Dynamic Trait Distribution as a Source for Shifts in Interaction Strength and Population Density.

AbstractIntraspecific trait variation has been increasingly recognized as an important factor in determining species interactions and diversity. Eco-evolutionary models have studied the distribution of trait values within a population that changes over the generations as a result of selection and heritability. Nonheritable traits that can change within the lifetime, such as behavior, can cause trait-mediated indirect effects, often studied by modeling the dynamics of a homogeneous trait. Complementary to these approaches, we study the distribution of traits within a population and its dynamics on short timescales due to ecological processes. We consider several mechanisms by which the trait distribution can shift dynamically: phenotypic plasticity within each individual, differential growth among individuals, and preferential consumption by the predator. Through a simple predator-prey model that explicitly tracks the trait distribution within the prey, we identify the density and trait effects from the predator. We show that the dynamic shift of the trait distribution can lead to the modification of interaction strength between species and result in otherwise unexpected consequences. A particular example is the emergent promotion of the prey by the predator, where the introduction of the predator causes the prey population to increase rather than decrease.

A theoretical perspective on Waddington's genetic assimilation experiments.

Genetic assimilation is the process by which a phenotype that is initially induced by an environmental stimulus becomes stably inherited in the absence of the stimulus after a few generations of selection. While the concept has attracted much debate after being introduced by C. H. Waddington 70 y ago, there have been few experiments to quantitatively characterize the phenomenon. Here, we revisit and organize the results of Waddington's original experiments and follow-up studies that attempted to replicate his results. We then present a theoretical model to illustrate the process of genetic assimilation and highlight several aspects that we think require further quantitative studies, including the gradual increase of penetrance, the statistics of delay in assimilation, and the frequency of unviability during selection. Our model captures Waddington's picture of developmental paths in a canalized landscape using a stochastic dynamical system with alternative trajectories that can be controlled by either external signals or internal variables. It also reconciles two descriptions of the phenomenon-Waddington's, expressed in terms of an individual organism's developmental paths, and that of Bateman in terms of the population distribution crossing a hypothetical threshold. Our results provide theoretical insight into the concepts of canalization, phenotypic plasticity, and genetic assimilation.

Crosstalk enables mutual activation of coupled quorum sensing pathways through "jump-start" and "push-start" mechanisms.

Many quorum sensing microbes produce more than one chemical signal and detect them using interconnected pathways that crosstalk with each other. While there are many hypotheses for the advantages of sensing multiple signals, the prevalence and functional significance of crosstalk between pathways are much less understood. We explore the effect of intracellular signal crosstalk using a simple model that captures key features of typical quorum sensing pathways: multiple pathways in a hierarchical configuration, operating with positive feedback, with crosstalk at the receptor and promoter levels. We find that crosstalk enables activation or inhibition of one output by the non-cognate signal, broadens the dynamic range of the outputs, and allows one pathway to modulate the feedback circuit of the other. Our findings show how crosstalk between quorum sensing pathways can be viewed not as a detriment to the processing of information, but as a mechanism that enhances the functional range of the full regulatory system. When positive feedback systems are coupled through crosstalk, several new modes of activation or deactivation become possible.

Internal cues for optimizing reproduction in a varying environment.

In varying environments, it is beneficial for organisms to utilize available cues to infer the conditions they may encounter and express potentially favourable traits. However, external cues can be unreliable or too costly to use. We consider an alternative strategy where organisms exploit internal sources of information. Even without sensing environmental cues, their internal states may become correlated with the environment as a result of selection, which then form a memory that helps predict future conditions. To demonstrate the adaptive value of such internal cues in varying environments, we revisit the classic example of seed dormancy in annual plants. Previous studies have considered the germination fraction of seeds and its dependence on environmental cues. In contrast, we consider a model of germination fraction that depends on the seed age, which is an internal state that can serve as a memory. We show that, if the environmental variation has temporal structure, then age-dependent germination fractions will allow the population to have an increased long-term growth rate. The more the organisms can remember through their internal states, the higher the growth rate a population can potentially achieve. Our results suggest experimental ways to infer internal memory and its benefit for adaptation in varying environments.

Heterogeneity of interaction strengths and its consequences on ecological systems.

Ecosystems are formed by networks of species and their interactions. Traditional models of such interactions assume a constant interaction strength between a given pair of species. However, there is often significant trait variation among individual organisms even within the same species, causing heterogeneity in their interaction strengths with other species. The consequences of such heterogeneous interactions for the ecosystem have not been studied systematically. As a theoretical exploration, we analyze a simple ecosystem with trophic interactions between two predators and a shared prey, which would exhibit competitive exclusion in models with homogeneous interactions. We consider several scenarios where individuals of the prey species differentiate into subpopulations with different interaction strengths. We show that in all these cases, whether the heterogeneity is inherent, reversible, or adaptive, the ecosystem can stabilize at a new equilibrium where all three species coexist. Moreover, the prey population that has heterogeneous interactions with its predators reaches a higher density than it would without heterogeneity, and can even reach a higher density in the presence of two predators than with just one. Our results suggest that heterogeneity may be a naturally selected feature of ecological interactions that have important consequences for the stability and diversity of ecosystems.

Effect of compositional fluctuation on the survival of bet-hedging species.

Understanding the coexistence of diverse species in a changing environment is an important problem in community ecology. Bet-hedging is a strategy that helps species survive in such changing environments. However, studies of bet-hedging have often focused on the expected long-term growth rate of the species by itself, neglecting competition with other coexisting species. Here we study the extinction risk of a bet-hedging species in competition with others. We show that there are three contributions to the extinction risk. The first is the usual demographic fluctuation due to stochastic reproduction and selection processes in finite populations. The second, due to the fluctuation of population growth rate caused by environmental changes, may actually reduce the extinction risk for small populations. Besides those two, we reveal a third contribution, which is unique to bet-hedging species that diversify into multiple phenotypes: The phenotype composition of the population will fluctuate over time, resulting in increased extinction risk. We compare such compositional fluctuation to the demographic and environmental contributions, showing how they have different effects on the extinction risk depending on the population size, generation overlap, and environmental correlation.

Nongenetic individuality, changeability, and inheritance in bacterial behavior.

Isogenic populations often display remarkable levels of phenotypic diversity even in constant, homogeneous environments. Such diversity results from differences between individuals ("nongenetic individuality") as well as changes during individuals' lifetimes ("changeability"). Yet, studies that capture and quantify both sources of diversity are scarce. Here we measure the swimming behavior of hundreds of Escherichia coli bacteria continuously over two generations and use a model-independent method for quantifying behavior to show that the behavioral space of E. coli is low-dimensional, with variations occurring mainly along two independent and interpretable behavioral traits. By statistically decomposing the diversity in these two traits, we find that individuality is the main source of diversity, while changeability makes a smaller but significant contribution. Finally, we show that even though traits of closely related individuals can be remarkably different, they exhibit positive correlations across generations that imply nongenetic inheritance. The model-independent experimental and theoretical framework developed here paves the way for more general studies of microbial behavioral diversity.

Bacterial Growth Control Mechanisms Inferred from Multivariate Statistical Analysis of Single-Cell Measurements.

Analysis of single-cell measurements of bacterial growth and division often relied on testing preconceived models of cell size control mechanisms. Such an approach could limit the scope of data analysis and prevent us from uncovering new information. Here, we take an "agnostic" approach by applying regression methods to multiple simultaneously measured cellular variables, which allow us to infer dependencies among those variables from their apparent correlations. Besides previously observed correlations attributed to particular cell size control mechanisms, we identify dependencies that point to potentially new mechanisms. In particular, cells born smaller than their sisters tend to grow faster and make up for the size difference acquired during division. We also find that sister cells are correlated beyond what single-cell, size-control models predict. These trends are consistently found in repeat experiments, although the dependencies vary quantitatively. Such variation highlights the sensitivity of cell growth to environmental variations and the limitation of currently used experimental setups.

Environment-to-phenotype mapping and adaptation strategies in varying environments.

Biological organisms exhibit diverse strategies for adapting to varying environments. For example, a population of organisms may express the same phenotype in all environments ("unvarying strategy") or follow environmental cues and express alternative phenotypes to match the environment ("tracking strategy"), or diversify into coexisting phenotypes to cope with environmental uncertainty ("bet-hedging strategy"). We introduce a general framework for studying how organisms respond to environmental variations, which models an adaptation strategy by an abstract mapping from environmental cues to phenotypic traits. Depending on the accuracy of environmental cues and the strength of natural selection, we find different adaptation strategies represented by mappings that maximize the long-term growth rate of a population. The previously studied strategies emerge as special cases of our model: The tracking strategy is favorable when environmental cues are accurate, whereas when cues are noisy, organisms can either use an unvarying strategy or, remarkably, use the uninformative cue as a source of randomness to bet hedge. Our model of the environment-to-phenotype mapping is based on a network with hidden units; the performance of the strategies is shown to rely on having a high-dimensional internal representation, which can even be random.

Benefits of phenotypic plasticity for population growth in varying environments.

Phenotypic plasticity refers to the capacity of the same organisms to exhibit different characteristics under varied environmental conditions. A plastic developmental program allows organisms to sense environmental cues in early stages of life and express phenotypes that are better fitted to environments encountered later in life. This is often considered an adaptive strategy for living in varying environments as long as the plastic response is sufficiently fast, is accurate, and is not too costly. However, despite direct costs of maintaining plasticity and producing phenotypes, a fundamental constraint on the benefit of phenotypic plasticity comes from the predictability of the future environment based on the environmental cues received during development. Here, we analyze a model of plastic development and derive the limits within which this strategy can promote population growth. An explicit expression for the long-term growth rate of a developmentally plastic population is found, which can be decomposed into several easily interpretable terms, representing the benefits and the limitations of phenotypic plasticity as an adaptation strategy. This growth rate decomposition has a remarkably similar form to the expressions previously obtained for the bet-hedging strategy, in which a population randomly diversifies into coexisting subgroups with different phenotypes, implying that those evolutionary strategies may be unified under a common general framework.

Bet Hedging against Demographic Fluctuations.

Biological organisms have to cope with stochastic variations in both the external environment and the internal population dynamics. Theoretical studies and laboratory experiments suggest that population diversification could be an effective bet-hedging strategy for adaptation to varying environments. Here we show that bet hedging can also be effective against demographic fluctuations that pose a trade-off between growth and survival for populations even in a constant environment. A species can maximize its overall abundance in the long term by diversifying into coexisting subpopulations of both "fast-growing" and "better-surviving" individuals. Our model generalizes statistical physics models of birth-death processes to incorporate dispersal, during which new populations are founded, and can further incorporate variations of local environments. In this way, we unify different bet-hedging strategies against demographic and environmental variations as a general means of adaptation to both types of uncertainties in population growth.

Evolutionary learning of adaptation to varying environments through a transgenerational feedback.

Organisms can adapt to a randomly varying environment by creating phenotypic diversity in their population, a phenomenon often referred to as "bet hedging." The favorable level of phenotypic diversity depends on the statistics of environmental variations over timescales of many generations. Could organisms gather such long-term environmental information to adjust their phenotypic diversity? We show that this process can be achieved through a simple and general learning mechanism based on a transgenerational feedback: The phenotype of the parent is progressively reinforced in the distribution of phenotypes among the offspring. The molecular basis of this learning mechanism could be searched for in model organisms showing epigenetic inheritance.

Unstable growth of curvature perturbations in nonsingular bouncing cosmologies.

Bouncing cosmologies require an ekpyrotic contracting phase (w≫1) in order to achieve flatness, homogeneity, and isotropy. Models with a nonsingular bounce further require a bouncing phase that violates the null energy condition (w<-1). We show that the transition from the ekpyrotic phase to the bouncing phase creates problems for cosmological perturbations. A component of the adiabatic curvature perturbations, though decaying and negligible during the ekpyrotic phase, is exponentially amplified just before w approaches -1, enough to spoil the scale-invariant perturbation spectrum.