Logistic Growth Process Research Articles

Uncertainty Reduction in Logistic Growth Regression Using Surrogate Systems Carrying Capacities: a COVID-19 Case Study

Logistic growth regressions present high uncertainties when data are not past their inflection points. In such conditions, the uncertainty in the estimated carrying capacity K, for example, can be of the order of K. Here, we present a method for uncertainty reduction in logistic growth regression using data from a surrogate logistic growth process. We illustrate the method using Richards’ growth function to predict the inflection points of COVID-19 first-wave accumulated causalities in Brazilian cities. First waves of epidemics are known to be reasonably well modeled a posteriori by Richard’s growth function. Yet, we make predictions using early data that end before or around the inflection point. For that goal, we estimate K by logistic growth regression using data from surrogate international cities where the epidemics are clearly past their inflection points. The constraint stabilizes the logistic growth regression for the Brazilian cities, reducing the uncertainty in the prediction parameters even when the surrogate K is a rough estimate. The predictions for COVID-19 first-wave peaks in Brazilian cities agree with official data. The method may be used for other logistic models and logistic processes, in areas such as economics and biology, when surrogate populations or systems are identified.

Effects of Demographic Stochasticity on Population Persistence in Advective Media

Many populations live and disperse in advective media. A fundamental question, known as the "drift paradox" in stream ecology, is how a closed population can survive when it is constantly being transported downstream by the flow. Recent population-level models have focused on the role of diffusive movement in balancing the effects of advection, predicting critical conditions for persistence. Here, we formulate an individual-based stochastic analog of the model described in (Lutscher et al., SIAM Rev. 47(4):749-772, 2005) to quantify the effects of demographic stochasticity on persistence. Population dynamics are modeled as a logistic growth process and dispersal as a position-jump process on a finite domain divided into patches. When there is no correlation in the interpatch movement of residents, stochasticity simply smooths the persistence-extinction boundary. However, when individuals disperse in "packets" from one patch to another and the flow field is memoryless on the timescale of packet transport, the probability of persistence is greatly enhanced. The latter transport mechanism may be characteristic of larval dispersal in the coastal ocean or wind-dispersed seed pods.

Optimal fishery harvesting rules under uncertainty

This paper derives the optimal fishery harvest policy in a real-option model with a stochastic logistic growth process, harvest-sensitive output price, and both fixed and variable harvesting costs. The policy specifies the harvest trigger and harvest size, while outputs from the model include the value of the fishery and the risk of extinction. The optimal policy is illustrated with data from the Pacific Halibut Fishery. For this particular case, the optimal policy recommends harvesting when the fish stock rises to about three-quarters the environmental carrying capacity, and the amount harvested should be approximately a quarter of the prevailing stock. This harvesting policy maximizes the value of the fishery, and importantly, the resulting risk of extinction is negligible. We also carry out some sensitivity analysis to see how the optimal policy (and the resulting fishery value and risk of extinction) change when the input parameters are varied, particularly the ecological parameters intrinsic growth rate and volatility of the stock, and also the economic parameters that have been ignored in previous papers (price sensitivity and fixed cost). If the optimal policy is followed, the risk of extinction will be negligible, except for very low growth rate and high volatility.

Absorption and fixation times for neutral and quasi-neutral populations with density dependence

We study a generalisation of Moran’s population-genetic model that incorporates density dependence. Rather than assuming fixed population size, we allow the number of individuals to vary stochastically with the same events that change allele number, according to a logistic growth process with density dependent mortality. We analyse the expected time to absorption and fixation in the ‘quasi-neutral’ case: both types have the same carrying capacity, achieved through a trade-off of birth and death rates. Such types would be competitively neutral in a classical, fixed-population Wright–Fisher model. Nonetheless, we find that absorption times are skewed compared to the Wright–Fisher model. The absorption time is longer than the Wright–Fisher prediction when the initial proportion of the type with higher birth rate is large, and shorter when it is small. By contrast, demographic stochasticity has no effect on the fixation or absorption times of truly neutral alleles in a large population. Our calculations provide the first analytic results on hitting times in a two-allele model, when the population size varies stochastically.

Influences of time delay on logistic growth process driven by colored correlated noises

The small time-delay approach is applied to logistic growth model when time-delayed feedback and colored correlated noises are included in the system. The steady state probability distribution Pst(x) of the tumor cell number is obtained. It is found that a configuration transition of multiple peaks to a single peak occurs due to the variation of delay time τ. An extremum appears in the curves of the mean of the steady-state tumor cell number 〈x〉, the second moment 〈x2〉, and the normalized variance Var versus λ. The positions and the peak values of the extrema can be effected by the time delay.

Anticipating Critical Reconfigurations in World Societal Fields

Qualitative change in pattern or configuration is starkly contrasted with quantitative change. A number of assumptions are stated regarding biological, psychological, social, economic, political, technological, and ecological forces and factors systemically causal to war or peace. The world system is considered to be a dynamic field of forces. Modern field theory is briefly reviewed. Several theoretical approaches, compatible mutually and compatible with the integrating framework of field theory, are discussed. These are the behavioral/social or sociotechnical, systems dynamics, entropy law, self-organization far from equilibrium, field theory in physics, catastrophe theory, and hyperbolic and logistic growth process approaches. A cusp and a butterfly catastrophe theory interpretation of revolutionary processes serve to illustrate the reconfigurational nature of societal fields under conditions of incipiently prestructured war or peace. Some problems of future concern are identified.

Regulated growth in random environments.

Conditions for extinction, convergence to a stationary distribution and attaining a carrying capacity are given for stochastic versions of the logistic growth process.