has become the standard to analyze intelligent…
Spatial Transcriptomics (ST) allows a high-resolution measurement of RNA sequence abundance by systematically connecting cell morphology depicted in Hematoxylin and Eosin (H&E) stained histology images to spatially resolved gene…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
Allocation of personnel and material resources is highly sensible in the case of firefighter interventions. This allocation relies on simulations to experiment with various scenarios. The main objective of this allocation is the global…
Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models…
The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations…
This article introduces the Stochastic Texture Difference method for analyzing data at prescribed spatial and value scales. This method relies on constrained random walks around each pixel, describing how nearby image values typically…
Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…
This paper introduces a methodology for generating synthetic annotated data to address data scarcity in semantic segmentation tasks within the precision agriculture domain. Utilizing Denoising Diffusion Probabilistic Models (DDPMs) and…
Spatial structure and species interactions jointly shape the dynamics and biodiversity of ecological systems, yet most theoretical models either neglect spatial heterogeneity or sacrifice analytical tractability. Here, we provide a unified…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…