Density-dependent Rates Research Articles

A New Framework for Understanding Recombination-Limited Charge Extraction in Disordered Semiconductors.

Recombination of free charges is a key loss mechanism limiting the performance of organic semiconductor-based photovoltaics such as solar cells and photodetectors. The carrier density-dependence of the rate of recombination and the associated rate coefficients are often estimated using transient charge extraction (CE) experiments. These experiments, however, often neglect the effect of recombination during the transient extraction process. In this work, the validity of the CE experiment for low-mobility devices, such as organic semiconductor-based photovoltaics, is investigated using transient drift-diffusion simulations. We find that recombination leads to incomplete CE, resulting in carrier density-dependent recombination rate constants and overestimated recombination orders; an effect that depends on both the charge carrier mobilities and the resistance-capacitance time constant. To overcome this intrinsic limitation of the CE experiment, we present an analytical model that accounts for charge carrier recombination, validate it using numerical simulations, and employ it to correct the carrier density-dependence observed in experimentally determined bimolecular recombination rate constants.

A predator-prey fractional model with disease in the prey species.

In this paper, we study a generalized eco-epidemiological model of fractional order for the predator-prey type in the presence of an infectious disease in the prey. The proposed model considers that the disease infects the prey, causing them to be divided into two classes, susceptible prey and infected prey, with different density-dependent predation rates between the two classes. We propose logistic growth in both the prey and predator populations, and we also propose that the predators have alternative food sources (i.e., they do not feed exclusively on these prey). The model is evaluated from the perspective of the global and local generalized derivatives by using the generalized Caputo derivative and the generalized conformable derivative. The existence, uniqueness, non-negativity, and boundedness of the solutions of fractional order systems are demonstrated for the classical Caputo derivative. In addition, we study the stability of the equilibrium points of the model and the asymptotic behavior of its solution by using the Routh-Hurwitz stability criteria and the Matignon condition. Numerical simulations of the system are presented for both approaches (the classical Caputo derivative and the conformable Khalil derivative), and the results are compared with those obtained from the model with integro-differential equations. Finally, it is shown numerically that the introduction of a predator population in a susceptible-infectious system can help to control the spread of an infectious disease in the susceptible and infected prey population.

Empirical evidence of type III functional responses and why it remains rare

More than 70 years after its introduction, the framework of resource density-dependent consumption rates, also known as predator-prey functional responses, remains a core concept in population and food web ecology. Initially, three types of responses were defined: linear (type I), hyperbolic (type II), and sigmoid (type III). Due to its potential to stabilize consumer-resource population dynamics, the sigmoid type III functional response immediately became a “holy grail” in population ecology. However, experimentally proving that type III functional responses exist, whether in controlled laboratory systems or in nature, was challenging. While theoretical and practical advances make identifying type III responses easier today, decades of research have brought only a limited number of studies that provide empirical evidence for type III response curves. Here, we review this evidence from laboratory- and field-based studies published during the last two decades. We found 107 studies that reported type III responses, but these studies ranged across various taxa, interaction types, and ecosystems. To put these studies into context, we also discuss the various biological mechanisms that may lead to the emergence of type III responses. We summarize how three different and mutually independent intricacies bedevil the empirical documentation of type III responses: (1) challenges in statistical modeling of functional responses, (2) inadequate resource density ranges and spacing, and (3) biologically meaningful and realistic design of experimental arenas. Finally, we provide guidelines on how the field should move forward based on these considerations.

Macroenvironmental interactions as driving indicators for detecting tetracycline resistance spread among A. hydrophila exposure to environmentally relevant oxytetracycline levels

There have been efforts dedicating to investigating the effect of high levels of oxytetracycline (OTC) on tetracycline (TC) resistance among zoonotic pathogen Aeromonas hydrophila (AH), an antibiotic-resistant bacterial indicator. However, the dynamic behavior of TC-resistant AH in response to environmentally relevant OTC concentrations at a population-level has not been fully understood. Here we developed a bacterial population dynamic model to quantify TC-resistant AH posed by OTC-dependent resistance selection pressure. The key environmental factors known as water temperature, water activity, and pH were incorporated into model to produce pattern-oriented simulation outcomes. We estimated resistance acquisition number (R0) and showed that R0 was >1 at water temperature <26 °C, indicating coexistence of resistant- and susceptible-AH. Sensitivity tests revealed that cell density-dependent conjugation rate indicated crucial for influencing R0 estimation. Our results also indicated that maximum fraction of TC-resistant AH was mostly affected by temperature/activity in water and increased with increasing of OTC concentrations. We estimated OTC concentrations causing 50 % maximum fold-change of TC-resistant AH fraction ranging from 7 to 19 µg/L. Our findings suggest that control of TC resistance in AH requires particularly attention to water with temperature 26 °C lower, water activity 0.95 higher with pH ∼ 5–8. Our mechanistic framework provides a useful tool-kit to improve our understanding of the critical role of OTC stress-induced macroenvironmental interactions in a TC resistance − AH system and highlights the potential for antimicrobial management to promote resilience in aquatic ecosystems.

A time-periodic reaction-diffusion population model of a species subjected to harvesting on the boundary of a protected habitat

The objective in this paper is to determine analytically a maximally sustainable pro-rata density-dependent harvest rate of a hypothetical biological species on the spatial boundary of a protected habitat (i.e. no harvesting of the species is allowed in the interior of the spatial domain). This is achieved by analysing an initial-boundary value model involving a reaction-diffusion equation in which the reaction term is a concave function of the population density, depends periodically on time, and varies spatially. The model is equipped with Robin boundary conditions modelling a continuum of potential pro-rata density-dependent harvest rates on the spatial boundary. A set of necessary and sufficient criteria for the existence of a unique positive periodic attractor of solutions to the model is established by employing the theory of comparison principles and monotone iteration schemes. Thereafter, a long-time asymptotic analysis of the population density is undertaken by invoking classical results from the theory of eigenproblems. In this way, the aforementioned necessary and sufficient conditions are rendered more practical in terms of an upper bound on the maximal allowable pro-rata density-dependent harvest rate. Moreover, important properties of the time-periodic attractor of solutions are established to guarantee the existence of a density pro-rata harvest rate which maximises the total harvest per unit time at equilibrium.

Streamlining sporozoite isolation from mosquitoes by leveraging the dynamics of migration to the salivary glands

BackgroundSporozoites isolated from the salivary glands of Plasmodium-infected mosquitoes are a prerequisite for several basic and pre-clinical applications. Although salivary glands are pooled to maximize sporozoite recovery, insufficient yields pose logistical and analytical hurdles; thus, predicting yields prior to isolation would be valuable. Preceding oocyst densities in the midgut is an obvious candidate. However, it is unclear whether current understanding of its relationship with sporozoite densities can be used to maximize yields, or whether it can capture the potential density-dependence in rates of sporozoite invasion of the salivary glands.MethodsThis study presents a retrospective analysis of Anopheles stephensi mosquitoes infected with two strains of the rodent-specific Plasmodium berghei. Mean oocyst densities were estimated in the midguts earlier in the infection (11–15 days post-blood meal), with sporozoites pooled from the salivary glands later in the infection (17–29 days). Generalized linear mixed effects models were used to determine if (1) mean oocyst densities can predict sporozoite yields from pooled salivary glands, (2) whether these densities can capture differences in rates of sporozoite invasion of salivary glands, and (3), if the interaction between oocyst densities and time could be leveraged to boost overall yields.ResultsThe non-linear effect of mean oocyst densities confirmed the role of density-dependent constraints in limiting yields beyond certain oocyst densities. Irrespective of oocyst densities however, the continued invasion of salivary glands by the sporozoites boosted recoveries over time (17–29 days post-blood meal) for either parasite strain.ConclusionsSporozoite invasion of the salivary glands over time can be leveraged to maximize yields for P. berghei. In general, however, invasion of the salivary glands over time is a critical fitness determinant for all Plasmodium species (extrinsic incubation period, EIP). Thus, delaying sporozoite collection could, in principle, substantially reduce dissection effort for any parasite within the genus, with the results also alluding to the potential for changes in sporozoites densities over time to modify infectivity for the next host.

Long-term demographic dynamics of a keystone scavenger disrupted by human-induced shifts in food availability.

Scavenging is a key ecological process controlling energy flow in ecosystems and providing valuable ecosystem services worldwide. As long-lived species, the demographic dynamics of vultures can be disrupted by spatiotemporal fluctuations in food availability, with dramatic impacts on their population viability and the ecosystem services provided. In Europe, the outbreak of bovine spongiform encephalopathy (BSE) in 2001 prompted a restrictive sanitary regulation banning the presence of livestock carcasses in the wild on a continental scale. In long-lived vertebrate species, the buffering hypothesis predicts that the demographic traits with the largest contribution to population growth rate should be less temporally variable. The BSE outbreak provides a unique opportunity to test for the impact of demographic buffering in a keystone scavenger suffering abrupt but transient food shortages. We studied the 42-year dynamics (1979-2020) of one of the world's largest breeding colonies of Eurasian griffon vultures (Gyps fulvus). We fitted an inverse Bayesian state-space model with density-dependent demographic rates to the time series of stage-structured abundances to investigate shifts in vital rates and population dynamics before, during, and after the implementation of a restrictive sanitary regulation. Prior to the BSE outbreak the dynamics was mainly driven by adult survival: 83% of temporal variance in abundance was explained by variability in this rate. Moreover, during this period the regulation of population size operated through density-dependent fecundity and subadult survival. However, after the onset of the European ban, a 1-month delay in average laying date, a drop in fecundity, and a reduction in the number of fledglings induced a transient increase in the impact of fledgling and subadult recruitment on dynamics. Although adult survival rate remained constantly high, as predicted by the buffering hypothesis, its relative impact on the temporal variance in abundance dropped to 71% during the sanitary regulation and to 54% after the ban was lifted. A significant increase in the relative impact of environmental stochasticity on dynamics was modeled after the BSE outbreak. These results provide empirical evidence on how abrupt environmental deterioration may induce dramatic demographic and dynamic changes in the populations of keystone scavengers, with far-reaching impacts on ecosystem functioning worldwide.

Mass gain and stopover dynamics among migrating songbirds are linked to seasonal, environmental, and life-history effects

Abstract During migration, birds must stopover at refueling sites to replenish energy stores, with the rate of refueling linked to stopover length, migration speed, and the timing of critical life stages, such as breeding. Under optimal migration theory, birds are expected to maximize fuel intake and minimize stopover length (the time minimization hypothesis). Within a multi-species framework, we demonstrate that time minimization behavior is context-dependent, as refueling rate, stopover length, and departure decisions vary between seasons, among species with different ecological traits (e.g., diet and migration distance), and in response to density-dependent factors and prevailing environmental conditions. Using long-term banding data (10 years) from southwestern British Columbia, Canada, we investigated the ecological processes shaping stopover dynamics among 5 warbler (Parulidae) and 5 sparrow species (Passerellidae). Specifically, we assessed variation in fuel deposition rates (FDRs) as well as the associations between mass gain, stopover length, and departure probability. FDR was greater in insectivorous warblers during spring migration and in species migrating long distances. FDR responded positively to temperature and habitat productivity, but negatively to precipitation events, particularly for insectivorous, long-distance migrants during spring migration. Similarly, density-dependent refueling rate was only observed in insectivores and long-distance migrants during spring migration, where higher densities of foliage-gleaning insectivores were associated with a lower FDR. Stopover duration was more closely associated with body condition upon arrival and subsequent mass gain than direct environmental effects, especially during northward spring migration, providing support for time minimization and a mass threshold influencing departure decisions. These results highlight that refueling rates and stopover quality vary among species depending on their life-history strategies, with particular implications for long-distance, migratory insectivores, which may be most susceptible to climate shifts.

Spatial patterns in ecological systems: from microbial colonies to landscapes.

Self-organized spatial patterns are ubiquitous in ecological systems and allow populations to adopt non-trivial spatial distributions starting from disordered configurations. These patterns form due to diverse nonlinear interactions among organisms and between organisms and their environment, and lead to the emergence of new (eco)system-level properties unique to self-organized systems. Such pattern consequences include higher resilience and resistance to environmental changes, abrupt ecosystem collapse, hysteresis loops, and reversal of competitive exclusion. Here, we review ecological systems exhibiting self-organized patterns. We establish two broad pattern categories depending on whether the self-organizing process is primarily driven by nonlinear density-dependent demographic rates or by nonlinear density-dependent movement. Using this organization, we examine a wide range of observational scales, from microbial colonies to whole ecosystems, and discuss the mechanisms hypothesized to underlie observed patterns and their system-level consequences. For each example, we review both the empirical evidence and the existing theoretical frameworks developed to identify the causes and consequences of patterning. Finally, we trace qualitative similarities across systems and propose possible ways of developing a more quantitative understanding of how self-organization operates across systems and observational scales in ecology.

Mathematical modeling and projections of a vector-borne disease with optimal control strategies: A case study of the Chikungunya in Chad

In this work, we extend existing models of vector-borne diseases by including density-dependent rates and some existing control mechanisms to decrease the disease burden in the human population. We begin by analyzing the vector model dynamics and by determining the offspring reproductive number denoted by N as well as the trivial and nontrivial equilibria. Using theory of cooperative systems and the general theory of Lyapunov, we prove that, although there is a possibility that the trivial equilibrium coexists with a positive equilibrium, it remains globally asymptotically stable whenever N ≤ 1 . The fact that the non-trivial equilibrium is globally asymptotically stable permits us to reduce the study of the full model to the study of a reduced model whenever N > 1 . Thus, we analyze the reduced model by computing the basic reproduction number R 0 , equilibrium points as well as asymptotic stability of each equilibrium point. We also explore the nature of the bifurcation for the disease-free equilibrium from R 0 = 1 . By the application of the centre manifold theory, we prove that the backward bifurcation phenomenon can occur in our model, which means that the necessary condition R 0 < 1 is not sufficient to guarantee the final extinction of the disease in human populations. To calibrate our model, we estimate model parameters on clinical data from the last Chikungunya epidemic which occurred in Chad, using the non-linear least-square method. We find out that R 0 = 1.8519 , which means that we are in an endemic state since R 0 > 1 . To determine model parameters that are responsible for disease spread in the human community, we perform sensitivity analysis (SA) using a global method. It follows that the density-dependent death rate of mosquitoes and the average number of mosquito bites are key parameters in the disease dynamics. Following this, we thus formulate an optimal control model by including in the autonomous model, four time-dependent control functions to fight the disease spread. Pontryagin’s maximum principle is used to characterize our optimal controls. Numerical simulations, using parameter values of Chikungunya transmission dynamics, and efficiency analysis, are conducted to determine the better control strategy which guaranteed the final extinction of the disease in human populations.

Stochastic dynamics of predator-prey interactions.

The interaction between a consumer (such as, a predator or a parasitoid) and a resource (such as, a prey or a host) forms an integral motif in ecological food webs, and has been modeled since the early 20th century starting from the seminal work of Lotka and Volterra. While the Lotka-Volterra predator-prey model predicts a neutrally stable equilibrium with oscillating population densities, a density-dependent predator attack rate is known to stabilize the equilibrium. Here, we consider a stochastic formulation of the Lotka-Volterra model where the prey’s reproduction rate is a random process, and the predator’s attack rate depends on both the prey and predator population densities. Analysis shows that increasing the sensitivity of the attack rate to the prey density attenuates the magnitude of stochastic fluctuations in the population densities. In contrast, these fluctuations vary non-monotonically with the sensitivity of the attack rate to the predator density with an optimal level of sensitivity minimizing the magnitude of fluctuations. Interestingly, our systematic study of the predator-prey correlations reveals distinct signatures depending on the form of the density-dependent attack rate. In summary, stochastic dynamics of nonlinear Lotka-Volterra models can be harnessed to infer density-dependent mechanisms regulating predator-prey interactions. Moreover, these mechanisms can have contrasting consequences on population density fluctuations, with predator-dependent attack rates amplifying stochasticity, while prey-dependent attack rates countering to buffer fluctuations.

An abstract mathematical model for sustainable harvesting of a biological species on the boundary of a protected habitat

The objective in this paper is to determine analytically the maximally sustainable pro-rata density-dependent harvest rate of a hypothetical biological species on the spatial boundary of its habitat, which is otherwise a protected zone (i.e. no harvesting of the species is allowed in the interior of its habitat). This is achieved by analysing an abstract mathematical model for the spatio-temporal evolution of the species density over its habitat if it is subjected to a continuum of potential pro-rata density-dependent harvest rates on the spatial boundary. The model takes the form of an initial-boundary value problem involving a reaction-diffusion equation in which the reaction term is a concave function of the population density and Robin boundary conditions are prescribed. A long-time asymptotic analysis of the population density is undertaken by invoking classical results from the theory of eigenproblems. In this way, necessary and sufficient conditions on the pro-rata density-dependent harvest rate are established for the existence of a strictly positive equilibrium attractor of model solutions. Moreover, important necessary properties of this equilibrium attractor are established to guarantee the existence of a density pro-rata harvest rate which maximises the total harvest per unit time at equilibrium.

Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics.

Stability analysis of an autonomous epidemic model of an age-structured sub-populations of susceptible, infected, precancerous and cancer cells and unstructured sub-population of human papilloma virus (HPV) (SIPCV epidemic model) aims to gain an insight into the features of cervical cancer disease. The model considers the immune functional response of organism to the virus population growing by the HPV-density dependent death rate, while the death rates of infected, precancerous and cancerous cells do not depend on the HPV quantity because the immune system of organism does not respond to its own cells. Interaction between susceptible cells and HPV is described by the Lotka-Voltera incidence rate and leads to the growth of infected cells. Some of infected cells become precancerous cells, and the other apoptosis when viruses leave infected cells and are ready to infect new susceptible cells. Precancerous cells partially become cancer cells with the density-dependent saturated rate. Conditions of existence of the endemic equilibrium of system were obtained. It was proved that this equilibrium is always locally asymptotically stable whenever it exists. We obtained: (i) the conditions of cancer tumor localization (asymptotically stable dynamical regimes), (ii) outbreak of cancer cell population (that may correspond to metastasis), (iii) outbreak of dysplasia (precancerous cells) which induces the outbreak of cancer cells (that may correspond to metastasis). In cases (ii), (iii) the conditions of existence of endemic equilibrium do not hold. All cases are illustrated by numerical experiments.

A General Theoretical Framework to Study the Influence of Electrical Fields on Mesenchymal Stem Cells.

Mesenchymal stem cell dynamics involve cell proliferation and cell differentiation into cells of distinct functional type, such as osteoblasts, adipocytes, or chondrocytes. Electrically active implants influence these dynamics for the regeneration of the cells in damaged tissues. How applied electric field influences processes of individual stem cells is a problem mostly unaddressed. The mathematical approaches to study stem cell dynamics have focused on the stem cell population as a whole, without resolving individual cells and intracellular processes. In this paper, we present a theoretical framework to describe the dynamics of a population of stem cells, taking into account the processes of the individual cells. We study the influence of the applied electric field on the cellular processes. We test our mean-field theory with the experiments from the literature, involving in vitro electrical stimulation of stem cells. We show that a simple model can quantitatively describe the experimentally observed time-course behavior of the total number of cells and the total alkaline phosphate activity in a population of mesenchymal stem cells. Our results show that the stem cell differentiation rate is dependent on the applied electrical field, confirming published experimental findings. Moreover, our analysis supports the cell density-dependent proliferation rate. Since the experimental results are averaged over many cells, our theoretical framework presents a robust and sensitive method for determining the effect of applied electric fields at the scale of the individual cell. These results indicate that the electric field stimulation may be effective in promoting bone regeneration by accelerating osteogenic differentiation.

Boundedness in a three-dimensional Keller–Segel–Stokes system with subcritical sensitivity

We consider a quasilinear Keller–Segel system with density-dependent migration rates, coupled to the incompressible Stokes equations through transport and buoyancy. By means of an apparently novel approach based on certain conditional estimates for the taxis gradient and the fluid field, for diffusion rates asymptotically controllable by power-tape majorants and minorants a result on global existence and boundedness is derived under an essentially optimal condition on the strength of cross-diffusion relative to diffusion.

A moving boundary problem with space-fractional diffusion logistic population model and density-dependent dispersal rate

In this article, we discuss a space-fractional diffusion logistic population model with Caputo fractional derivative and density-dependent dispersal rate. The numerical solution of the problem is obtained by using a finite difference scheme. The consistency and stability of the scheme for our solution to the problem are also discussed. The effect of the density-dependent dispersal rate and order of the space-fractional derivative are analyzed for the population density and expanding front (moving boundary).

Nonlinear Effects of Intraspecific Competition Alter Landscape-Wide Scaling Up of Ecosystem Function.

A major focus of ecology is to understand and predict ecosystem function across scales. Many ecosystem functions are measured only at local scales, while their effects occur at a landscape level. Here we investigate how landscape-scale predictions of ecosystem function depend on intraspecific competition, a fine-scale process, by manipulating intraspecific density of shredding macroinvertebrates and examining effects on leaf litter decomposition, a key function in freshwater ecosystems. For two species, we found that per capita leaf processing rates declined with increasing density following power functions with negative exponents, likely due to interference competition. To demonstrate consequences of this nonlinearity, we scaled up estimates of leaf litter processing from shredder abundance surveys in 10 replicated headwater streams. In accordance with Jensen's inequality, applying density-dependent consumption rates reduced estimates of catchment-scale leaf consumption by an order of magnitude relative to density-independent rates. Density-dependent consumption estimates aligned closely with metabolic requirements in catchments with large-but not small-shredder populations. Importantly, shredder abundance was not limited by leaf litter availability, and catchment-level leaf litter supply was much higher than estimated consumption. Thus leaf litter processing was not limited by resource supply. Our work highlights the need for scaling up, which accounts for intraspecific interactions.

Informing Amphibian Conservation Efforts with Abundance-Based Metapopulation Models

Science-based management strategies are needed to halt or reverse the global decline of amphibians. In many cases, sound management requires reliable models built using monitoring data. Historically, monitoring and statistical modeling efforts have focused on estimating occupancy using detection–nondetection data. Spatial occupancy models are useful for studying colonization–extinction dynamics, but richer insights can be gained from estimating abundance and density-dependent demographic rates. We developed an integrated abundance-based metapopulation model of the processes contributing to spatiotemporal variation in patch population density. We fit our model to a combination of detection–nondetection and count data from a 14-yr study of a reintroduced metapopulation of federally threatened Chiricahua Leopard Frogs (Lithobates chiricahuensis). Pond-specific population growth rate was influenced by pond hydroperiod and frog density, such that permanent and semipermanent ponds with low densities of adult frogs experienced the highest annual population growth rates. Immigration rate declined as the distance among ponds increased. After reintroduction in 2003, metapopulation-level abundance increased and appeared to stabilize around 1300 adult frogs (95% CI = 1192–1471) by year 2015. Further, changes in metapopulation abundance were driven mostly by changes in abundance at a few ponds. These high-density populations, which would not have been identifiable with traditional occupancy-based metapopulation models, are likely especially important for species recovery in the area. Abundance-based metapopulation models can be widely applied to inform conservation efforts, by providing higher quality information needed to prioritize habitat patches for management and can be used to make more accurate predictions of metapopulation extinction risk.

A Lyapunov–Schmidt method for detecting backward bifurcation in age-structured population models

Backward bifurcation is an important property of infectious disease models. A centre manifold method has been developed by Castillo-Chavez and Song for detecting the presence of backward bifurcation and deriving a necessary and sufficient condition for its occurrence in Ordinary Differential Equations (ODE) models. In this paper, we extend this method to partial differential equation systems. First, we state a main theorem. Next we illustrate the application of the new method on a chronological age-structured Susceptible-Infected-Susceptible (SIS) model with density-dependent recovery rate, an age-since-infection structured HIV/AIDS model with standard incidence and an age-since-infection structured cholera model with vaccination.

Dynamical analysis of mathematical model for Bovine Tuberculosis among human and cattle population

Bovine Tuberculosis (BTB) is a disease that can attack humans through cattle.The process of transmission can occur through the air and cattle products that are not treated properly. When humans are infected with BTB, reinfection, and relapse may occur. This phenomenon is modeled as an eleven-dimension dynamical system. Our aim is to gain insight into the effect of separation of human activity area into the transmission dynamics of BTB. The model incorporates (among many others features) the dynamics of BTB among human and cattle population, density-dependent infection rate, and reinfection, are rigorously analyzed and simulated. The trivial disease-free equilibrium of the model is shown to be locally asymptotically stable when the two associated basic reproduction number are less than unity. Although the non-trivial equilibrium cannot be shown explicitly, for a special case, this equilibrium is still possible to show and discuss further. Our results suggest that controlling BTB in cattle population may indirectly control the spread of BTB in human. An example of controlling the infected population of infected cattle can be done with the annihilation of infected cattle.