Population Dynamics Model Research Articles

Modeling and dissociation of intrinsic and input-driven neural population dynamics underlying behavior

Neural dynamics can reflect intrinsic dynamics or dynamic inputs, such as sensory inputs or inputs from other brain regions. To avoid misinterpreting temporally structured inputs as intrinsic dynamics, dynamical models of neural activity should account for measured inputs. However, incorporating measured inputs remains elusive in joint dynamical modeling of neural-behavioral data, which is important for studying neural computations of behavior. We first show how training dynamical models of neural activity while considering behavior but not input or input but not behavior may lead to misinterpretations. We then develop an analytical learning method for linear dynamical models that simultaneously accounts for neural activity, behavior, and measured inputs. The method provides the capability to prioritize the learning of intrinsic behaviorally relevant neural dynamics and dissociate them from both other intrinsic dynamics and measured input dynamics. In data from a simulated brain with fixed intrinsic dynamics that performs different tasks, the method correctly finds the same intrinsic dynamics regardless of the task while other methods can be influenced by the task. In neural datasets from three subjects performing two different motor tasks with task instruction sensory inputs, the method reveals low-dimensional intrinsic neural dynamics that are missed by other methods and are more predictive of behavior and/or neural activity. The method also uniquely finds that the intrinsic behaviorally relevant neural dynamics are largely similar across the different subjects and tasks, whereas the overall neural dynamics are not. These input-driven dynamical models of neural-behavioral data can uncover intrinsic dynamics that may otherwise be missed.

Reduction in size-at-maturity in unprecedentedly strong cohorts of redfish (Sebastes mentella and S. fasciatus) in the Gulf of St. Lawrence and Laurentian Channel.

Life-history traits, such as size-at-maturity, are key parameters to model population dynamics used to inform fisheries management. Fishery-induced evolution, density-dependent effects, and global warming have been shown to affect size- and age-at-maturity, and resulting spawning stock biomass (SSB) in a wide range of commercial fish stocks. Marked changes in redfish biomass and environmental conditions in the Gulf of St. Lawrence and Laurentian Channel over the past decade called for a review and update of size-at-maturity for commercially important deepwater redfish Sebastes mentella and Acadian redfish Sebastes fasciatus stocks. Following a 25-year moratorium, local redfish biomass has recently reached unprecedented levels, co-occurring with an overall warming of bottom water temperatures. Our objectives were (1) to perform a histological assessment of redfish reproduction stages, including the validation and fine-tuning of a robust visual chart to facilitate monitoring of size-at-maturity and SSB in a transforming environment, and (2) to evaluate changes in size-at-maturity in unprecedentedly strong cohorts of redfish, and consequences for stock status assessment and fisheries management. Each specimen was genetically identified to species, and gonad reproduction stages were determined by histology and macroscopic appearances. The present study enabled a robust visual chart for continued and cost-effective monitoring of redfish reproduction stages to be refined and validated, and has shown a large decrease in redfish length when 50% of the individuals are considered mature that led to an increase in estimates of SSB during the 2011-2021 period for S. mentella and S. fasciatus. These changes modified the perception of stock status, thus having significant implications for fisheries management. Given that fishery-induced evolution and community structure changes along with global warming are affecting numerous stocks worldwide, the present study outlines a major and global challenge for scientists and resources managers. As shown by our results, the monitoring and frequent updates of life-history traits in transforming environments are needed to provide reliable science advice for sustainable fisheries.

Local existence of solutions to a nonlinear autonomous PDE model for population dynamics with nonlocal transport and competition

In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to qualitatively describe temporal changes in population densities over space through accounting for location desirability and fast, long-range travel. Beginning with sufficiently regular initial conditions, through smoothing the PDE and employing energy arguments, we obtain a sequence of approximators converging to a classical solution.

Abstract IA016: Bayesian phylodynamics to quantify cancer growth across space and time

Abstract Phylogenetics has traditionally inferred shared genetic histories of species over macroevolutionary time. With the expansion of cancer multi-region and single-cell sequencing, phylogenetic approaches have found new uses mapping the evolutionary histories of tumors as well. Recently developed “phylodynamic” methods that integrate phylogenetic and population dynamic modeling offer further promise - uncovering cancer growth dynamics from the topologies and branch lengths of tumor trees. Here, I discuss two recent efforts in this area: 1) Heterogeneous growth rates across a tumor become encoded in the branching patterns of phylogenetic trees built from multi-region sequencing. We introduce a cancer-specific extension to a class of multi-state birth-death models to infer these growth rate differences across space. We apply our model (SDevo) to a sample of hepatocellular carcinomas and infer that these tumor peripheries grow 2-6 times faster than their interiors. 2) Tumors experience differential growth rates over time as they acquire new driver mutations and invade their surrounding tissues, and these growth dynamics similarly leave characteristic signatures in their phylogenies. We employ Bayesian skyline models to dissect tumor growth dynamics from a dataset of diverse cancers and reveal variation in cancer growth rates over time. As cancer sequencing continues to proliferate, phylodynamic approaches are poised to reveal new quantitative insights into cancer growth dynamics across time and space. Citation Format: Maya Lewinsohn, Trevor Bedford, Nicola F. Müller, Alison Feder. Bayesian phylodynamics to quantify cancer growth across space and time [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Translating Cancer Evolution and Data Science: The Next Frontier; 2023 Dec 3-6; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_2):Abstract nr IA016.

Population dynamic life history models of the birds and mammals of the world

With life history traits determining the natural selection fitnesses of individuals and growth of populations, estimates of their variation are essential to advance evolutionary understanding and ecological management during times of global change. As life history data are incomplete or missing for most species, I combine data and natural selection theory to construct a meta natural selection model of the population dynamic life history (PDLH) variation in birds and mammals. This generates PDLH models for 11,187 species of birds and 4936 mammals, covering 29 life history and ecological traits per species. The inter-specific variation of the meta model is used to illustrate underlying natural selection mechanisms, and to explain a diverse range of population dynamic trajectories by the inclusion of population dynamic regulation. This provides essential steps towards improved evolutionary analyses and freely accessible ready-to-use online population dynamic simulations, covering most species of birds and mammals.

Faster inference from state space models via GPU computing

Inexpensive Graphics Processing Units (GPUs) offer the potential to greatly speed up computation by employing their massively parallel architecture to perform arithmetic operations more efficiently. Population dynamics models are important tools in ecology and conservation. Modern Bayesian approaches allow biologically realistic models to be constructed and fitted to multiple data sources in an integrated modelling framework based on a class of statistical models called state space models. However, model fitting is often slow, requiring hours to weeks of computation. We demonstrate the benefits of GPU computing using a model for the population dynamics of British grey seals, fitted with a particle Markov chain Monte Carlo algorithm. Speed-ups of two orders of magnitude were obtained for estimations of the log-likelihood, compared to a traditional ‘CPU-only’ implementation, allowing for an accurate method of inference to be used where this was previously too computationally expensive to be viable. GPU computing has enormous potential, but one barrier to further adoption is a steep learning curve, due to GPUs' unique hardware architecture. We provide a detailed description of hardware and software setup, and our case study provides a template for other similar applications. We also provide a detailed tutorial-style description of GPU hardware architectures, and examples of important GPU-specific programming practices.

A Coupled Model of Population, Poaching, and Economic Dynamics to Assess Rhino Conservation Through Legal Trade

A Coupled Model of Population, Poaching, and Economic Dynamics to Assess Rhino Conservation Through Legal Trade

A generalized model for the population dynamics of a two stage species with recruitment and capture using a nonstandard finite difference scheme

The aim of this work is to formulate and analyze a new and generalized discrete-time population dynamics model for a two-stage species with recruitment and capture factors. This model is derived from a well-known continuous-time population dynamics model of a two-stage species with recruitment and capture developed by Ladino and Valverde and the nonstandard finite difference (NSFD) methodology proposed by Mickens. We establish positivity and asymptotic stability of the proposed discrete-time population dynamics model. As an important consequence, the population dynamics of the new discrete-time model is determined fully. Also, a set of numerical examples is conducted to illustrate the theoretical results and to demonstrate advantages of the new model. The theoretical results and numerical examples show that the proposed discrete-time model not only preserves correctly the population dynamics of the continuous one but is also easy to be implemented. However, some discrete-time models based on the standard Runge–Kutta methods fail to preserve the population dynamics of the continuous-time model. As a result, they generate numerical approximations which are not only non-negative but also unstable.

Estimations of length-weight relationships and consumption rates of odontocetes in the Mediterranean Sea from stranding data

Stranding data provide fundamental information on biometric traits of cetaceans useful to increase knowledge on ecological traits and their consumption patterns. In this study, the length weight (L-W) relationships through the power regression model (W=a×Lb) were calculated for three dolphin species (the striped dolphin, the common bottlenose dolphin and the Risso's dolphin) in several Mediterranean subregions and at the scale of the entire basin. Length (L) and weight (W) data were collected from stranding records during the period from 1983 to 2021 acquired from several databases and the literature. Starting from L-W relationships, a bootstrap method was applied to estimate the mean body weights, the daily ingested biomass (IB) and annual food consumption (AFC) rates of different dolphin species. In particular, four different equations were used to estimate the IB rates. Prey consumption by dolphin species was calculated through AFC rates and the available diet information (expressed in weight fractions) of dolphin species for different Mediterranean subregions.Considering the L-W relationships in the Mediterranean Sea, b coefficient values were equal to 2.578, 2.975 and 2.988 for the striped, the common bottlenose and the Risso's dolphin, respectively. At the Mediterranean scale, the AFC values estimated were 3913 kg (CI 2469–5306) for the Risso's dolphin, 2571 kg (1372–3963) for the common bottlenose dolphin and 1118 kg (531–1570) for the striped dolphin. Prey consumption pattern showed a clear partitioning among the investigated species, where the common bottlenose dolphin exploits neritic demersal and pelagic fishes (e.g. eel fishes, sparids), the striped dolphin exploits mesopelagic fishes and myctophids, and the Risso's dolphin was specialized on bathyal cephalopods of Histioteuthidae family.The results obtained in this study provide new information for the investigated species in several Mediterranean subregions providing a first consistent baseline to support the population dynamics modelling. At the same time, the wide uncertainty ranges of some parameters, as well as the lack of information for some species, stress the necessity of improving the data collection associated to stranding events, especially in the southern Mediterranean areas.

Regime shifts, extinctions and long transients in models of population dynamics with density-dependent dispersal

Predicting extinctions resulting from ecosystems' regime shifts has long been a focus of biological conservation and ecological management. Mathematical modelling plays a key role in assessing the possibility of such events. Traditionally, however, models focused on long-term, asymptotic behaviour of ecosystems. Meanwhile, the environment is usually non-stationary, which may mean that the long-term behaviour is never observed. Correspondingly, over the last two decades there has been a growing appreciation of the role of transients both in empirical ecology and theoretical studies, in particular in the context of species extinctions. In this paper, we theoretically explore long transients and extinctions occurring in several paradigmatic models of increasing complexity, such as single species, two-species and three-species systems. We consider the population dynamics in a local ‘patch’, the patch being connected to the rest of the population via density-dependent dispersal. We consider both deterministic and stochastic scenarios. We discover many different patterns of long transient dynamics with quick regime shifts between ‘safe’ (persistent) dynamics and unsafe ones resulting in extinctions. Remarkably, delayed extinction can occur after thousands of generations of apparently safe population dynamics. We classify transient regimes and reveal their underlying mechanisms. Environmental noise can either shorten transients or can create a new type of a long transient. Our study suggests that not only are long transients ubiquitous, but there is also a great variety of them. The omnipresence of long transients emphasizes the need to account for them in nature conservation programs as well as future theoretical research.

Lytic and temperate phage naturally coexist in a dynamic population model.

When phage infect their bacterial hosts, they may either lyse the cell and generate a burst of new phage, or lysogenize the bacterium, incorporating the phage genome into it. Phage lysis/lysogeny strategies are assumed to be highly optimized, with the optimal tradeoff depending on environmental conditions. However, in nature, phage of radically different lysis/lysogeny strategies coexist in the same environment, preying on the same bacteria. How can phage preying on the same bacteria coexist if one is more optimal than the other? Here, we address this conundrum within a modeling framework, simulating the population dynamics of communities of phage and their lysogens. We find that coexistence between phage of different lysis/lysogeny strategies is a natural outcome of chaotic population dynamics that arise within sufficiently diverse communities, which ensure no phage is able to absolutely dominate its competitors. Our results further suggest a bet-hedging mechanism at the level of the phage pan-genome, wherein obligate lytic (virulent) strains typically outcompete temperate strains, but also more readily fluctuate to extinction within a local community.

Feasibility of engineered Bacillus subtilis for use as a microbiome-based topical drug delivery platform.

Non-adherence to medication is a major challenge in healthcare that results in worsened treatment outcomes for patients. Reducing the frequency of required administrations could improve adherence but is challenging for topical drug delivery due to the generally short residence time of topical formulations on the skin. In this study, we sought to determine the feasibility of developing a microbiome-based, long-acting, topical delivery platform using Bacillus subtilis for drug production and delivery on the skin, which was assessed using green fluorescent protein as a model heterologous protein for delivery. We developed a computational model of bacteria population dynamics on the skin and used its qualitative predictions to guide experimental design choices. Using an ex vivo pig skin model and a human skin tissue culture model, we saw persistence of delivered bacteria for multiple days and observed little evidence of cytotoxicity to human keratinocyte cells in vitro. Finally, using an in vivo mouse model, we found that the delivered bacteria persisted on the skin for at least 1 day during every-other-day application and did not appear to present safety concerns. Taken together, our results support the feasibility of using engineered B. subtilis for topical drug delivery.

Existence and Uniqueness of a Solution for a Four‐Stage Age‐Structured Population Dynamics Model With Spatial Diffusion for Desert Locusts

We consider a linear system based on a population dynamics model dependent on age, space and nonlocal boundary conditions. Note that our population dynamics model is a four‐step model with a second derivative with respect to the age variable and a second derivative with respect to the space variable. Population growth at each stage depends on time and space. We prove the uniqueness and existence of a positive solution by combining the Galerkin’s variational method and the Banach’s fixed point theorem.

Definition of information in computer science

Purpose of this study is to formulate a working definition of information to meet the needs of computer science. There is currently no strict definition of this term. There is a methodological contradiction: the development and application of information technologies requires accuracy and rigor, but at the same time the development is based on a vague, intuitive concept. Materials and methods. The materials for the study are existing classical approaches to understanding information, and the main method is the analysis of these approaches. The proposed definition is constructed taking into account two mathematical transformations: the selection of a certain subset and the mapping between sets. To formalize the allocation procedure, it is used apparatus of fuzzy sets. Results. A definition of information is proposed as the result of a mapping in which the selection of a subset from a set of prototypes leads to the selection of a corresponding subset from a set of images. The selected subset can be understood as fuzzy, then an equivalent definition of information is acceptable as a result of mapping, in which an increase in the heterogeneity of the distribution of the presence indicator on the set of prototypes leads to an increase in the heterogeneity of the distribution of the corresponding indicator on the set of images. The essence of the new definition is demonstrated using models of population dynamics in discrete time. The significance of the proposed approach for information technology is revealed using the example of the numerical method of multi-extremal optimization. It is shown that the proposed definition makes it possible to formulate effective stopping conditions for the numerical method of stochastic optimization, which guarantees the receipt of a given amount of information. Conclusion. The proposed understanding of information allows us to overcome the shortcomings of previous approaches to understanding the essence of information, retains all the advantages of the classical approach and is consistent with other well-known approaches in the field of computer science. This definition can be used to improve numerical optimization methods, as well as other information technology tools.

Solution of logistic differential equation in an uncertain environment using neutrosophic numbers

The modeling and forecasting of population dynamics, as well as growth in biological systems more generally, have required the construction of various growth models. This paper presents the logistic growth model, which is a modified version of the exponential growth model and offers a more flexible framework to capture fluctuations and potential deviations from deterministic predictions. This paper aims to advance the model of a logistic growth differential equation within a neutrosophic environment, with a focus on validating the proposed framework by applying it to predict the projected population of India from the year 2001 to 2050. We investigated the neutrosophic solutions and validated them with the exact solution with available projected data on the portal of UNITED NATION. The developed logistic growth differential equation in a neutrosophic environment is visually elucidated through graphical representation, enhancing the clarity and accessibility of the presented model.

Pushing coarse-grained models beyond the continuum limit using equation learning

Mathematical modelling of biological population dynamics often involves proposing high-fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an approximate coarse-grained differential equation that captures population-level features only. These coarse-grained models are only accurate in certain asymptotic parameter regimes, such as enforcing that the time scale of individual motility far exceeds the time scale of birth/death processes. When these coarse-grained models are accurate, the discrete model still abides by conservation laws at the microscopic level, which implies that there is some macroscopic conservation law that can describe the macroscopic dynamics. In this work, we introduce an equation learning framework to find accurate coarse-grained models when standard continuum limit approaches are inaccurate. We demonstrate our approach using a discrete mechanical model of epithelial tissues, considering a series of four case studies that consider problems with and without free boundaries, and with and without proliferation, illustrating how we can learn macroscopic equations describing mechanical relaxation, cell proliferation, and the equation governing the dynamics of the free boundary of the tissue. While our presentation focuses on this biological application, our approach is more broadly applicable across a range of scenarios where discrete models are approximated by approximate continuum-limit descriptions.

ОСОБЕННОСТИ СИНХРОНИЗАЦИИ ДИНАМИКИ ЧИСЛЕННОСТИ В СИСТЕМЕ ТРЕХ МИГРАЦИОННО СВЯЗАННЫХ ПОПУЛЯЦИЙ

The article is devoted to the study of oscillations (cycles) synchronization in a system of three populations coupled by migration in a circle. We consider a discrete time model of population dynamics, which is a system of three identical dissipatively connected logistic maps. One-dimensional bifurcation diagrams (trees) were constructed, supplemented with the capture index of the population numbers cycles phases at adjacent sites. We conducted numerical experiments that show phase multistability – the cycles coexistence with different phases. Using qualitative methods for studying dynamic systems, a complete phase portrait of the model is constructed, showing that in the phase space there are several periodic points corresponding to elements of synchronous (in-phase) and asynchronous (out-of-phase) cycles. The 2- and 3-cycle stability conditions are investigated. It is shown that these two cycles are represented by three options: 1) a fully synchronous regime, when the abundances in the three populations coincide at any point in time; 2) a partially synchronous regime, when abundances coincide only for two populations, 3) a non-synchronous (out-of-phase) regime, when all three numbers have different values. For a 2-cycle, the third regime is unstable, possible as part of a long transition process. We found that for the 3-cycle, besides to the synchronous and partially synchronous regime, it is possible a stable out-of-phase behavior of three populations. It is shown that stable and unstable periodic points lie on certain surfaces (invariant manifolds), which separate the areas of attraction for regimes with different degrees of phase synchronization.

МОДЕЛЬНЫЙ АНАЛИЗ ДЕМОГРАФИЧЕСКИХ ПРОЦЕССОВ В ПОПУЛЯЦИЯХ ПУШНЫХ ОХОТНИЧЬИХ ЖИВОТНЫХ (НА ПРИМЕРЕ ЕВРЕЙСКОЙ АВТОНОМНОЙ ОБЛАСТИ)

Among biological resources, hunting animals, including fur-bearing species, take a special place. The study of such populations dynamics is a crucial stage in fur harvesting planning and organizing. This work aims to describe and analyze by mathematical modeling methods the dynamics of fur-bearing animal populations inhabiting the Jewish Autonomous region. We consider the populations whose newborn individuals reach maturity by the next breeding season, for example, squirrel, white hare, Manchurian hare, raccoon dog, and weasel. The study is based on the discrete-time model of population dynamics with a simple stage structure. To take into account density-dependent regulation of population growth in the model, birth or survival rates of the immature class are represented by exponential functions of the total population size. To estimate the model parameters, we propose the use of data corresponding to the total population size. The obtained point estimates, based on this approach, are demonstrated to be within the range of biologically meaningful parameter values and exhibit the population dynamics similar to those observed in nature. Specifically, according to the model estimates, squirrel and hare populations are characterized by unstable dynamics with sharp annual fluctuations. In general, the proposed approach for parameter estimation allows for analyzing and modeling the age composition of the animal population, as well as determining demographic parameters that characterize the animal population dynamics based on the total population size data.

Study on Sex Ratio and Resource Utilization Based on Logistic Dynamic Population Model

Study on Sex Ratio and Resource Utilization Based on Logistic Dynamic Population Model

Learning mechanism for a collective classifier based on competition driven by training examples

The purpose of this work is to modify the learning mechanism of a collective classifier in order to provide learning by population dynamics alone, without requiring an external sorting device. A collective classifier is an ensemble of non-identical simple elements, which do not have any intrinsic dynamics neither variable parameters; the classifier admits learning by adjusting the composition of the ensemble, which was provided in the preceding literature by selecting the ensemble elements using a sorting device. Methods. The population dynamics model of a collective classifier is extended by adding a “learning subsystem”, which is controlled by a sequence of training examples and, in turn, controls the strength of intraspecific competition in the population dynamics. The learning subsystem dynamics is reduced to a linear mapping with random parameters expressed via training examples. The solution to the mapping is an asymptotically stationary Markovian random process, for which we analytically find asymptotic expectation and show its variance to vanish in the limit under the specified assumptions, thus allowing an approximate deterministic description of the coupled population dynamics based on available results from the preceding literature. Results. We show analytically and illustrate it by numerical simulation that the decision rule of our classifier in the course of learning converges to the Bayesian rule under assumptions which are essentially in line with available literature on collective classifiers. The implementation of the required competitive dynamics does not require an external sorting device. Conclusion. We propose a conceptual model for a collective classifier, whose learning is fully provided by its own population dynamics. We expect that our classifier, similarly to the approaches taken in the preceding literature, can be implemented as an ensemble of living cells equipped with synthetic genetic circuits, when a mechanism of population dynamics with synthetically controlled intraspecific competition becomes available.