Population Dynamics Model Research Articles

Null controllability of a nonlinear age, space and two-sex structured population dynamics model

<p style='text-indent:20px;'>In this paper, we study the null controllability of a nonlinear age, space and two-sex structured population dynamics model. This model is such that the nonlinearity and the couplage are at birth level. We consider a population with males and females and we are dealing with two cases of null controllability problems.</p><p style='text-indent:20px;'>The first problem is related to the total extinction, which means that, we estimate a time <inline-formula><tex-math id="M1">\begin{document}$ T $\end{document}</tex-math></inline-formula> to bring the male and female subpopulation density to zero. The second case concerns null controllability of male or female subpopulation. Since the absence of males or females in the population stops births; so, if we have the total extinction of the females at time <inline-formula><tex-math id="M2">\begin{document}$ T, $\end{document}</tex-math></inline-formula> and if <inline-formula><tex-math id="M3">\begin{document}$ A $\end{document}</tex-math></inline-formula> is the life span of the individuals, at time <inline-formula><tex-math id="M4">\begin{document}$ T+A $\end{document}</tex-math></inline-formula> one will get certainly the total extinction of the population. Our method uses first an observability inequality related to the adjoint of an auxiliary system, a null controllability of the linear auxiliary system, and after the Schauder's fixed point theorem.</p>

Biometric relationships for the bivalve Ark shell Arca noae(Bivalvia; arcidae) from the Bizerte lagoon (Northern Tunisia)

Bivalves are known to exhibit wide morphological variations, which are closely linked to their ecology and reproductive activity. Therefore, the study of growth is necessary to model population dynamics, which, in turn, is crucial to support the exploitation and management of the stock. The current study aimed to analyze the shell morphological variations in the bivalve Ark shell Arca noae collected monthly from the Bizerte lagoon (northern Tunisian coasts) from October 2013 to September 2014. Allometric relationships established between linear variables (shell length and height); weight variables (total weight) and the relative growth between variables (isometry vs allometry) were analyzed. All morphometric relationships were highly significant with high correlation coefficients (R2: 0.604-0.903). Seasonal monitoring of the linear and weight relationship of the A. noae population suggested the presence of a negative allometric growth during the seasons which indicated that Ark shells are growing faster in length than in height and weight. Overall, linear and weight growth in A. noae from the Bizerte lagoon was found to be uniform and synchronous over the seasons and seems not to be influenced by the species’ reproductive cycle. This preliminary study will be useful for further research studies in biology, ecology and stock management of this non-exploited marine resource.

Coupled stochastic systems of Skorokhod type: Well‐posedness of a mathematical model and its applications

Population dynamics with complex biological interactions, accounting for uncertainty quantification, are critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation of the corresponding problems faces the challenge that the corresponding stochastic processes should, in most cases, be considered in bounded domains. We propose a model based on a coupled system of reflecting Skorokhod‐type stochastic differential equations with jump‐like exit from a boundary. The setting describes the population dynamics of active and passive populations. As main working techniques, we use compactness methods and Skorokhod's representation of solutions to SDEs posed in bounded domains to prove the well‐posedness of the system. This functional setting is a new point of view in the field of modeling and simulation of population dynamics. We provide the details of the model, as well as representative numerical examples, and discuss the applications of a Wilson–Cowan‐type system, modeling the dynamics of two interacting populations of excitatory and inhibitory neurons. Furthermore, the presence of random input current, reflecting factors together with Poisson jumps, increases firing activity in neuronal systems.

Random walk with multiple memory channels.

A class of one-dimensional, discrete-time random walk models with memory, termed "random walk with n memory channels" (RWnMC), is proposed. In these models the information of n (n∈Z) previous steps from the walker's entire history is needed to decide a future step. Exact calculation of the mean and variance of position of the RW2MC (n=2) has been done, which shows that it can lead to asymptotic diffusive and superdiffusive behavior in different parameter regimes. A connection between RWnMC and a Pólya-type urn model evolving by drawing n balls at a time has also been reported. This connection for the RW2MC is discussed in detail and suggests the applicability of RW2MC in many population dynamics models with multiple competing species.

Gene drive designs for efficient and localisable population suppression using Y-linked editors.

The sterile insect technique (SIT) has been successful in controlling some pest species but is not practicable for many others due to the large number of individuals that need to be reared and released. Previous computer modelling has demonstrated that the release of males carrying a Y-linked editor that kills or sterilises female descendants could be orders of magnitude more efficient than SIT while still remaining spatially restricted, particularly if combined with an autosomal sex distorter. In principle, further gains in efficiency could be achieved by using a self-propagating double drive design, in which each of the two components (the Y-linked editor and the sex ratio distorter) boosted the transmission of the other. To better understand the expected dynamics and impact of releasing constructs of this new design we have analysed a deterministic population genetic and population dynamic model. Our modelling demonstrates that this design can suppress a population from very low release rates, with no invasion threshold. Importantly, the design can work even if homing rates are low and sex chromosomes are silenced at meiosis, potentially expanding the range of species amenable to such control. Moreover, the predicted dynamics and impacts can be exquisitely sensitive to relatively small (e.g., 25%) changes in allele frequencies in the target population, which could be exploited for sequence-based population targeting. Analysis of published Anopheles gambiae genome sequences indicates that even for weakly differentiated populations with an FST of 0.02 there may be thousands of suitably differentiated genomic sites that could be used to restrict the spread and impact of a release. Our proposed design, which extends an already promising development pathway based on Y-linked editors, is therefore a potentially useful addition to the menu of options for genetic biocontrol.

Stability Analysis of a Population Dynamics Model of Daphnia

Stability Analysis of a Population Dynamics Model of Daphnia

Global maps of lake surface water temperatures reveal pitfalls of air‐for‐water substitutions in ecological prediction

In modeling species distributions and population dynamics, spatially‐interpolated climatic data are often used as proxies for real, on‐the‐ground measurements. For shallow freshwater systems, this practice may be problematic as interpolations used for surface waters are generated from terrestrial sensor networks measuring air temperatures. Using these may therefore bias statistical estimates of species' environmental tolerances or population projections – particularly among pleustonic and epilimnetic organisms. Using a global database of millions of daily satellite‐derived lake surface water temperatures (LSWT), I trained machine learning models to correct for the correspondence between air and LSWT as a function of atmospheric and topographic predictors, resulting in the creation of monthly high‐resolution global maps of air‐LSWT offsets, corresponding uncertainty measures and derived LSWT‐based bioclimatic layers for use by the scientific community. I then compared the performance of these LSWT layers and air temperature‐based layers in population dynamic and ecological niche models (ENM). While generally high, the correspondence between air temperature and LSWT was quite variable and often nonlinear depending on the spatial context. These LSWT predictions were better able to capture the modeled population dynamics and geographic distributions of two common aquatic plant species. Further, ENM models trained with LSWT predictors more accurately captured lab‐measured thermal response curves. I conclude that these predicted LSWT temperatures perform better than raw air temperatures when used for population projections and environmental niche modeling, and should be used by practitioners to derive more biologically‐meaningful results. These global LSWT predictions and corresponding error estimates and bioclimatic layers have been made freely available to all researchers in a permanent archive.

TiPS: Rapidly simulating trajectories and phylogenies from compartmental models

Abstract Stochastic population dynamics simulations are essential for many ecological and epidemiological studies to generate time series and genealogies that capture the relatedness between individuals. Many software packages allow one to simulate phylogenetic trees but these tend to suffer from one or two major limitations. First, the underlying population dynamics model is often simplistic (e.g. constant population size or exponential growth). Second, the software packages are not appropriate to simulate a large number of trees. We introduce TiPS, an R package to generate trajectories and phylogenetic trees associated with a compartmental model. Trajectories are simulated using Gillespie's exact or approximate stochastic simulation algorithm, or a newly proposed mixed version of the two. Phylogenetic trees are simulated from a trajectory under a backwards‐in‐time approach (i.e. coalescent). TiPS is based on the Rcpp package, allowing to combine the flexibility of R for model definition and the speed of C++ for simulations execution. The model is defined in R with a set of reactions, which allow capturing heterogeneity in life cycles or any sort of population structure. TiPS converts the model into C++ code and compiles it into a simulator that is interfaced in R via a function. TiPS is flexible, easy‐to‐use and available on the CRAN at https://cran.r‐project.org/package=TiPS. Plus, benchmarking analyses show that TiPS is faster than existing packages. This package is particularly well suited for population genetics and phylodynamics studies that need to generate a large number of phylogenies used for population dynamics studies.

Economic benefits of conservation biocontrol: A spatially explicit bioeconomic model for insect pest management in agricultural landscapes

Spatially explicit population dynamic models have been successfully used to explore management scenarios in terms of pest suppression across a wide range of systems. However, the economic implications of pest management, particularly in the case of biological control and non-crop management strategies, have not been well considered. A bioeconomic spatially explicit simulation model was developed, that integrates models of pest population dynamics, pest movement and economics of management. The utility of the model is demonstrated here usingNysius vinitor, a pest of grain crops in Australia. The model estimates the short- and long-term economic benefits of three pest management strategies: (1) in-field pesticide spray; (2) pest suppression through weed management in non-crop habitat; and (3) bolstering biocontrol through revegetation with, or maintenance of, native vegetation. Across all management types, high yield and low relative management cost resulted in a greater chance of a gross profit. The impacts of the pests themselves were shown to be non-linear, with an intermediate level of pest pressure maximizing the economic gain from management. Pest dispersal capacity influenced the profitability of management of non-crop vegetation, with lower pest dispersal resulting in a greater likelihood of benefit, as benefits from non-crop management are localized (e.g., increased beneficial insect populations). In an intensively cropped landscape, pesticide management was most profitable over the short-term. Once a 10-year horizon was reached, then the profitability of revegetation was greater and continued to increase. While weeding requirements are low, it is likely to always be profitable in the long-term to maintain or restore native vegetation in good condition to control this pest in an intensively cropped landscape. Using pesticide alongside revegetation gave some short-term gain, but the negative impact of pesticide on beneficials outweighed the benefit and in the long-term it is less profitable. These results do not hold in a low production landscape, due to increased pest pressure and costs of managing non-crop habitat. In summary, when quantified over a 10–20 year time horizon, revegetation or conserving native remnants in good (i.e., non-weedy) condition could be economically more beneficial to control an insect pest than ongoing pesticide use, in intensively cropped landscapes.

Stability of Cycles in a Game of Rock-Scissors-Paper-Lizard-Spock

We study a system of ordinary differential equations in $R^5$ that is used as a model both in population dynamics and in game theory, and is known to exhibit a heteroclinic network formed by three types of elementary heteroclinic cycles. We show the asymptotic stability of the network for parameter values in a range compatible with the two interpretations of the equations. We obtain estimates of the relative attractiveness of each one of the cycles by computing their stability indices. For the parameter values ensuring the asymptotic stability of the network we show that if one of the cycles has a weak form of attractiveness, then the other two are completely unstable. We also show the existence of an open region in parameter space where all three cycles are completely unstable and the network is asymptotically stable, giving rise to intricate dynamics that has been observed numerically by other authors.

EcoEvoApps: Interactive apps for theoretical models in ecology and evolutionary biology.

The integration of theory and data drives progress in science, but a persistent barrier to such integration in ecology and evolutionary biology is that theory is often developed and expressed in the form of mathematical models that can feel daunting and inaccessible for students and empiricists with variable quantitative training and attitudes towards math. A promising way to make mathematical models more approachable is to embed them into interactive tools with which one can visually evaluate model structures and directly explore model outcomes through simulation. To promote such interactive learning of quantitative models, we developed EcoEvoApps, a collection of free, open-source, and multilingual R/Shiny apps that include model overviews, interactive model simulations, and code to implement these models directly in R. The package currently focuses on canonical models of population dynamics, species interactions, and landscape ecology. These apps help illustrate fundamental results from theoretical ecology and can serve as valuable teaching tools in classroom settings. We present data from student surveys which show that students rate these apps as useful learning tools, and that using interactive apps leads to substantial gains in students' interest and confidence in working with mathematical models. This points to the potential for interactive activities to make theoretical models more accessible to a wider audience, and thus facilitate the feedback between theory and data across ecology and evolutionary biology.

An introduction to the Markov chain Monte Carlo method

We present an intuitive, conceptual, and semi-rigorous introduction to the Markov Chain Monte Carlo method using a simple model of population dynamics and focusing on a few elementary distributions. We start from two states, then three states, and finally generalize to many states with both discrete and continuous distributions. Despite the mathematical simplicity, our examples include the essential concepts of the Markov Chain Monte Carlo method, including ergodicity, global balance and detailed balance, proposal or selection probability, acceptance probability, the underlying stochastic matrix, and error analysis. Our experience suggests that most senior undergraduate students in physics can follow these materials without much difficulty.

Bayesian Nonparametric Density Autoregression with Lag Selection

We develop a Bayesian nonparametric autoregressive model applied to flexibly estimate general transition densities exhibiting nonlinear lag dependence. Our approach is related to Bayesian density regression using Dirichlet process mixtures, with the Markovian likelihood defined through the conditional distribution obtained from the mixture. This results in a Bayesian nonparametric extension of a mixtures-of-experts model formulation. We address computational challenges to posterior sampling that arise from the Markovian structure in the likelihood. The base model is illustrated with synthetic data from a classical model for population dynamics, as well as a series of waiting times between eruptions of Old Faithful Geyser. We study inferences available through the base model before extending the methodology to include automatic relevance detection among a pre-specified set of lags. Inference for global and local lag selection is explored with additional simulation studies, and the methods are illustrated through analysis of an annual time series of pink salmon abundance in a stream in Alaska. We further explore and compare transition density estimation performance for alternative configurations of the proposed model. Supplementary materials are available online.

Predator discrimination of prey promotes the predator-mediated coexistence of prey species.

The predator discrimination of prey can affect predation intensity and the prey density dependence of predators, which has the potential to alter the coexistence of prey species. We used a predator-prey population dynamics model accounting for the predator's adaptive diet choice and predator discrimination of prey to investigate how the latter influences prey coexistence. The model revealed that (i) prey species that are perceived as belonging to the same species by a predator are attacked in the same manner, and it is more difficult for them to coexist than those that are recognized as different prey species, and (ii) prey species that are not discriminated by a predator-and therefore cannot coexist-may coexist in the presence of an alternative predator that does discriminate between them. These results suggest that prey diversity, which favours the predator discrimination of prey, and the different capabilities of predators to identify prey species both enhance prey coexistence.

Dynamics of a predator–prey system with inducible defense and disease in the prey

Establishing and researching a population dynamical model based on the differential equation is of great significance. In this paper, a predator–prey system with inducible defense and disease in the prey is built from biological evolution and Eco-epidemiology. The effect of disease on population stability in the predator–prey system with inducible defense is studied. Firstly, we verify the positivity and uniform boundedness of the solutions of the system. Then the existence and stability of the equilibria are studied. There are no more than nine equilibrium points in the system. We use a sophisticated parameter transformation to study the properties of the coexistence equilibrium points of the system. A sufficient condition is established for the existence of Hopf bifurcation. Numerical simulations are performed to make analytical studies more complete.

A large-scale neural network training framework for generalized estimation of single-trial population dynamics.

Achieving state-of-the-art performance with deep neural population dynamics models requires extensive hyperparameter tuning for each dataset. AutoLFADS is a model-tuning framework that automatically produces high-performing autoencoding models on data from a variety of brain areas and tasks, without behavioral or task information. We demonstrate its broad applicability on several rhesus macaque datasets: from motor cortex during free-paced reaching, somatosensory cortex during reaching with perturbations, and dorsomedial frontal cortex during a cognitive timing task.

Regulatory Processes in Populations of Forest Insects (A Case Study of Insect Species Damaging the Pine Pinus sylvestris L. in Forests of SIBERIA)

The present study addresses the population dynamics of five species of phyllophagous forest insects in five habitats located in the Krasnoturansk pine forest (south Middle Siberia). Based on the data of insect surveys obtained during 1979–2016, autoregressive (AR) models of population dynamics have been proposed, with the current population density being dependent on population densities of the preceding years. Methods of calculation of the autoregression order and coefficients of AR equations have been presented. The study shows that, for different insect species in different habitats, the lags between the current population density and the densities of the previous years are not the same. AR equations characterize positive and negative feedbacks regulating population dynamics. By using AR equations, up to 90% of population density variance can be taken into account. Stability margin, which is calculated from coefficients of AR models, has been proposed as a parameter to assess the stability of population dynamics. A small stability margin indicates a high risk of outbreak of an insect species.

Forced waves for a three-species predator-prey system with nonlocal dispersal in a shifting environment

We consider a three-species predator-prey system involving two competing predators and one prey. The species diffuse with nonlocal dispersal kernels with possibly non-compact support, and they interact in a heterogeneous environment moving with a positive forced speed such that the environment is favorable to the prey in the absence of predators far ahead of the shifting boundary and it is unfavorable far behind. Such systems arise in the modeling of population dynamics under the effect of a shifting environment, such as climate change. We show on the one hand the existence of waves connecting the trivial state to the unique constant positive co-existence state for any value of the forced speed. On the other hand, we show the existence of critical positive speeds for the existence of waves connecting the trivial state to the states corresponding to the absence of one or two predators.

Effects of early life mass mortality events on fish populations

AbstractMass mortality events are ubiquitous in nature and can be caused by, for example, diseases, extreme weather and human perturbations such as contamination. Despite being prevalent and rising globally, how mass mortality in early life causes population‐level effects such as reduced total population biomass, is not fully explored. In particular for fish, mass mortality affecting early life may be dampened by compensatory density‐dependent processes. However, due to large variations in year‐class strength, potentially caused by density‐independent variability in survival, the impact at the population level may be high in certain years. We quantify population‐level impacts at two levels of mass mortality (50% and 99% additional mortality) during early life across 40 fish species using age‐structured population dynamics models. The findings from these species‐specific models are further supported by an analysis of detailed stock‐specific models for three of the species. We find that population impacts are highly variable between years and species. Short‐lived species that exhibit a low degree of compensatory density dependence and high interannual variation in survival experience the strongest impacts at the population level. These quantitative and general relationships allow predicting the range of potential impacts of mass mortality events on species based on their life history. This is critical considering that the frequency and severity of mass mortality events are increasing worldwide.

Host plant status and damage threshold of spinach (Spinacia oleracea) for the temperate root-knot nematode Meloidogyne chitwoodi

Summary Problems with plant-parasitic nematodes remain a major challenge in most field vegetable crops worldwide. In agricultural fields in Belgium, these problems have increased in recent years. A major problem is the quarantine root-knot nematode Meloidogyne chitwoodi. The host plant status of the most commonly grown cultivars of spinach (Spinacia oleracea) and the damage threshold for M. chitwoodi were determined in a climate-controlled glasshouse and in a naturally infested field. The yield data with the final population densities were fitted to Seinhorst’s yield and population dynamic models, respectively. The damage threshold values (T) for the relative fresh weight yield were 0.14, 1.08, 11.53 J2 (100 cm3 soil)−1, minimum yield (m) of 0.84, 0.64, 0.52 and maximum yield () of 12.51, 12.44 and 9.60 for ‘Gnu’, ‘Meerkat’ and ‘Whale’ spinach cultivars, respectively. The maximum multiplication rates (a) were 3.81, 2.38 and 2.72, whilst the maximum population densities (M) were 563, 916, and 922 J2 (100 cm3 soil)−1 for ‘Gnu’, ‘Meerkat’ and ‘Whale’, respectively. Meloidogyne chitwoodi had an impact on the spinach yield. The higher the nematode density the lower the yield and vice versa. The tested cultivars were all hosts for M. chitwoodi but differences between cultivars occurred. ‘Kolibri’ and ‘Rhino’ were tested as the least sensitive cultivars for M. chitwoodi during the host screening test and bring opportunities for resistance breeding. This is the first report of spinach as a host for M. chitwoodi.