arXiv subjects

Swati Patel

Publications and source records attributed to Swati Patel.

8 recordsLinked to original sources

arXiv2026

Persistence of n-Species Lotka-Volterra Models with Periodic Pulses

Periodic impulsive interventions arise naturally in the management of biological populations, including chemotherapy, pesticide application, and infectious-disease treatment. We develop general conditions for permanence in n-species population models subject to periodic multiplicative pulse disturbances. Our main result provides a sufficient condition for permanence in terms of weighted long-term growth rates on a Morse decomposition of the extinction set, explicitly separating the contributions of continuous population dynamics from those of the periodic pulse. To establish this result, we transform the impulsive system into an associated autonomous continuous-time dynamical system and use this correspondence to extend classical permanence theory to periodically pulsed models. We further show that the same conditions imply robust permanence under sufficiently small perturbations to the continuous dynamics, pulse period, and pulse effects. We illustrate the framework with two Lotka-Volterra models motivated by biological control: competition between chemotherapy-sensitive and chemotherapy-resistant cancer cells, and integrated control of an agricultural pest using pesticides and parasitoids. These examples demonstrate how intervention frequency and intensity interact with underlying ecological interactions to determine whether populations coexist or are excluded. Our results provide a general framework for analyzing persistence in ecological systems subject to repeated discrete disturbances.

q-bio.PE↗

arXiv2026

On the formulation and analysis of a stage-structured eco-evolutionary model with pulsed disturbances

Motivated by the pulsed control and resulting evolution of harmful biological populations, we develop and analyze an ordinary differential equation model of an n-dimensional stage-structured population undergoing periodic disturbances. The eco-evolutionary model couples both ecological dynamics through life cycle information, and evolutionary dynamics of allele frequency changes. Building off prior work in eco-evolutionary models and theory of linear systems, we show that if a resistant allele is present in the population, the population will always approach full resistance. Furthermore, we establish persistence conditions and show that these depend solely on system dynamics at full resistance. Finally, we demonstrate the utility of this model via an application to the Spotted-Winged Drosophila, an invasive species often treated periodically with insecticides. We use a parameterized model to further understand the complexities of relationships between ecological and evolutionary features of a species and its resistance evolution due to pulsed disturbances.

q-bio.PE↗

arXiv2025

Unique steady states for population models in a heterogeneous environment

We revisit a model proposed by Freedman etal in \cite{freedman} which describes the dynamics of a population diffusing in a patchy environment. From their work it is known that positive steady states exist for this model, but not whether they are unique. Here, we provide sufficient conditions guaranteeing that steady states are unique. These conditions are satisfied when the reaction rates are generalized logistic growth rates. Our proofs critically exploit Chicone's ideas in \cite{chicone}, which were used to establish that the period map associated to a continuous family of periodic solutions of certain planar Hamiltonian systems is monotone.

math.DS↗

arXiv2023

On the spectral radius properties of a key matrix in periodic impulse control

In this work, we consider the periodic impulse control of a system modeled as a set of linear differential equations. We define a matrix that governs the qualitative behavior of the controlled system. This matrix depends on the period and effects of the control interventions. We investigate properties of the spectral radius of this matrix and in particular, how it depends on the period of the interventions. Our main result is on the convexity of the spectral radius with respect to this period. We discuss implications of this convexity on establishing an optimal and maximum period for effective control. Finally, we provide an example motivated from a real-life scenario.

math.OC↗

arXiv2023

A tutorial on the Bayesian statistical approach to inverse problems

Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input-output pairs and (2) given a model of the system, reconstruct the input to it that caused some observed output. Applied inverse problems are challenging because a solution may (i) not exist, (ii) not be unique, or (iii) be sensitive to measurement noise contaminating the data. Bayesian statistical inversion (BSI) is an approach to tackle ill-posed and/or ill-conditioned inverse problems. Advantageously, BSI provides a "solution" that (i) quantifies uncertainty by assigning a probability to each possible value of the unknown parameter/input and (ii) incorporates prior information and beliefs about the parameter/input. Herein, we provide a tutorial of BSI for inverse problems, by way of illustrative examples dealing with heat transfer from ambient air to a cold lime fruit. First, we use BSI to infer a parameter in a dynamic model of the lime temperature from measurements of the lime temperature over time. Second, we use BSI to reconstruct the initial condition of the lime from a measurement of its temperature later in time. We demonstrate the incorporation of prior information, visualize the posterior distributions of the parameter/initial condition, and show posterior samples of lime temperature trajectories from the model. Our tutorial aims to reach a wide range of scientists and engineers.

stat.ME↗

arXiv2017

Evolution as a coexistence mechanism: Does genetic architecture matter?

Species sharing a prey or a predator species may go extinct due to exploitative or apparent competition. We examine whether evolution of the shared species acts as a coexistence mechanism and to what extent the answer depends on the genetic architecture underlying trait evolution. In our models of exploitative and apparent competition, the shared species evolves its defense or prey use. Evolving species are either haploid or diploid. A single locus pleiotropically determines prey nutritional quality and predator attack rates. When pleiotropy is sufficiently antagonistic (e.g. nutritional prey are harder to capture), eco-evolutionary assembly culminates in one of two stable states supporting only two species. When pleiotropy is weakly antagonistic or synergistic, assembly is intransitive: species-genotype pairs are cyclically displaced by rare invasions of the missing genotypes or species. This intransitivity allows for coexistence if, along its equilibria, the geometric mean of recovery rates exceeds the geometric mean of loss rates of the rare genotypes or species. By affecting these rates, synergistic pleiotropy can mediate coexistence, while antagonistic pleiotropy does not. For diploid populations experiencing weak antagonistic pleiotropy, superadditive allelic contributions to fitness can mitigate coexistence via an eco-evolutionary storage effect. Density-dependence and mutations also promote coexistence. These results highlight how the efficacy of evolution as a coexistence mechanism may depend on the underlying genetic architecture.

q-bio.PE↗

arXiv2016

Robust permanence for ecological equations with internal and external feedbacks

Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist or communities of species coexist. To provide a general mathematical framework for studying these effects, we develop a theorem for coexistence for ecological models accounting for internal and external feedbacks. Specifically, we use average Lyapunov functions and Morse decompositions to develop sufficient and necessary conditions for robust permanence, a form of coexistence robust to large perturbations of the population densities and small structural perturbations of the models. We illustrate how our results can be applied to verify permanence in non-autonomous models, structured population models, including those with frequency-dependent feedbacks, and models of eco-evolutionary dynamics. In these applications, we discuss how our results relate to previous results for models with particular types of feedbacks.

q-bio.PE↗

arXiv2015

Evolutionarily induced alternative states and coexistence in systems with apparent competition

Predators often consume multiple prey and by mutually subsidizing a shared predator, the prey may reciprocally harm each other. When predation levels are high, this apparent competition can culminate in a prey species being displaced. Coupling quantitative genetics and Lotka-Volterra models, we study how predator evolution alters this and other ecological outcomes. These models account for a trade-off between the predator's attack rates on two prey species. We provide a mathematical characterization of a strong form of persistence--permanence--for which there is a global attractor bounded away from extinction. When the evolutionary dynamics occur at a sufficiently slower time scale than the ecological dynamics, we also characterize attractors and their basins' of attraction using singular perturbation theory and a graphical approach to the eco-evolutionary dynamics. Our results show that eco-evolutionary feedbacks can mediate permanence at intermediate trade-offs in the attack rates. However, at strong trade-offs, permanence is lost. Despite this loss of permanence, there can be attractors supporting coexistence. These attractors, however, may coincide with attractors at which the predator is excluded. Our results highlight that evo-evolutionary feedbacks can alter community structure by mediating coexistence or leading to trait-dependent alternative stable states.

q-bio.PE↗