Cooperation in species: Interplay of population regulation and extinction through global population dynamics database

Interconnection between density-regulation and stability in competitive ecological network

In natural ecosystems, species can be characterized by the nonlinear density-dependent self-regulation of their growth profile. Species of many taxa show a substantial density-dependent reduction for low population size. Nevertheless, many show the opposite trend; density regulation is minimal for small populations and increases significantly when the population size is near the carrying capacity. The theta-logistic growth equation can portray the intraspecific density regulation in the growth profile, theta being the density regulation parameter. In this study, we examine the role of these different growth profiles on the stability of a competitive ecological community with the help of a mathematical model of competitive species interactions. This manuscript deals with the random matrix theory to understand the stability of the classical theta-logistic models of competitive interactions. Our results suggest that having more species with strong density dependence, which self-regulate at low densities, leads to more stable communities. With this, stability also depends on the complexity of the ecological network. Species network connectance (link density) shows a consistent trend of increasing stability, whereas community size (species richness) shows a context-dependent effect. We also interpret our results from the aspect of two different life history strategies: r and K-selection. Our results show that the stability of a competitive network increases with the fraction of r-selected species in the community. Our result is robust, irrespective of different network architectures.

Revisiting and redefining return rate for determination of the precise growth status of a species

Growth curve models play an instrumental role in quantifying the growth of biological processes and have immense practical applications across all disciplines. The most popular growth metric to capture the species fitness is the "Relative Growth Rate" in this domain. The different growth laws, such as exponential, logistic, Gompertz, power, and generalized Gompertz or generalized logistic, can be characterized based on the monotonic behavior of the relative growth rate (RGR) to size or time. Thus, in this case, species fitness can be determined truly through RGR. However, in nature, RGR is often non-monotonic and specifically bell-shaped, especially in the situation when a species is adapting to a new environment [1]. In this case, species may experience with the same fitness (RGR) for two different time points. The species precise growth and maturity status cannot be determined from this RGR function. The instantaneous maturity rate (IMR), as proposed by [2], helps to determine the correct maturity status of the species. Nevertheless, the metric IMR suffers from severe drawbacks; (i) IMR is intractable for all non-integer values of a specific parameter. (ii) The measure depends on a model parameter. The mathematical expression of IMR possesses the term "carrying capacity" which is unknown to the experimenter. (iii) Note that for identifying the precise growth status of a species, it is also necessary to understand its response when the populations are deflected from their equilibrium position at carrying capacity. This is an established concept in population biology, popularly known as the return rate. However, IMR does not provide information on the species deflection rate at the steady state. Hence, we propose a new growth measure connected with the species return rate, termed the "reverse of relative of relative growth rate" (henceforth, RRRGR), which is treated as a proxy for the IMR, having similar mathematical properties. Finally, we introduce a stochastic RRRGR model for specifying precise species growth and status of maturity. We illustrate the model through numerical simulations and real fish data. We believe that this study would be helpful for fishery biologists in regulating the favorable conditions of growth so that the species can reach a steady state with optimum effort.

Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our nonparametric method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether the dynamics occur through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited sample sizes, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.

A noble extended stochastic logistic model for cell proliferation with density-dependent parameters

Cell proliferation often experiences a density-dependent intrinsic proliferation rate (IPR) and negative feedback from growth-inhibiting molecules in culture media. The lack of flexible models with explanatory parameters fails to capture such a proliferation mechanism. We propose an extended logistic growth law with the density-dependent IPR and additional negative feedback. The extended parameters of the proposed model can be interpreted as density-dependent cell-cell cooperation and negative feedback on cell proliferation. Moreover, we incorporate further density regulation for flexibility in the model through environmental resistance on cells. The proposed growth law has similarities with the strong Allee model and harvesting phenomenon. We also develop the stochastic analog of the deterministic model by representing possible heterogeneity in growth-inhibiting molecules and environmental perturbation of the culture setup as correlated multiplicative and additive noises. The model provides a conditional maximum sustainable stable cell density (MSSCD) and a new fitness measure for proliferative cells. The proposed model shows superiority to the logistic law after fitting to real cell culture datasets. We illustrate both conditional MSSCD and the new cell fitness for a range of parameters. The cell density distributions reveal the chance of overproliferation, underproliferation, or decay for different parameter sets under the deterministic and stochastic setups.

COVID-19 pandemic models revisited with a new proposal: Plenty of epidemiological models outcast the simple population dynamics solution

We have put an effort to estimate the number of publications related to the modelling aspect of the corona pandemic through the web search with the corona associated keywords. The survey reveals that plenty of epidemiological models outcast the simple population dynamics solution. Most of the future predictions based on these epidemiological models are highly unreliable because of the complexity of the dynamical equations and the poor knowledge of realistic values of the model parameters. The incidence time series of top ten corona infected countries are erratic and sparse. But in comparison, the incidence and disease fitness relationships are uniform and concave upward in nature. These simple profiles with the acceleration curves have fundamental implications in understanding the instinctive dynamics of the corona pandemic. We propose a simple population dynamics solution based on the incidence-fitness relationship in predicting that a plateau or steady state of SARS-CoV-2 will be reached using the basic concept of geometry.

An extended stochastic Allee model with harvesting and the risk of extinction of the herring population

Overexploitation of commercially beneficial fish is a serious ecological problem around the world. The growth profiles of most of the species are likely to follow density regulated theta-logistic model irrespective of any taxonomy group [Sibly et al., Science, 2005]. Rapid depletion of population size may cause reduced fitness, and the species is exposed to Allee phenomena. Here sustainability is addressed by modelling the herring population as a stochastic process and computing the probability of extinction and expected time to extinction. The models incorporate an Allee effect, crowding effect which reduce birth and death rates at large populations, and two possible choices of harvesting models viz. linear harvesting and nonlinear harvesting. A seminal attempt is made by Saha [Saha et al., Ecol. Model, 2013] for this economically beneficial fish, but ignored the vital phenomena of harvesting. Moreover, in this model, the demographic stochasticity is introduced through the white-noise term, which has certain limitations when harvesting is introduced into the system. White noise is appropriate for such a system where immigration and emigration are allowed, but a harvesting model is rational for a closed system. The demographic stochasticity is introduced by replacing an ordinary differential equation model with a stochastic differential equation model, where the instantaneous variance in the SDE is derived directly from the birth and death rates of a birth-death process. The modelling parameters are fit to data of the herring populations collected from Global Population Dynamics Database (GPDD), and the risk of extinction of each population is computed under different harvesting protocols. A threshold for handling times is computed beneath which the risk of extinction is high. This is proposed as a recommendation to management for sustainable harvesting.

A Novel Unification Method to Characterize a Broad Class of Growth Curve Models Using Relative Growth Rate

Growth curve models serve as the mathematical framework for the quantitative studies of growth in many areas of applied science. The evolution of novel growth curves can be categorized in two notable directions, namely generalization and unification. In case of generalization, a modeler starts with a simple mathematical form to describe the behavior of the data and increases the complexity of the equation by incorporating more parameters to obtain a more flexible shape. The unification refers to the process of obtaining a compact representation of a large number of growth equations. An enormous number of growth equations are made available in the literature by means of the generalization of existing growth laws. However, the unification of growth equations has received relatively less attention from the researchers. Two significant unification functions are available in the literature, namely the Box-Cox transformation by Garcia (For Biometry Model Inf Sci 1:63-68, 2005) and generalized logarithmic and exponential functions by Martinez et al. (Phys A 387:5679-5687, 2008; Phys A 388:2922-2930, 2009). Existing unification approaches are found to have limited applications if the growth equation is characterized by the relative growth rate (RGR). RGR has immense practical value in biological growth curve analysis, which has been amplified by the construction of size and time covariate models, in which; RGR is represented either as a function of size or time or both. The present study offers a unification function for the RGR growth curves. The proposed function combines a broad class of the growth curves and possesses a greater generality than the existing unification functions. We also propose the notion of generalized RGR, which is capable of making interrelations among the unifying functions. Our proposed method is expected to enhance the generality of software and may aid in choosing an optimal model from a set of competitor growth equations.

A simple approximation of moments of the quasi-equilibrium distribution of an extended stochastic theta-logistic model with non-integer powers

The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (Nasell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database.