Negative frequency‐dependent interactions can underlie phenotypic heterogeneity in a clonal microbial population

Genetically identical cells in microbial populations often exhibit a remarkable degree of phenotypic heterogeneity even in homogenous environments. Such heterogeneity is commonly thought to represent a bet‐hedging strategy against environmental uncertainty. However, evolutionary game theory predicts that phenotypic heterogeneity may also be a response to negative frequency‐dependent interactions that favor rare phenotypes over common ones. Here we provide experimental evidence for this alternative explanation in the context of the well‐studied yeast GAL network. In an environment containing the two sugars glucose and galactose, the yeast GAL network displays stochastic bimodal activation. We show that in this mixed sugar environment, GAL‐ON and GAL‐OFF phenotypes can each invade the opposite phenotype when rare and that there exists a resulting stable mix of phenotypes. Consistent with theoretical predictions, the resulting stable mix of phenotypes is not necessarily optimal for population growth. We find that the wild‐type mixed strategist GAL network can invade populations of both pure strategists while remaining uninvasible by either. Lastly, using laboratory evolution we show that this mixed resource environment can directly drive the de novo evolution of clonal phenotypic heterogeneity from a pure strategist population. Taken together, our results provide experimental evidence that negative frequency‐dependent interactions can underlie the phenotypic heterogeneity found in clonal microbial populations.     

Exclusion rules, bottlenecks and the evolution of stochastic phenotype switching

Stochastic phenotype switching--often considered a bet hedging or risk-reducing strategy--can enhance the probability of survival in fluctuating environments. A recent experiment provided direct evidence for an adaptive origin by showing the de novo evolution of switching in bacterial populations propagated under a selective regime that captured essential features of the host immune response. The regime involved strong frequency-dependent selection realized via dual imposition of an exclusion rule and population bottleneck. Applied at the point of transfer between environments, the phenotype common in the current environment was assigned a fitness of zero and was thus excluded from participating in the next round (the exclusion rule). In addition, also at the point of transfer, and so as to found the next bout of selection, a single phenotypically distinct type was selected at random from among the survivors (the bottleneck). Motivated by this experiment, we develop a mathematical model to explore the broader significance of key features of the selective regime. Through a combination of analytical and numerical results, we show that exclusion rules and population bottlenecks act in tandem as potent selective agents for stochastic phenotype switching, such that even when initially rare, and when switching engenders a cost in Malthusian fitness, organisms with the capacity to switch can invade non-switching populations and replace non-switching types. Simulations demonstrate the robustness of our findings to alterations in switching rate, fidelity of exclusion, bottleneck size, duration of environmental state and growth rate. We also demonstrate the relevance of our model to a range of biological scenarios such as bacterial persistence and the evolution of sex.     

Modeling stochastic noise in gene regulatory systems

The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady-states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.     

Clonal variation of gene expression as a source of phenotypic diversity in parasitic protozoa

Within a cellular clone, individual cells can express different members of a gene family. If the difference in expression is transmitted to daughter cells, 'phenotypic clones' are formed. Such clonal phenotypic variation has evolved independently in phylogenetically distant parasitic protozoa under similar selective pressure: the need for phenotypic diversity at several steps of their life cycle. Here, I review clonal phenotypic variation processes, outline their role in parasite biology and argue that clonal phenotypic variation is complementary to sexual reproduction as a source of phenotypic diversity.     

Evolution in the real world: stochastic variation and the determinants of fitness in Carlina vulgaris

Empirical studies of life histories often ignore stochastic variation, despite theoretical demonstrations of its potential impact on life-history evolution. Here we use a novel approach to explore the effects of stochastic variation on life-history evolution and estimate the selection pressures operating on the monocarpic perennial Carlina vulgaris, in which flowering may be delayed by up to eight years. The approach is novel in that we use modern theoretical techniques to estimate selection pressures and the fitness landscape from a fully parameterised individual-based model. These approaches take into account temporal variation in demographic rates and density dependence. Analysis of 16 years' data revealed significant temporal variation in growth, mortality, and recruitment in our study population. Flowering was strongly size dependent and, unusually for such a species, also age dependent. Individual-based models of the flowering strategy, parameterized using field data, consistently underestimated the size at flowering, when temporal variation in demographic rates was ignored. In contrast, models that incorporated temporal variation in growth, mortality, and recruitment predicted sizes at flowering not significantly different from those observed in the field. Temporal variation in mortality, which had the largest effect on the flowering strategy, selected for increased size at flowering. An analytical approximation is presented to explain this result, extending the "1-year look-ahead criterion" presented in Rees et al. (2000). A fitness landscape generated by following the fate of rare mutant invaders with a broad range of alternative flowering strategies demonstrated that the observed parameters were adaptive. However, the fitness landscape reveals that approximately equal fitness is achieved by a broad range of strategies, providing a mechanism for the maintenance of genetic variation. To understand how the different parameters that defined our models determine the fitness of rare mutants, we numerically estimated the elasticities and sensitivities of mutant fitness. This demonstrated strong selection on a number of the parameters. Elasticities and sensitivities estimated in constant and random environments were significantly positively correlated, and both were negatively related to the standard error of the parameter. This last result is surprising and, we argue, reflects the genetic and phenotypic responses to selection.     

Effects of developmental stress on animal phenotype and performance: a quantitative review

Developmental stressors are increasingly recognised for their pervasive influence on the ecology and evolution of animals. In particular, many studies have focused on how developmental stress can give rise to variation in adult behaviour, physiology, and performance. However, there remains a poor understanding of whether general patterns exist in the effects and magnitude of phenotypic responses across taxonomic groups. Furthermore, given the extensive phenotypic variation that arises from developmental stressors, it remains important to ascertain how multiple processes may explain these responses. We compiled data from 111 studies to examine and quantify the effect of developmental stress on animal phenotype and performance from juveniles to adulthood, including studies from birds, reptiles, fish, mammals, insects, arachnids, and amphibians. Using meta‐analytic approaches, we show that across all studies there is, on average, a moderate to large negative effect of developmental stress exposure (posterior mean effect: |d| = ?0.51) on animal phenotype or performance. Additionally, we demonstrate that interactive effects of timing of stressor onset and the duration of exposure to stressors best explained variation in developmental stress responses. Animals exposed to stressors earlier in development had more‐positive responses than those with later onset, whereas longer duration of exposure to a stressor caused responses to be stronger in magnitude. However, the high amount of heterogeneity in our results, and the low degree of variance explained by fixed effects in both the meta‐analysis (R² = 0.034) and top‐ranked meta‐regression model (R² = 0.02), indicate that phenotypic responses to developmental stressors are likely highly idiosyncratic in nature and difficult to predict. Despite this, our analyses address a critical knowledge gap in understanding what effect developmental stress has on phenotypic variation in animals. Additionally, our results highlight important environmental and proximate factors that may influence phenotypic responses to developmental stressors.     

Evolution and population dynamics in stochastic environments

Inter-generational temporal variability of the environment is important in the evolution and adaptation of phenotypic traits. We discuss a population-dynamic approach which plays a central role in the analysis of evolutionary processes. The basic principle is that the phenotypes with the greatest long-term average growth rate will dominate the entire population. The calculation of longterm average growth rates for populations under temporal stochasticity can be highly cumbersome. However, for a discrete non-overlapping population, it is identical to the geometric mean of the growth rates (geometric mean fitness), which is usually different from the simple arithmetic mean of growth rates. Evolutionary outcomes based on geometric mean fitness are often very different from the predictions based on the usual arithmetic mean fitness. In this paper we illustrate the concept of geometric mean fitness in a few simple models. We discuss its implications for the adaptive evolution of phenotypes, e.g. foraging under predation risks and clutch size. Next, we present an application: the risk-spreading egg-laying behaviour of the cabbage white butterfly, and develop a two-patch population dynamic model to show how the optimal solution diverges from the ssual arithmetic mean approach. The dynamics of these stochastic models cannot be predicted from the dynamics of simple deterministic models. Thus the inclusion of stochastic factors in the analyses of populations is essential to the understanding of not only population dynamics, but also their evolutionary dynamics.     

Diapause and bet-hedging strategies in insects: a meta-analysis of reaction norm shapes

Many organisms escape from lethal climatological conditions by entering a resistant resting stage called diapause, which needs to be optimally timed with seasonal change. As climate change exerts selection pressure on phenology, the evolution of mean diapause timing, but also of phenotypic plasticity and bet-hedging strategies is expected. The potential of the latter strategy as a means of coping with environmental unpredictability has received little attention in the climate change literature. Populations should be adapted to spatial variation in local conditions; contemporary patterns of phenological strategies across a geographic range may hence provide information about their evolvability. We thus extracted 458 diapause reaction norms from 60 studies. First, we correlated mean diapause timing with mean winter onset. Then we partitioned the reaction norm variance into a temporal component (phenotypic plasticity) and among-offspring variance (diversified bet-hedging) and correlated this variance composition with variability of winter onset. Mean diapause timing correlated reasonably well with mean winter onset, except for populations at high latitudes, which apparently failed to track early onsets. Variance among offspring was, however, limited and correlated only weakly with environmental variability, indicating little scope for bet-hedging. The apparent lack of phenological bet-hedging strategies may pose a risk in a less predictable climate, but we also highlight the need for more data on alternative strategies.     

Bistability in feedback circuits as a byproduct of evolution of evolvability

Noisy bistable dynamics in gene regulation can underlie stochastic switching and is demonstrated to be beneficial under fluctuating environments. It is not known, however, if fluctuating selection alone can result in bistable dynamics. Using a stochastic model of simple feedback networks, we apply fluctuating selection on gene expression and run in silico evolutionary simulations. We find that independent of the specific nature of the environment–fitness relationship, the main outcome of fluctuating selection is the evolution of increased evolvability in the network; system parameters evolve toward a nonlinear regime where phenotypic diversity is increased and small changes in genotype cause large changes in expression level. In the presence of noise, the evolution of increased nonlinearity results in the emergence and maintenance of bistability. Our results provide the first direct evidence that bistability and stochastic switching in a gene regulatory network can emerge as a mechanism to cope with fluctuating environments. They strongly suggest that such emergence occurs as a byproduct of evolution of evolvability and exploitation of noise by evolution.     

Population density, phenotype and reproductive output in the grasshopper Chorthippus brunneus

ABSTRACT. 1. The effects of population density on the reproductive output of individual female grasshoppers ( Chorthippus brunneus Thunberg) and the relationships between reproductive output and component elements of each female's phenotype, were investigated.
2. Reproductive output was primarily determined by the rate of egg-pod production. Increased density led to significant reductions in the rate of egg-pod production and reproductive output.
3. Exoskeleton size (reflecting nymphal experience) was positively correlated with clutch size at both high and low densities, but condition (reflecting adult experience) showed no such correlation. At high density, exoskeleton size was more strongly correlated with the rate of egg-pod production and reproductive output than condition. It is concluded that the nymphal aspects of size are more important than the adult aspects.
4. At low density, females with small exoskeletons compensated for their smaller clutches by producing egg-pods at a faster rate. Thus, there was no overall relationship between reproductive output and any of the phenotypic characteristics.
5. The effects of competition were weakly asymmetric in high density populations. The weakness of the asymmetry suggests scramble-like interactions for resources. It is concluded that not only are the effects of competition influenced by individual differences, but also that competition may reveal differences that would not otherwise be apparent.     

Phenotypic variation in colour pattern and seasonal plasticity in Eristalis hoverflies (Diptera: Syrphidae)

Abstract.

• 1 An examination of phenotypic variation in colour pattern was carried out on four Eristalis hoverfly species using museum material.
• 2 The amount of phenotypic variation varied substantially among the species with E.arbustorum being the most variable. The other species showed a wide colour pattern range but less variation within that range (E.abusivus and E.nemorum), or a narrow range of colour variation (E.horticola).
• 3 Sexual colour dimorphism was apparent in all four species, but most pronounced in E.abusivus and E.nemorum.
• 4 There were good phenotype-season relationships shown by both sexes in all species, except for female E.abusivus and E.nemorum, with paler insects being more abundant during the warmer summer months.
• 5 Female, but not male, E.arbustorum collected at inland sites were on average paler than those collected at coastal sites. This observation is considered with respect to temperature during the developmental stages.
• 6 The function of colour plasticity in hoverflies is discussed with reference to the need to maintain optimal thermal conditions for activity.

     

Diagnostic challenges in retinitis pigmentosa: genotypic multiplicity and phenotypic variability

Retinitis pigmentosa (RP) is a heterogeneous group of inherited retinal disorders. Diagnosis can be challenging as more than 40 genes are known to cause non-syndromic RP and phenotypic expression can differ significantly resulting in variations in disease severity, age of onset, rate of progression, and clinical findings. We describe the clinical manifestations of RP, the more commonly known causative gene mutations, and the genotypic-phenotypic correlation of RP.     

Fever and phenotype: transgenerational effect of disease on desert locust phase state

Natural enemy attack can cause transgenerational shifts in phenotype such that offspring are less vulnerable to future attack. Desert locusts (Schistocerca gregaria) show density‐dependent variation in their resistance to pathogens, such that they are less vulnerable to pathogens when in the high‐density gregarious phase state (when they would probably be more exposed to pathogens) than when in the solitarious phase state. We therefore hypothesized that infected gregarious parents would maintain this phenotype in their offspring. We infected gregarious desert locust nymphs with the fungal pathogen Metarhizium anisopliae var. acridum, and allowed them to survive to reproduction by means of behavioural fever. The phase state of the locust offspring was assessed by their colouration and behavioural assays. Contrary to our hypothesis, we found an increase in solitarization in the infected population (14.6% solitarious offspring from infected parents, vs. <2% from uninfected counterparts at equivalent density). In a second experiment, we simulated behavioural fever temperatures and obtained a similar result (13.6% solitarious offspring vs. 4.4% from controls), implying that the phenomenon is probably a side‐effect of the hosts’ fever response. Identification of this novel environmental factor affecting locust phase state could have important implications for the biological control of these major pests.     

Fitness and entropy production in a cell population dynamics with epigenetic phenotype switching

Motivated by recent understandings in the stochastic natures of gene expression, biochemical signaling, and spontaneous reversible epigenetic switchings, we study a simple deterministic cell population dynamics in which subpopulations grow with different rates and individual cells can bi-directionally switch between a small number of different epigenetic phenotypes. Two theories in the past, the population dynamics and thermodynamics of master equations, separately defined two important concepts in mathematical terms: the fitness in the former and the (non-adiabatic) entropy production in the latter. Both of them play important roles in the evolution of the cell population dynamics. The switching sustains the variations among the subpopulation growth, thus sustains continuous natural selection. As a form of Price’s equation, the fitness increases with (i) natural selection through variations and (ii) a positive covariance between the per capita growth and switching, which represents a Lamarchian-like behavior. A negative covariance balances the natural selection in a fitness steady state --- “the red queen” scenario. At the same time the growth keeps the proportions of subpopulations away from the “intrinsic” switching equilibrium of individual cells, thus leads to a continuous entropy production. A covariance, between the per capita growth rate and the “chemical potential” of subpopulation, counteracts the entropy production. Analytical results are obtained for the limiting cases of growth dominating switching and vice versa.