Stackelberg Population Dynamics: A Predictive-Sensitivity Approach

Hierarchical decision-making processes traditionally modeled as bilevel optimization problems are widespread in modern engineering and social systems. In this work, we deal with a leader with a population of followers in a hierarchical order of play. In general, this problem can be modeled as a leader–follower Stackelberg equilibrium problem using a mathematical program with equilibrium constraints. We propose two interconnected dynamical systems to dynamically solve a bilevel optimization problem between a leader and follower population in a single time scale by a predictive-sensitivity conditioning interconnection. For the leader’s optimization problem, we developed a gradient descent algorithm based on the total derivative, and for the followers’ optimization problem, we used the population dynamics framework to model a population of interacting strategic agents. We extended the concept of the Stackelberg population equilibrium to the differential Stackelberg population equilibrium for population dynamics. Theoretical guarantees for the stability of the proposed Stackelberg population learning dynamics are presented. Finally, a distributed energy resource coordination problem is solved via pricing dynamics based on the proposed approach. Some simulation experiments are presented to illustrate the effectiveness of the framework.

Genetic Mutations in TNFSF11 Were Associated With the Chronicity of Hepatitis C Among Chinese Han Population

Background: Recently, several studies have reported that the host immune response can be related to the RANKL/RANK/OPG signaling pathway. However, the associations of TNFSF11, TNFRSF11A, and TNFRSF11B gene polymorphisms in the RANKL/RANK/OPG pathway with hepatitis C virus (HCV) infection outcomes remain unclear.Methods: In this case-control study, 768 persistent HCV infection and 503 spontaneous HCV clearance cases, and 1,259 control subjects were included. The Taman-MGB probe method was utilized to detect TNFSF11 rs9525641, TNFRSF11A rs8686340, and TNFRSF11B rs2073618 genotypes. The distribution of three single nucleotide polymorphisms (SNPs) genotypes was analyzed using stata14.0.Results: SNPs rs9525641, rs8086340, and rs2073618 genotype frequencies followed the Hardy-Weinberg natural population equilibrium (p = 0.637, 0.250, and 0.113, respectively). Also, rs9525641 was significantly associated with HCV chronicity risk in recessive (OR = 1.203, 95% CI: 1.018–1.420, p = 0.030) and additive models (OR = 1.545, 95% CI: 1.150–2.075, p = 0.004). The stratified analysis showed that rs9525641 variant genotypes were associated with HCV chronicity among people older than 50 years (OR =1.562, 95% CI: 1.079–2.262, p = 0.018), females (OR = 1.667, 95% CI: 1.145–2.429, p = 0.008), ALT <40 U/L (OR = 1.532, 95% CI: 1.074–2.286, p = 0.018), and AST < 40 U/L (OR = 1.552, 95% CI: 1.095–2.201, p = 0.014).Conclusion:TNFRSF11 rs9525641 was significantly associated with HCV chronicity in the Chinese population.

U-5 Equilibrium of Population and Resources: Interpretation and Approach

Population and resources have an interdisciplinary relationship. The establishment of a sustainable society depends upon a balanced family. Environment, health, and socio-economic peace and prosperity are tempered due to rapid variations. The population and resources gap is misinterpreted in particularly in Muslim societies. The population has been recognized symbol of power for a country. Shortage of resources is not caused by population growth but a result of mismanagement. This crisis requires contemporary interpretation and some indirect approaches. Islam is a balanced religion and encourages balanced life and society. The article in hand will review the policies taken by various Muslim countries. It will denote governmental campaigns for management of family and resources. This paper will provide Islamic instructions on the equilibrium of population and resources. It will discuss minutely legitimacy of the population equilibrium campaign. This research will highlight the approachable zones to address this burning issue. It will introduce swift actions to be taken by individuals and the community at large.

Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior

This paper discusses the analysis of the Rosenzweig-MacArthur predator-prey model with anti-predator behavior. The analysis is started by determining the equilibrium points, existence, and conditions of the stability. Identifying the type of Hopf bifurcation by using the divergence criterion. It has shown that the model has three equilibrium points, i.e., the extinction of population equilibrium point (E0), the non-predatory equilibrium point (E1), and the co-existence equilibrium point (E2). The existence and stability of each equilibrium point can be shown by satisfying several conditions of parameters. The divergence criterion indicates the existence of the supercritical Hopf-bifurcation around the equilibrium point E2. Finally, our model's dynamics population is confirmed by our numerical simulations by using the 4th-order Runge-Kutta methods.

Use of a spatially explicit individual-based model to predict population trajectories and habitat connectivity for a reintroduced ursid

Reintroductions of large carnivore species present unique opportunities to model population dynamics as populations can be monitored from the beginning of a reintroduction. However, analysis of the population dynamics of such reintroduced populations is rare and may be limited in incorporating the complex movements and environmental interactions of large carnivores. Starting in 2004, Asiatic black bears Ursus thibetanus were reintroduced and tracked in the Republic of Korea, along with their descendants, using radio telemetry, yielding 33,924 tracking points over 12 years. Along with information about habitat use, landscape, and resource availability, we estimated the population equilibrium and dispersal capability of the reintroduced population. We used a mixed modelling approach to determine suitable habitat areas, population equilibria for three different resources-based scenarios, and least-cost pathways (i.e. corridors) for dispersal. Our population simulations provided a mean population equilibrium of 64 individuals at the original reintroduction site and a potential maximum of 1,438 individuals in the country. The simulation showed that the bear population will disperse to nearby mountainous areas, but a second reintroduction will be required to fully restore U. thibetanus. Northern suitable habitats are currently disconnected and natural re-population is unlikely to happen unless supported. Our methodologies and findings are also relevant for determining the outcome and trajectories of reintroduced populations of other large carnivores.

A Theoretical Treatment of Memetic Traits Using Gene-Meme, Meme-Meme and Population Equilibrium

Background: The term meme includes vertical trait transmission and laterally transmitted ideas that can be lasting or transient. Memes may sometimes follow the logic of population genetics, e.g. learned birdsong, but not when laterally transmitted. Much current work focuses on selection of memes rather than hosts. This paper investigates mathematically the interaction of behaviorally transmitted traits with host selection fitness. Methods: We analyze equilibrium between gene-meme and meme-meme competing propagators and consider whether a meme is linked to reproduction (e.g. vertical culture transmission), or not. We employ a genetic component and combined meme-induced fitness components for hosts, while memes have replication factors to distinguish from what’s good for the host (fitness). We use a Monte Carlo simulation roughly calibrated to the Industrial Revolution to study meme effects on population stability. Results: A basic effective calculus of memetic trait competition and interaction with genes is derived and analyzed. The transient nature of many lateral memes may be a defense against accumulation of deleterious memes. Laterally transmitted (panmictic) memes with high spreading rate will often not equalize with a genetic trait, spreading outside of natural selection of the hosts, presenting a cumulative existential threat. Vertical transmission reduces replication rate and allows group selection against deleterious memes. Competing mutually exclusive memes contribute to inequality and altruism, but compete through adverse fitness since exclusivity assumes low conversion. Conclusions: The advantage of a portfolio of groups or species may not accrue to a single group. This understanding elevates meme-risk to the level of a candidate solution to the so-called Fermi Paradox.

Spatial modeling could not differentiate early SARS-CoV-2 cases from the distribution of humans on the basis of climate in the United States

The SARS-CoV-2 coronavirus is wreaking havoc globally, yet, as a novel pathogen, knowledge of its biology is still emerging. Climate and seasonality influence the distributions of many diseases, and studies suggest at least some link between SARS-CoV-2 and weather. One such study, building species distribution models (SDMs), predicted SARS-CoV-2 risk may remain concentrated in the Northern Hemisphere, shifting northward in summer months. Others have highlighted issues with SARS-CoV-2 SDMs, notably: the primary niche of the virus is the host it infects, climate may be a weak distributional predictor, global prevalence data have issues, and the virus is not in population equilibrium. While these issues should be considered, we believe climate’s relationship with SARS-CoV-2 is still worth exploring, as it may have some impact on the distribution of cases. To further examine if there is a link to climate, we build model projections with raw SARS-CoV-2 case data and population-scaled case data in the USA. The case data were from across March 2020, before large travel restrictions and public health policies were impacting cases across the country. We show that SDMs built from population-scaled case data cannot be distinguished from control models (built from raw human population data), while SDMs built on raw case data fail to predict the known distribution of cases in the U.S. from March. The population-scaled analyses indicate that climate did not play a central role in early U.S. viral distribution and that human population density was likely the primary driver. We do find slightly more population-scaled viral cases in cooler areas. Ultimately, the temporal and geographic constraints on this study mean that we cannot rule out climate as a partial driver of the SARS-CoV-2 distribution. Climate’s role on SARS-CoV-2 should continue to be cautiously examined, but at this time we should assume that SARS-CoV-2 will continue to spread anywhere in the U.S. where governmental policy does not prevent spread.

The effect of acute and chronic food shortage on human population equilibrium in a subsistence setting

Background World population is projected to reach 9–11 billion by 2050, raising concerns about food system security and sustainability. Modeling food systems are often a way to understand current and future dynamics. The most common model, first articulated by Malthus (Malthusian), shows population growth as an exponential function and food production as a linear function, concluding that human carrying capacity will be reached leading to mass starvation. Another prominent model was introduced by Boserup (Boserupian), which explains increases in food production as a function of population growth. Methodology Here, we explore which food systems dynamics exist at equilibrium and after perturbation. The model introduced explores food availability in an isolated village and then in a line of villages. The isolated village model includes three key parameters: maximum calorie production (a), food production resilience (b), and minimum calorie requirement per person (c). The multiple village model adds an additional parameter for trade. Results Isolated village populations are more resilient to famine than Malthusian theory predicts, suggesting that Malthus’ premise may be inaccurate. Predictably, across multiple villages increasing access and production reduce famine. However, under certain conditions large amounts of transport can lead to antagonist relationships leading to rapid changes in population. Conclusion Food systems under both production and access scenarios proved to be resilient to small perturbations, requiring a large catastrophe to induce mortality; this appeared to discount the Malthusian model. This model can create dynamics where different modes of famine relief apply, but here we see that a balanced approach of both access and production appears to be the most resilient to famine.

Quantifying the spatial pattern of dialect words spreading from a central population

Some dialect words are shared among geographically distant groups of people without close interaction. Such a pattern may indicate the current or past presence of a cultural centre exerting a strong influence on peripheries. For example, concentric distributions of dialect variants in Japan may be explicable by repeated inventions of new variants at Kyoto, the ancient capital, with subsequent outward diffusion. Here we develop a model of linguistic diffusion within a population network to quantify the distribution of variants created at the central population. Equilibrium distributions of word ages are obtained for idealized networks and for a realistic network of Japanese prefectures. Our model successfully replicates the observed pattern, supporting the notion that a centre–periphery social structure underlies the emergence of concentric patterns. Unlike what has previously been claimed, our model indicates that a novelty bias in linguistic transmission is not always necessary to account for the concentric pattern, whereas some bias in the direction of transmission between populations is needed to be consistent with the observed absence of old words near the central population. Our analysis on the realistic network also suggests that the process of linguistic transmission was not much affected by between-prefecture differences in population size.

Spatial modeling cannot currently differentiate SARS-CoV-2 coronavirus and human distributions on the basis of climate in the United States

The SARS-CoV-2 coronavirus is wreaking havoc globally, yet knowledge of its biology is limited. Climate and seasonality influence the distributions of many diseases, and studies suggest a link between SARS-CoV-2 and cool weather. One such study, building species distribution models (SDMs), predicted SARS-CoV-2 risk may remain concentrated in the Northern Hemisphere, shifting northward in summer months. Others have highlighted issues with SARS-CoV-2 SDMs, notably: the primary niche of the virus is the host it infects, climate may be a weak distributional predictor, global prevalence data have issues, and the virus is not in a population equilibrium. While these issues should be considered, climate still may be important for predicting the future distribution of SARS-CoV-2. To further examine if there is a link, we model with raw cases and population scaled cases for SARS-CoV-2 county-level data from the United States. We show that SDMs built from population scaled cases data cannot be distinguished from control models built from raw human population data, while SDMs built on raw data fail to predict the current known distribution of cases in the US. The population scaled analyses indicate that climate may not play a central role in current US viral distribution and that human population density is likely a primary driver. Still, we do find slightly more population scaled viral cases in cooler areas. This coupled with our geographically constrained focus make it so we cannot rule out climate as a partial driver of the US SARS-CoV-2 distribution. Climate’s role on SARS-CoV-2 should continue to be cautiously examined, but at this time we should assume that SARS-CoV-2 can spread anywhere in the US.