Per-capita Growth Rate Research Articles

Impact of Nanomaterial in the Marine Environment: Through Mathematical Modelling by Eco-Path Framework

We propose and analyze a simple modification to the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model to account for the interference of the predators with the impacts of nanoparticles. We have taken into account the influence of predators by quantifying the impact of nanoparticles in actual environments. It is shown that the influence of the nanoparticles may reduce the prey's maximum physiological per-capita growth rate. An elementary Lotka-Volterra uptake term is taken into consideration in order to investigate the nanoparticle dynamics or interactions. Most importantly, our research shows that phytoplankton growth suppression caused by nanoparticles can destabilize the system and cause periodic oscillation. Additionally, it was demonstrated that a decrease in the equilibrium densities of both phytoplankton and zooplankton might occur from an increase in the rate of interaction between the nanoparticles and phytoplankton. Additionally, the study shows that the stable coexistence of the system dynamics depends critically on the aquatic system's nanoparticles being depleted. We also looked into the system using different kinds of functional reactions. Compared to other commonly used ecology, The complex relationship that exists between phytoplankton and nanoparticles in the natural environment is better described by the Monod-Haldane functional response.

Thermodynamic dissipation does not bound replicator growth and decay rates

In a well-known paper, Jeremy England derived a bound on the free energy dissipated by a self-replicating system [J. L. England, “Statistical physics of self-replication,” J. Chem. Phys. 139, 121923 (2013)]. This bound is usually interpreted as a universal relationship that connects thermodynamic dissipation to replicator per-capita decay and growth rates. We argue from basic thermodynamic principles against this interpretation. In fact, we suggest that such a relationship cannot exist in principle, because it is impossible for a thermodynamically consistent replicator to undergo both per-capita growth and per-capita decay back into reactants. Instead, replicator may decay into separate waste products, but in that case, replication and decay are two independent physical processes, and there is no universal relationship that connects their thermodynamic and dynamical properties.

Demographic effects of aggregation in the presence of a component Allee effect.

The component Allee effect (AE) is the positive correlation between an organism's fitness component and population density. Depending on the population spatial structure, which determines the interactions between organisms, a component AE might lead to positive density dependence in the population per-capita growth rate and establish a demographic AE. However, existing spatial models impose a fixed population spatial structure, which limits the understanding of how a component AE and spatial dynamics jointly determine the existence of demographic AEs. We introduce a spatially explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. This framework predicts various spatial patterns depending on its specific parametrization, including evenly spaced aggregates of organisms, which determine the demographic-level by-products of the component AE. We find that aggregation increases population abundance and allows population survival in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component AE from manifesting at the population level or restrict it to the level of each independent aggregate. These results provide a mechanistic understanding of how component AEs might operate for different spatial structures and manifest at larger scales.

Cultural transmission, competition for prey, and the evolution of cooperative hunting

Although cooperative hunting is widespread among animals, its benefits are unclear. At low frequencies, cooperative hunting may allow predators to escape competition and access bigger prey that could not be caught by a lone cooperative predator. Cooperative hunting is a more successful strategy when it is common, but its spread can result in overhunting big prey, which may have a lower per-capita growth rate than small prey. We construct a one-predator species, two-prey species model in which predators either learn to hunt small prey alone or learn to hunt big prey cooperatively. Predators first learn vertically from parents, then horizontally (i.e. socially) from random individuals or siblings. After horizontal transmission, they hunt with their learning partner if both are cooperative, and otherwise they hunt alone. Cooperative hunting cannot evolve when initially rare unless predators (a) interact with siblings, or (b) horizontally transmit the cooperative behavior to potential hunting partners. Whereas competition for small prey favors cooperative hunting when this cooperation is initially rare, the frequency of cooperative hunting cannot reach 100% unless big prey is abundant. Furthermore, a mutant that increases horizontal learning can invade if cooperative hunting is present, but not at 100%, because horizontal learning allows pairs of predators to have the same strategy. Our results reveal that the interactions between prey availability, social learning, and degree of cooperation among predators may have important effects on ecosystems.

Africa's Great Moderation

Abstract Over the past 30 years, African economies have experienced remarkable improvements in macroeconomic conditions, characterised by higher and more stable real per-capita growth rates and lower and more stable inflation. This paper documents the persistent decline in macroeconomic volatility at the aggregate and sectoral levels and seeks to provide explanations. Sectoral analysis shows a particularly strong reduction of growth volatility in agriculture and, to a lesser extent, in services. Classical structural change only explains a small fraction of the moderation. Analysis of further factors yields that changes in structural characteristics such as institutions, trade intensity and diversification, natural resource dependence or conflict incidence do not explain the moderation. On the positive side, the paper provides evidence to suggest that changes in the external environment, improved macroeconomic policy frameworks and ‘softer’ structural improvements, such as the deepening of the domestic financial sector, were important in reducing macroeconomic volatility on the continent.

Modelling the historic total global human population

The historic total global human population dataset is available on Wikipedia and provides an opportunity for modelling with simple models such as the exponential and logistic differential equations for population. Using the per-capita population growth rate (PPGR) predicted by these two models and estimated PPGR from the data, we are able to estimate parameters for the exponential model and discover that we cannot estimate parameters for the logistic model. However, we are able to create a new differential equation that models this data using ideas from the derivation of the logistic model. This is the superexponential model that goes to infinity in finite time. While the initial exponential and superexponential models are good for approximating the population data, neither really matches the PPGRs estimated from the data. We switch to a hybrid model that better matches the estimated PPGRs. It is superexponential for the first portion of the data and logistic for the rest. This hybrid model greatly reduces the modelling error and can extrapolate from the data. We note that the model switches between superexponential and logistic around 1960, the year the FDA-approved oral contraceptives, a fascinating historical tie-in with our modelling.

Building modern coexistence theory from the ground up: The role of community assembly.

Modern coexistence theory (MCT) is one of the leading methods to understand species coexistence. It uses invasion growth rates-the average, per-capita growth rate of a rare species-to identify when and why species coexist. Despite significant advances in dissecting coexistence mechanisms when coexistence occurs, MCT relies on a 'mutual invasibility' condition designed for two-species communities but poorly defined for species-rich communities. Here, we review well-known issues with this component of MCT and propose a solution based on recent mathematical advances. We propose a clear framework for expanding MCT to species-rich communities and for understanding invasion resistance as well as coexistence, especially for communities that could not be analysed with MCT so far. Using two data-driven community models from the literature, we illustrate the utility of our framework and highlight the opportunities for bridging the fields of community assembly and species coexistence.

A global perspective on the intrinsic dimensionality of COVID-19 data

We develop a novel global perspective of the complexity of the relationships between three COVID-19 datasets, the standardised per-capita growth rate of COVID-19 cases and deaths, and the Oxford Coronavirus Government Response Tracker COVID-19 Stringency Index (CSI) which is a measure describing a country’s stringency of lockdown policies. We use a state-of-the-art heterogeneous intrinsic dimension estimator implemented as a Bayesian mixture model, called Hidalgo. Our findings suggest that these highly popular COVID-19 statistics may project onto two low-dimensional manifolds without significant information loss, suggesting that COVID-19 data dynamics are generated from a latent mechanism characterised by a few important variables. The low dimensionality imply a strong dependency among the standardised growth rates of cases and deaths per capita and the CSI for countries over 2020–2021. Importantly, we identify spatial autocorrelation in the intrinsic dimension distribution worldwide. The results show how high-income countries are more prone to lie on low-dimensional manifolds, likely arising from aging populations, comorbidities, and increased per capita mortality burden from COVID-19. Finally, the temporal stratification of the dataset allows the examination of the intrinsic dimension at a more granular level throughout the pandemic.

Nutrients strengthen density dependence of per-capita growth and mortality rates in the soil bacterial community.

Density dependence in an ecological community has been observed in many macro-organismal ecosystems and is hypothesized to maintain biodiversity but is poorly understood in microbial ecosystems. Here, we analyze data from an experiment using quantitative stable isotope probing (qSIP) to estimate per-capita growth and mortality rates of bacterial populations in soils from several ecosystems along an elevation gradient which were subject to nutrient addition of either carbon alone (glucose; C) or carbon with nitrogen (glucose + ammonium-sulfate; C + N). Across all ecosystems, we found that higher population densities, quantified by the abundance of genomes per gram of soil, had lower per-capita growth rates in C + N-amended soils. Similarly, bacterial mortality rates in C + N-amended soils increased at a significantly higher rate with increasing population size than mortality rates in control and C-amended soils. In contrast to the hypothesis that density dependence would promote or maintain diversity, we observed significantly lower bacterial diversity in soils with stronger negative density-dependent growth. Here, density dependence was significantly but weakly responsive to nutrients and was not associated with higher bacterial diversity.

Permanence via invasion graphs: incorporating community assembly into modern coexistence theory

To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to average per-capita growth rates of one species with respect to an ergodic measure supporting other species. In the ecological literature, coexistence often is equated with the invasion growth rates being positive. Intuitively, positive invasion growth rates ensure that species recover from being rare. To provide a mathematically rigorous framework for this approach, we prove theorems that answer two questions: (i) When do the signs of the invasion growth rates determine coexistence? (ii) When signs are sufficient, which invasion growth rates need to be positive? We focus on deterministic models and equate coexistence with permanence, i.e., a global attractor bounded away from extinction. For models satisfying certain technical assumptions, we introduce invasion graphs where vertices correspond to proper subsets of species (communities) supporting an ergodic measure and directed edges correspond to potential transitions between communities due to invasions by missing species. These directed edges are determined by the signs of invasion growth rates. When the invasion graph is acyclic (i.e. there is no sequence of invasions starting and ending at the same community), we show that permanence is determined by the signs of the invasion growth rates. In this case, permanence is characterized by the invasibility of all -i communities, i.e., communities without species i where all other missing species have negative invasion growth rates. To illustrate the applicability of the results, we show that dissipative Lotka-Volterra models generically satisfy our technical assumptions and computing their invasion graphs reduces to solving systems of linear equations. We also apply our results to models of competing species with pulsed resources or sharing a predator that exhibits switching behavior. Open problems for both deterministic and stochastic models are discussed. Our results highlight the importance of using concepts about community assembly to study coexistence.

Extrapolating Contaminant Effects from Individuals to Populations: A Case Study on Nanoparticle Toxicity to Daphnia Fed Environmentally Relevant Food Levels

Ecological risk assessment (ERA) is charged with assessing the likelihood a chemical will have adverse environmental or ecological effects. When assessing the risk of a potential contaminant to biological organisms, ecologists are most concerned with the sustainability of populations of organisms, rather than protecting every individual. However, ERA most commonly relies on data on the effect of a potential contaminant on individuals because these experiments are more feasible than costly population-level exposures. In this work, we address the challenge of extrapolating these individual-level results to predict population-level effects. Previous per-capita population growth rate estimates calculated from individual-level exposures of Daphnia pulicaria to silver nanoparticles (AgNPs) at different food rations predict a critical daily food requirement for daphnid populations exposed to 200μg/L AgNPs to avoid extinction. To test this, we exposed daphnid populations to the same AgNP concentration at three different food inputs, with the lowest ration close to the extinction threshold predicted from data on individuals. The two populations with the higher food inputs persisted, and the population with the lowest food input went extinct after 50days but did persist through two generations. We demonstrate that we can extrapolate between these levels of biological organization by parameterizing an individual-level biomass model with data on individuals' response to AgNPs and using these parameters to predict the outcome for control and AgNP-exposed populations. Key to successful extrapolation is careful modeling of temporal changes in resource density, driven by both the experimental protocols and feedback from the consumer. The implication for ecotoxicology is that estimates of extinction thresholds based on studies of individuals may be reliable predictors of population outcomes, but only with careful treatment of resource dynamics.

A classification of the dynamics of three-dimensional stochastic ecological systems

The classification of the long-term behavior of dynamical systems is a fundamental problem in mathematics. For both deterministic and stochastic dynamics specific classes of models verify Palis’ conjecture: the long-term behavior is determined by a finite number of stationary distributions. In this paper we consider the classification problem for stochastic models of interacting species. For a large class of three-species, stochastic differential equation models, we prove a variant of Palis’ conjecture: the long-term statistical behavior is determined by a finite number of stationary distributions and, generically, three general types of behavior are possible: 1) convergence to a unique stationary distribution that supports all species, 2) convergence to one of a finite number of stationary distributions supporting two or fewer species, 3) convergence to convex combinations of single species, stationary distributions due to a rock-paper-scissors type of dynamic. Moreover, we prove that the classification reduces to computing Lyapunov exponents (external Lyapunov exponents) that correspond to the average per-capita growth rate of species when rare. Our results stand in contrast to the deterministic setting where the classification is incomplete even for three-dimensional, competitive Lotka–Volterra systems. For these SDE models, our results also provide a rigorous foundation for ecology’s modern coexistence theory (MCT) which assumes the external Lyapunov exponents determine long-term ecological outcomes.

Long-term monitoring of two endangered freshwater mussels (Bivalvia: Unionidae) reveals how demographic vital rates are influenced by species life history traits.

To meet monitoring and recovery planning needs, demographic vital rates of two endangered freshwater mussels (Bivalvia: Unionidae)-the Cumberlandian Combshell (Epioblasma brevidens, Lea 1831) and Oyster Mussel (Epioblasma capsaeformis, Lea 1834), species endemic to the Tennessee and Cumberland river basins, U.S.A-were estimated and compared using census methodologies. Annual variation in population density and size, recruitment rate, mortality rate, sex ratios, and female fecundity of both species were observed from 2004-2014 at three fixed sites, spanning a 33.8 kilometer (KM) reach of the Clinch River, Hancock County, Tennessee. Mean population size of E. brevidens estimated from 11 censuses was 2,598 individuals at Swan Island (KM 277.1), 8,744 at Frost Ford (KM 291.8), and 879 at Wallen Bend (KM 309.6); collectively, these demes grew at an annual rate of 7% over the study period. Mean population size of E. capsaeformis was 7,846 individuals at Swan Island, 265,442 at Frost Ford, and 11,704 at Wallen Bend; collectively, these demes grew at an annual rate of 6%. Population size, variability in population growth, recruitment, and mortality of the shorter-lived E. capsaeformis (maximum age = 16 yrs, rarely >10 yrs) were higher than those of the longer-lived E. brevidens (maximum age = 25 yrs). Stream discharge was associated with realized per-capita population growth rate for both species when juvenile (Ages 1-3) data was included. Linear regression analysis showed that the growth rate of E. brevidens was negatively associated with median annual discharge (p = 0.0274) and that growth rate of E. capsaeformis was negatively associated with the number of days having extreme high discharge preceding a census (p = 0.0381). Fecundity of female E. brevidens averaged 34,947 (SE = 2,492) glochidia and ranged from 18,987 to 56,151, whereas fecundity of female E. capsaeformis averaged 9,558 (SE = 603) glochidia and ranged from 3,456 to 22,182. Estimated vital rates indicated that the two species are characterized by different life-history strategies, with E. brevidens exhibiting a periodic strategy (between K- and r-selected) and E. capsaeformis an opportunistic strategy (r-selected). These life history strategies are likely influenced by each species' longevity and habitat preference, in addition to the life histories and population dynamics of their primary fish hosts.

On a reaction–diffusion system of flocculation type

This paper is devoted to the mathematical analysis of a flocculation system that arises in biology. Under certain sufficient conditions, we first establish a few global existence results corresponding, respectively, to the cases of bounded rates and non-monotonic per-capita growth rates as well as to that of unbounded flocculation rates by using Monod-type growth functions. We then focus on the behaviour of the time-dependent solutions, and prove the stability of the trivial solution and the existence of a non-trivial, positive steady state. We also examine the role played by the parameters of the model. Our arguments rely on the invariant region method, fixed point theory, and spectral theory. Finally, we provide some numerical simulations for different values of the diffusion coefficients to show that the competition between species does not depend on the diffusion of nutrients.

Invasive dynamics for a predator–prey system with Allee effect in both populations and a special emphasis on predator mortality

We considered a non-linear predator–prey model with an Allee effect on both populations on a two spatial dimension reaction-diffusion setup. Special importance to predator mortality was given as it may be often controlled through human-made harvesting processes. The local dynamics of the model was studied through boundedness, equilibrium, and stability analysis. An extensive numerical stability analysis was performed and found that bi-stability is not possible for the non-spatial model. By analyzing the spatial model, we found the condition for successful invasion and the persistence region of the species based on the predator Allee effect and its mortality parameter. Four different dynamics in this region of the parameter space are mainly explored. First, the Allee effect on both populations leads to various new types of species spread. Second, for a high value of per-capita growth rate, two completely new spreads (e.g., sun surface, colonial) have been found depending on the Allee effect parameter. Third, the Allee coefficient on the predator population leads to spatiotemporal chaos via a patchy spread for both linear and quadratic mortality rates. Finally, a more rigorous analysis is performed to study the chaotic nature of the system within the whole persistence domain. We have studied the possibility of chaos through temporal variation in different invasion regions. Furthermore, the chaotic fluctuation is studied through the sensitivity of initial conditions and by investigating the dominant Lyapunov exponent value.

Delay in budget allocation for vaccination and awareness induces chaos in an infectious disease model

In this paper, we propose a model to assess the impacts of budget allocation for vaccination and awareness programs on the dynamics of infectious diseases. The budget allocation is assumed to follow logistic growth, and its per capita growth rate increases proportional to disease prevalence. An increment in per-capita growth rate of budget allocation due to increase in infected individuals after a threshold value leads to onset of limit cycle oscillations. Our results reveal that the epidemic potential can be reduced or even disease can be eradicated through vaccination of high quality and/or continuous propagation of awareness among the people in endemic zones. We extend the proposed model by incorporating a discrete time delay in the increment of budget allocation due to infected population in the region. We observe that multiple stability switches occur and the system becomes chaotic on gradual increase in the value of time delay.

The P^* rule in the stochastic Holt-Lawton model of apparent competition

<p style='text-indent:20px;'>In 1993, Holt and Lawton introduced a stochastic model of two host species parasitized by a common parasitoid species. We introduce and analyze a generalization of these stochastic difference equations with any number of host species, stochastically varying parasitism rates, stochastically varying host intrinsic fitnesses, and stochastic immigration of parasitoids. Despite the lack of direct, host density-dependence, we show that this system is dissipative i.e. enters a compact set in finite time for all initial conditions. When there is a single host species, stochastic persistence and extinction of the host is characterized using external Lyapunov exponents corresponding to the average per-capita growth rates of the host when rare. When a single host persists, say species <inline-formula><tex-math id="M3">\begin{document}$ i $\end{document}</tex-math></inline-formula>, a explicit expression is derived for the average density, <inline-formula><tex-math id="M4">\begin{document}$ P_i^* $\end{document}</tex-math></inline-formula>, of the parasitoid at the stationary distributions supporting both species. When there are multiple host species, we prove that the host species with the largest <inline-formula><tex-math id="M5">\begin{document}$ P_i^* $\end{document}</tex-math></inline-formula> value stochastically persists, while the other host species are asymptotically driven to extinction. A review of the main mathematical methods used to prove the results and future challenges are given.

Scientific and Innovative Aspects of Regional Economic Development

Innovation-driven development of the Russian economy requires a consistent national policy aimed at boosting scientific and innovative activity in the regions, which would facilitate the development of entrepreneurship and technology. It also plays an important role in ensuring the socio-economic progress of the regions and efficiency of income distribution.Aim. The presented study aims to examine the potential directions for optimizing scientific and innovative activity in regional socio-economic development and to identify factors that facilitate the intensification of innovative activity in the regions.Tasks. The authors conduct a correlation analysis between scientific and economic development of the regions with allowance for such factors as the level of education of the population and the number of researchers engaged in research and development (R&amp;D). They also assess the current state of scientific and innovative activity and the national policy on the formation of the scientific and innovative potential of the regions.Methods. The methodological basis of the study of the scientific and innovative aspects of regional economic development includes correlation-regression analysis and abstract logical methods.Results. This study substantiates the role of scientific and innovative activity in regional economic development; determines a positive correlation between regional economic growth and the number of researchers; establishes an inverse correlation between scientific and economic development based on the dependence of innovative activity in the regions on the accumulated scientific potential; empirically assesses the impact of innovative factors on regional economic growth and proposes directions for improving the efficiency of the regional system of science and innovation.Conclusions. Concentrations of knowledge are analyzed as agglomerations of expenses on research and development, science and technology. This leads to an increase in the number of scientists, engineers, scientific and technological personnel of innovative enterprises in various Russian regions. A correlation analysis between scientific and economic regional development shows that per-capita GRP growth rate by the number of researchers is statistically significant, which means there are several factors affecting this dependence: geographical accessibility of higher education, university expenses on infrastructure and services, job creation, additional revenue from students from other countries and regions. It is established that efficient regional higher education systems and innovative development have a positive effect on regional economic development. The conducted analysis shows that a policy on the innovative development of resource regions should be based on government support that would facilitate the creation of innovations and strengthening of scientific potential.

The competitive exclusion principle in stochastic environments.

In its simplest form, the competitive exclusion principle states that a number of species competing for a smaller number of resources cannot coexist. However, it has been observed empirically that in some settings it is possible to have coexistence. One example is Hutchinson's 'paradox of the plankton'. This is an instance where a large number of phytoplankton species coexist while competing for a very limited number of resources. Both experimental and theoretical studies have shown that temporal fluctuations of the environment can facilitate coexistence for competing species. Hutchinson conjectured that one can get coexistence because nonequilibrium conditions would make it possible for different species to be favored by the environment at different times. In this paper we show in various settings how a variable (stochastic) environment enables a set of competing species limited by a smaller number of resources or other density dependent factors to coexist. If the environmental fluctuations are modeled by white noise, and the per-capita growth rates of the competitors depend linearly on the resources, we prove that there is competitive exclusion. However, if either the dependence between the growth rates and the resources is not linear or the white noise term is nonlinear we show that coexistence on fewer resources than species is possible. Even more surprisingly, if the temporal environmental variation comes from switching the environment at random times between a finite number of possible states, it is possible for all species to coexist even if the growth rates depend linearly on the resources. We show in an example (a variant of which first appeared in Benaim and Lobry '16) that, contrary to Hutchinson's explanation, one can switch between two environments in which the same species is favored and still get coexistence.

Modeling the effects of density dependent emigration, weak Allee effects, and matrix hostility on patch-level population persistence.

The relationship between conspecific density and the probability of emigrating from a patch can play an essential role in determining the population-dynamic consequences of an Allee effect. In this paper, we model a population that inside a patch is diffusing and growing according to a weak Allee effect per-capita growth rate, but the emigration probability is dependent on conspecific density. The habitat patch is one-dimensional and is surrounded by a tuneable hostile matrix. We consider five different forms of density dependent emigration (DDE) that have been noted in previous empirical studies. Our models predict that at the patch-level, DDE forms that have a positive slope will counteract Allee effects, whereas, DDE forms with a negative slope will enhance them. Also, DDE can have profound effects on the dynamics of a population, including producing very complicated population dynamics with multiple steady states whose density profile can be either symmetric or asymmetric about the center of the patch. Our results are obtained mathematically through the method of subsuper solutions, time map analysis, and numerical computations using Wolfram Mathematica.