Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models

Sensitivity analysis on the declining population in Japan: Effects of prefecture-specific fertility and interregional migration

Japan has been facing a population decline since 2010 due to low birth rates, interregional migration, and regional traits. In this study, we modeled the demographic dynamics of Japan using a transition matrix model. Then, from the mathematical structure of the model, we quantitatively evaluated the domestic factors of population decline. To achieve this, we constructed a multi-regional Leslie matrix model and developed a method for representing the reproductive value and stable age distribution using matrix entries. Our method enabled us to interpret the mathematical indices using the genealogies of the migration history of individuals and their ancestors. Furthermore, by combining our method with sensitivity analysis, we analyzed the effect of region-specific fertility rates and interregional migration rates on the population decline in Japan. We found that the sensitivity of the population growth rate to the migration rate from urban areas with large populations to prefectures with high fertility rates was greatest for people aged under 30. In addition, compared to other areas, the fertility rates of urban areas exhibited higher sensitivity for people aged over 30. Because this feature is robust in comparison with those in 2010 and 2015, it can be said to be a unique structure in Japan in recent years. We also established a method to represent the reproductive value and stable age distribution in an irreducible non-negative matrix population model by using the matrix entries. Furthermore, we show the effects of fertility and migration rates numerically in urban and non-urban areas on the population growth rates for each age group in a society with a declining population.

Evolution of heterogeneity under constant and variable environments

Various definitions of fitness are essentially based on the number of descendants of an allele or a phenotype after a sufficiently long time. However, these different definitions do not explicate the continuous evolution of life histories. Herein, we focus on the eigenfunction of an age-structured population model as fitness. The function generates an equation, called the Hamilton-Jacobi-Bellman equation, that achieves adaptive control of life history in terms of both the presence and absence of the density effect. Further, we introduce a perturbation method that applies the solution of this equation to the long-term logarithmic growth rate of a stochastic structured population model. We adopt this method to realize the adaptive control of heterogeneity for an optimal foraging problem in a variable environment as the analyzable example. The result indicates that the eigenfunction is involved in adaptive strategies under all the environments listed herein. Thus, we aim to systematize adaptive life histories in the presence of density effects and variable environments using the proposed objective function as a universal fitness candidate.

Effectiveness of adulticide and larvicide in controlling high densities of Aedes aegypti in urban environments

Current management and control of Aedes aegypti populations in urban areas are based on the spraying of insecticides. Here, we evaluated the effectiveness of spraying larvicide (Bacillus thuringiensis israelensis) using a truck-mounted Buffalo Turbine and adulticide (Deltamethrin) using a Grizzly ULV Sprayer in an urban area with high densities of Ae. aegypti and many cryptic and difficult to reach aquatic breeding habitats. Experiments were conducted in a tire shop located in Miami-Dade County, Florida with approximately 100,000 used airplane tires. Insecticide interventions were performed after a baseline survey consisting of 3 weeks of collections, followed by two insecticide interventions: (i) application of the adulticide followed by the application of larvicide on the subsequent week; and (ii) application of both adulticide and larvicide on two consecutive weeks. The first insecticide intervention resulted in a non-significant decrease in the relative abundance of Ae. aegypti. On the other hand, the second insecticide intervention significantly reduced the Ae. aegypti relative abundance (P < 0.002). Our results demonstrated that the combined insecticide interventions on two consecutive weeks significantly reduced the relative abundance of Ae. aegypti. This result indicated that the larvicide was successfully propelled reaching cryptical and difficult to reach aquatic habitats. However, even though the number of mosquitoes was greatly reduced, it was still greatly above the 10-mosquito threshold by trap night used by the Miami-Dade Mosquito Control Division to deploy an inspector to survey the area. Considering the lack of new and effective mosquito control tools, efficient and mobile insecticide propellers such as Buffalo Turbine can be of great help to manage mosquito populations in urban areas.

Deconstructing the eradication of new world screwworm in North America: retrospective analysis and climate warming effects

Before its eradication from North America, the subtropical-tropical new world screwworm fly Cochliomyia hominivorax (Coquerel) invaded southwestern temperate areas of the U.S.A., where it caused myiasis in wildlife and livestock. Outbreaks of the fly occurred during years when adult migrants were carried northward on North American monsoon winds from the northern areas of Mexico and south Texas. We deconstruct, retrospectively, the biology and the effect of weather on the eradication of the fly in North America. Screwworm was found to be an ideal candidate for eradication using the sterile insect technique (SIT) because females mate only once, whereas males are polygynous, and, although it has a high reproductive potential, field population growth rates are low in tropical areas. In northern areas, eradication was enhanced by cool-cold weather, whereas eradication in tropical Mexico and Central America is explained by the SIT. Despite low average efficacy of SIT releases (approximately 1.7%), the added pressure of massive SIT releases reduced intrinsically low fly populations, leading to mate-limited extinction. Non-autochthonous cases of myiasis occur in North America and, if the fly reestablishes, climate warming by 2045-2055 will expand the area of favourability and increase the frequency and severity of outbreaks.

Fitness response relation of a multitype age-structured population dynamics

We construct a pathwise formulation for a multitype age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational representation of the stationary population growth rate; the representation comprises a tradeoff relation between growth effects and a single-cell intrinsic dynamics described by a semi-Markov process. This variational representation leads to a response relation of the stationary population growth rate, in which statistics on a retrospective history work as the response coefficients. These results contribute to predicting and controlling growing populations based on experimentally observed cell-lineage information.