Effects of intraspecific cooperative interactions in large ecosystems

We analyze the role of the Allee effect - a positive correlation between population density and mean individual fitness - for ecological communities formed by a large number of species. Our study is performed using the generalized Lotka-Volterra model with random interactions between species. We obtain the phase diagram and analyze the nature of the multiple equilibria phase. Remarkable differences emerge with respect to the logistic growth case, thus revealing the major role played by the functional response in determining aggregate behaviors of large ecosystems.

Stochastic dynamics of chemotactic colonies with logistic growth

The interplay between cellular growth and cell-cell signaling is essential for the aggregation and proliferation of bacterial colonies, as well as for the self-organization of cell tissues. To investigate this interplay, we focus here on the collective properties of dividing chemotactic cell colonies by studying their long-time and large-scale dynamics through a renormalization group (RG) approach. The RG analysis reveals that a relevant but unconventional chemotactic interaction -- corresponding to a polarity-induced mechanism -- is generated by fluctuations at macroscopic scales, even when an underlying mechanism is absent at the microscopic level. This emerges from the interplay of the well-known Keller--Segel (KS) chemotactic nonlinearity and cell birth and death processes. At one-loop order, we find no stable fixed point of the RG flow equations. We discuss a connection between the dynamics investigated here and the celebrated Kardar--Parisi--Zhang (KPZ) equation with long-range correlated noise, which points at the existence of a strong-coupling, nonperturbative fixed point.

Chaoslike states can be expected before and after logistic growth

Instabilities associated with population growth can be simulated by putting the logistic growth curve in a discrete form. In contrast to the usual derivation of chaos, which can only explain instabilities at the top of the curve, this method can also account for fluctuations during the early phases of the niche-filling process. Precursors, a steep initial rise, and final instabilities can all be interrelated. Industrial examples are given of logistic growth alternating with periods of chaotic fluctuations.

EFFECT OF ADDITIONAL FOOD ON PREDATOR–PREY INTERACTIONS WITH WATER-LEVEL FLUCTUATION

Significant variations of the water-level of the lake can have a strong impact on the persistence of species. Indeed, when the water-level is low, during the autumn, the contact between the predator and the prey is more frequent, and the predation increases. Conversely, when the water-level is high, in the spring, it is more difficult for the predator to find a prey and the predation decreases. In this paper, we consider a seasonally varying predator–prey model to study the influence of water-level variations on the interaction between two species of fishes in an artificial lake. A seasonal variation of the water-level is introduced in the predation rate. The predator population is provided some additional food apart from the focal prey, and follows logistic growth in the absence of prey population. As control upon the over predation, the predator population is harvested. Sensitivity analysis shows that the biomass of predator population is highly sensitive to the additional food and water variations. In the absence of additional food, our results show bursting patterns of fishes whereas positive periodic solution arises if the additional food is available in sufficient amount. The positive periodic solution is shown to be globally stable. Higher values of water-level fluctuations induce double periodic oscillations. Our findings show that providing additional food source to the generalist predator together with water-level fluctuations exerts a strong influence on the interaction between fishes.

Stability Analysis of SEIL Tuberculosis Epidemic Model with Logistic Growth in Susceptible Compartment

This article discusses modifications to the SEIL model that involve logistical growth. This model is used to describe the dynamics of the spread of tuberculosis disease in the population. The existence of the model's equilibrium points and its local stability depends on the basic reproduction number. If the basic reproduction number is less than unity, then there is one equilibrium point that is locally asymptotically stable. The equilibrium point is a disease-free equilibrium point. If the basic reproduction number ranges from one to three, then there are two equilibrium points. The two equilibrium points are disease-free equilibrium and endemic equilibrium points. Furthermore, for this case, the endemic equilibrium point is locally asymptotically stable.

Strengths and weaknesses of S-curves

For the last 22 years I have been fitting logistic S-curves to data points of historical time series at an average rate of about 2–3 per day. This amounts to something between 15,000 and 20,000 fits. Combined with the 40,000 fits of the Monte Carlo study we did with Alain Debecker to quantify the uncertainties in logistic fits [1], probably qualifies me for an entry in the Guinness Book of Records as the man who carried out the greatest number of logistic fits.It hasn't all been fun and games. There have also been blood and tears and not only from human errors. There have been what I came to recognize as “misbehaviors” of reality. I have seen cases where an excellent fit and ensuing forecast were invalidated by later data. But well-established logistic growth reflects the action of a natural law. A disproved forecast is tantamount to violating this law. A law that becomes violated is not much of a law. What is going on? There is something here that needs to be sorted out.

Long-Term GDP Forecasts and the Prospects for Growth

The growth of GDP is considered as a natural-growth process amenable to description by the logistic-growth equation. The S-shaped logistic pattern provides good descriptions and forecasts for both nominal and real GDP per capita in the US over the last 80 years. This enables the calculation of a long-term forecast for inflation, which is to enter a declining trend not so far in the future. The two logistics are well advanced, more so for nominal GDP. The assumption for logistic growth works even better for Japan whose nominal GDP per capita has already completed tracing out an entire logistic trajectory. The economic woes of industrialized countries could be attributed to the saturation of growth there, as if a niche in nature had been filled to capacity. In contrast, GDP growth in China and India is in the very early stages of logistic growth still indistinguishable from exponential patterns. The ceiling of these logistics can be anywhere between 7 and 15 times today’s levels.