Fitness response relation of a multitype age-structured population dynamics

Kobayashi T. Population dynamics models for various forms of adaptation

Adaptability to changing environments is one of the universal characteristics of living organisms. Because individual modes of adaptation are diverse, a unified understanding of these diverse modes is essential to comprehend adaptation. Adaptations can be categorized from at least two perspectives with respect to information. One is the passivity and activity of adaptation and the other is the type of information transmission. In Darwinian natural selection, organisms are selected among randomly generated traits under which individual organisms are passive in the sense that they do not process any environmental information. On the other hand, organisms can also adapt by sensing their environment and changing their traits. This is an active adaptation in that it makes use of environmental information. In terms of information transfer, adaptation through phenotypic heterogeneity, such as bacterial bet-hedging, is intragenerational in which traits are not passed on to the next generation. In contrast, adaptation through genetic diversity is intergenerational. The theory of population dynamics enables us to unify these various modes of adaptations and their properties can be analyzed qualitatively and quantitatively using techniques from quantitative genetics and information thermodynamics. In addition, such methods can be applied to situations where organisms can learn from past experiences and pass them on from generation to generation. In this work, we introduce the unified theory of biological adaptation based on population dynamics and show its potential applications to evaluate the fitness value of information and to analyze experimental lineage tree data. Finally, we discuss future perspectives for its development. This review article is an extended version of the Japanese article in SEIBUTSU BUTSURI Vol. 57, p. 287-290 (2017).

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.

Linking lineage and population observables in biological branching processes

Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels is derived. One of these relations implies specific inequalities comparing the population doubling time with the mean generation time at the lineage or population levels. While these inequalities have been derived before for age-controlled models with negligible mother-daughter correlations, we show that they also hold for a broad class of size-controlled models. We discuss the implications of this result for the interpretation of a recent experiment in which the growth of bacteria strains has been probed at the single-cell level.