The characterization of plasticity, robustness, and evolvability, an important issue in biology, is studied in terms of phenotypic fluctuations. By numerically evolving gene regulatory networks, the proportionality between the phenotypic variances of epigenetic and genetic origins is confirmed. The former is given by the variance of the phenotypic fluctuation due to noise in the developmental process; and the latter, by the variance of the phenotypic fluctuation due to genetic mutation. The relationship suggests a link between robustness to noise and to mutation, since robustness can be defined by the sharpness of the distribution of the phenotype. Next, the proportionality between the variances is demonstrated to also hold over expressions of different genes (phenotypic traits) when the system acquires robustness through the evolution. Then, evolution under environmental variation is numerically investigated and it is found that both the adaptability to a novel environment and the robustness are made compatible when a certain degree of phenotypic fluctuations exists due to noise. The highest adaptability is achieved at a certain noise level at which the gene expression dynamics are near the critical state to lose the robustness. Based on our results, we revisit Waddington's canalization and genetic assimilation with regard to the two types of phenotypic fluctuations.
Relationship among Phenotypic Plasticity, Genetic and Epigenetic Fluctuations, Robustness, and Evolovability; Waddington's Legacy revisited under the Spirit of Einstein
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations. Adaptive changes in high-dimensional phenotypes were shown to be restricted within a low-dimensional slow manifold, from which a macroscopic law for cellular states was derived, which was confirmed by adaptation experiments on bacteria under stress. Next, the theory was extended to phenotypic evolution, leading to proportionality between phenotypic responses agai…
Plasticity-led evolution is a form of evolution where a change in the environment induces novel traits via phenotypic plasticity, after which the novel traits are genetically accommodated over generations under the novel environment. This mode of evolution is expected to resolve the problem of gradualism (i.e., evolution by the slow accumulation of mutations that induce phenotypic variation) implied by the Modern Evolutionary Synthesis, in the face of a large environmental change. While experimental works are essential for validating that plasticity-led evolution indeed happened, we need compu…
How adaptive evolution to one environmental stress improves or suppresses adaptation to another is an important problem in evolutionary biology. For instance, in microbiology, the evolution of bacteria to be resistant to different antibiotics is a critical issue that has been investigated as cross-resistance. In fact, recent experiments on bacteria have suggested that the cross-resistance of their evolution to various stressful environments can be predicted by the changes to their transcriptome upon application of stress. However, there are no studies so far that explain a possible theoretical…
The diversity and quality of natural systems have been a puzzle and inspiration for communities studying artificial life. It is now widely admitted that the adaptation mechanisms enabling these properties are largely influenced by the environments they inhabit. Organisms facing environmental variability have two alternative adaptation mechanisms operating at different timescales: \textit{plasticity}, the ability of a phenotype to survive in diverse environments and \textit{evolvability}, the ability to adapt through mutations. Although vital under environmental variability, both mechanisms are…
The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous population of stem cells (SCs) and their associated progenitors. The fate of a malignant mutation is determined not only by overall stem cell and differentiated cell growth rates but also differentiation and dedifferentiation rates. We investigate the effect of such a complex population structure on the evolution of malignant mutations. We derive exact anal…
In general, cellular phenotypes, as measured by concentrations of cellular components, involve large degrees of freedom. However, recent measurement has demonstrated that phenotypic changes resulting from adaptation and evolution in response to environmental changes are effectively restricted to a low-dimensional subspace. Thus, uncovering the origin and nature of such a drastic dimension reduction is crucial to understanding the general characteristics of biological adaptation and evolution. Herein, we first formulated the dimension reduction in terms of dynamical systems theory: considering …
Hypoxia-resistance heterogeneity in tumours: the impact of geometrical characterization of environmental niches and evolutionary trade-offs. A mathematical approach
Although many phenotypic traits are determined by a large number of genetic variants, how a polygenic trait adapts in response to the changes in the environment is still poorly understood. Here we study the adaptation dynamics of a polygenic trait that is determined by a finite number of genetic loci in an infinitely large population which is evolving under stabilising selection and recurrent mutations. We find that in a changing environment, modeled here by a linearly moving phenotypic optimum, the mean trait also moves linearly with time. But its speed is smaller than that of the phenotypic …
The evolution and function of imitation have always been placed within the confines of animal learning and associated with its crucial role in cultural transmission and cultural evolution. Can imitation evolve as a form of phenotypic plasticity in the absence of cultural transmission, in phenotypes beyond behavior? We investigate a model in which imitation is unbundled from cultural transmission: an organism's adult phenotype is plastically altered by its experiences as a juvenile of other juveniles' genetically determined traits. The only information transmitted between generations is genetic…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the adaptation of asexual species to periodically fluctuating environmental conditions. These deterministic continuum models are usually defined on the basis of population-scale phenomenological assumptions and cannot capture adaptive phenomena that are driven by stochastic variability in the evolutionary paths of single individuals. In this paper, we develop a sto…
The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context of antibiotic treatments or exponential growth in constant environments, non-genetic variability has shown to have significant effects on population dynamics. Here, we review research that elucidates the relationship between cell-to-cell variability and population dynamics. After summarizing the relevant experimental observations, we discuss models of bet-he…
At odds with a traditional view of molecular evolution that seeks a descent-with-modification relationship between functional sequences, new functions can emerge {\it de novo} with relative ease. At early times of molecular evolution, random polymers could have sufficed for the appearance of incipient chemical activity, while the cellular environment harbors a myriad of proto-functional molecules. The emergence of function is facilitated by several mechanisms intrinsic to molecular organization, such as redundant mapping of sequences into structures, phenotypic plasticity, modularity, or coope…
Evolutionary adaptation through bet-hedging in finite populations under fluctuating environments
Grupo Interdisciplinar de Sistemas Complejos (GISC) and Departamento de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid（马德里康普顿斯大学复杂系统跨学科小组及物质结构、热学与电子学系）
Quantitative Genetics and Functional-Structural Plant Growth Models: Simulation of Quantitative Trait Loci Detection for Model Parameters and Application to Potential Yield Optimization
In order to target threatening pathogens, the adaptive immune system performs a continuous reorganization of its lymphocyte repertoire. Following an immune challenge, the B cell repertoire can evolve cells of increased specificity for the encountered strain. This process of affinity maturation generates a memory pool whose diversity and size remain difficult to predict. We assume that the immune system follows a strategy that maximizes the long-term immune coverage and minimizes the short-term metabolic costs associated with affinity maturation. This strategy is defined as an optimal decision …
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous mathematical models have jointly captured the dynamic changes in species' population distributions and the selective evolution of fitness-related phenotypic traits in the presence of an environmental gradient. These models inevitably include some unrealistic assumptions, and biologically reasonable ranges of values for their parameters are not easy to specify. As a …
A key goal in studies of ecology and evolution is understanding the causes of phenotypic diversity in nature. Most traits of interest, such as those relating to morphology, life-history, immunity and behaviour are quantitative, and phenotypic variation is driven by the cumulative effects of genetic and environmental variation. The field of quantitative genetics aims to quantify the additive genetic component of this trait variance (i.e. the "heritability"), often with the underlying assumption that trait variance is driven by many loci of infinitesimal effects throughout the genome. This appro…
