Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays

We examine the role of the travel time of a predator along a spatial network on predator-prey population interactions, where the predator is able to partially or fully sustain itself on a resource subsidy. The impact of access to food resources on the stability and behaviour of the predator-prey-subsidy system is investigated, with a primary focus on how incorporating travel time changes the dynamics. The population interactions are modelled by a system of delay differential equations, where travel time is incorporated as discrete delay in the network diffusion term in order to model time taken to migrate between spatial regions. The model is motivated by the Arctic ecosystem, where the Arctic fox consumes both hunted lemming and scavenged seal carcass. The fox travels out on sea ice, in addition to quadrennially migrating over substantial distances. We model the spatial predator-prey-subsidy dynamics through a “stepping-stone” approach. We find that a temporal delay alone does not push species into extinction, but rather may stabilize or destabilize coexistence equilibria. We are able to show that delay can stabilize quasi-periodic or chaotic dynamics, and conclude that the incorporation of dispersal delay has a regularizing effect on dynamics, suggesting that dispersal delay can be proposed as a solution to the paradox of enrichment

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Modeling adaptive dynamics in microbial populations with applications to the evolution of cellular resource allocation trade-offs

Adaptive evolution is the process by which natural selection, acting on variation within a population, promotes the survival of individuals that are more successful at reproducing and contributing to future generations. Evolutionary processes in microbes occur at the intersection of population genetics, natural selection, and underlying mechanistic constraints, to give rise to the repertoire of adaptation observed in nature. Understanding microbial adaptive evolution is of critical importance for human health for example, through the emergence of pathogenicity and antibiotic resistance. Moreover, the stability and function of natural and artificial ecosystems is contingent on the evolving interactions between microbes, and between microbes and the environment. We present a modelling framework, based on the theory of adaptive dynamics, to investigate how cellular resource allocation trade-offs affect the adaptation process. We used resource-consumer theory, which explicitly models the interactions between cells and their environment, together with matrix models of structured populations, to implement phenotype-determined cellular strategies of resource allocation between mutually exclusive processes. We then analyse the outcome of competitions between different phenotypes across environmental and competitive conditions. We applied our methods to the evolution of strategies (phenotypes) for resource allocation between two competing cellular process in microbial populations growing in chemostat-like environments. We calculated the adaptively stable strategies for several models and showed how state-structured population models can be mapped to simpler chemostat models on invariant manifolds. We then extended our analysis to the case where a limiting nutrient may be utilized using two alternative metabolic pathways. We described how the total population fitness of a metabolic strategy can be constructed from the individual decisions of its constituent members. We developed numerical methods to simulate and analyse general models of adaptive dynamics using principles from graph theory and discrete Markov processes. The methods were used to explore the evolution of nutrient use strategies for microbial populations growing on two and three substitutable nutrients. We highlight the importance of the ancestral phenotype in channelling the adaptation process, which, together with the choice of the mutational kernel, influences the adaptively stable strategies and modes of co-existence. In a related finding, we show how some phenotypes are adaptively stable only in the presence of a competitor lineage that modifies the environment in a manner that permits another phenotype to invade. Our methods also reveal instances where historical contingency and chance have an important effect on determining the stable nutrient use strategies. Finally, we demonstrate the existence of adaptively stable periodic solutions whereby, under some conditions, phenotype successions are cyclical. Our work builds on the foundation of adaptive dynamics theory to provide a general framework for analysing models of microbial adaptation. We focused on understanding the implications of underlying constraints and cellular resource allocation trade-offs in the context of adaptive evolution

The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts

The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe

Synthesis and analysis of nonlinear, analog, ultra low power, Bernoulli cell based CytoMimetic circuits for biocomputation

A novel class of analog BioElectronics is introduced for the systematic implementation of ultra-low power microelectronic circuits, able to compute nonlinear biological dynamics. This class of circuits is termed ``CytoMimetic Circuits'', in an attempt to highlight their actual function, which is mimicking biological responses, as observed experimentally. Inspired by the ingenious Bernoulli Cell Formalism (BCF), which was originally formulated for the modular synthesis and analysis of linear, time-invariant, high-dynamic range, logarithmic filters, a new, modified mathematical framework has been conceived, termed Nonlinear Bernoulli Cell Formalism (NBCF), which forms the core mathematical framework, characterising the operation of CytoMimetic circuits. The proposed nonlinear, transistor-level mathematical formulation exploits the striking similarities existing between the NBCF and coupled ordinary differential equations, typically appearing in models of naturally encountered biochemical systems. The resulting continuous-time, continuous-value, low-power CytoMimetic electronic circuits succeed in simulating with good accuracy cellular and molecular dynamics and found to be in very good agreement with their biological counterparts. They usually occupy an area of a fraction of a square millimetre, while consuming between hundreds of nanowatts and few tenths of microwatts of power. The systematic nature of the NBCF led to the transformation of a wide variety of biochemical reactions into nonlinear Log-domain circuits, which span a large area of different biological model types. Moreover, a detailed analysis of the robustness and performance of the proposed circuit class is also included in this thesis. The robustness examination has been conducted via post-layout simulations of an indicative CytoMimetic circuit and also by providing fabrication-related variability simulations, obtained by means of analog Monte Carlo statistical analysis for each one of the proposed circuit topologies. Furthermore, a detailed mathematical analysis that is carefully addressing the effect of process-parameters and MOSFET geometric properties upon subthreshold translinear circuits has been conducted for the fundamental translinear blocks, CytoMimetic topologies are comprised of. Finally, an interesting sub-category of Neuromorphic circuits, the ``Log-Domain Silicon Synapses'' is presented and representative circuits are thoroughly analysed by a novel, generalised BC operator framework. This leads to the conclusion that the BC operator consists the heart of such Log-domain circuits, therefore, allows the establishment of a general class of BC-based silicon synaptic circuits, which includes most of the synaptic circuits, implemented so far in Log-domain.Open Acces

PSA 2018

These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2018