A SIMULATION OF WRIGHT'S SHIFTING-BALANCE PROCESS: MIGRATION AND THE THREE PHASES

Wright partitioned the shifting-balance process into three phases. Phase one is the shift of a deme within a population to the domain of a higher adaptive peak from that of the historical peak. Phase two is mass selection within a deme towards that higher peak. Phase three is the conversion of additional demes to the higher peak. The migration rate between demes is critical for the existence of phases one and three. Phase one requires small effective population sizes, hence low migration rates. Phase three is optimal under high migration rates that spread the most-fit genotype from deme to deme. Thus, a population-wide peak shift requires intermediate levels of migration. By altering the rates of phases one and three, migration affects the predominant direction of mass selection within a population. This study examines the degree to which migration, through its effects on phases one and three, determines the probability of a simulated population arriving at its genotypic optimum after 12,000 generations. These simulations reveal that there is a range of migration rates for which an entire population might be expected to shift to a higher peak. Below m = 0.001 peak shifts occur frequently (phases I and II) but are not successfully exported out of subpopulations (phase III), and above 0.01 peak shifts within demes (phase I and II), required to initiate phase III, become increasingly uncommon. Because it is unlikely that real populations will have uniform migration rates from generation to generation, the probable effects of varying migration rates on broadening the range of conditions producing peak shifts are discussed.     

PHASE THREE OF WRIGHT'S SHIFTING-BALANCE THEORY

We examine the third phase of Wright's shifting-balance theory of evolution, the exportation by migration of favorable gene combinations from a fitter subgroup to the rest of the population. The equations are deterministic and are studied numerically. Most of the models studied involve 2–9 loci in which all intermediates between two extreme genotypes are equally unfit. If the favored combination consists of dominant alleles, it is usually fixed even if the migration rate is two orders of magnitude less than the selection coefficient, and if the combination is recessive, one order. Although Wright thought of migration as being essentially one-way, two-way migration does not significantly alter the results. We conclude that, whatever weaknesses the Wright theory may have, they are not in phase III.     

PEAK SHIFTS AND POLYMORPHISM DURING PHASE THREE OF WRIGHT'S SHIFTING-BALANCE PROCESS

The third phase of Wright's shifting-balance theory involves the export of adaptive gene combinations from one subpopulation to another. Previous results have demonstrated that this can occur at very low migration rates, but it has been argued that this simply reflects the ability of migration to overcome selection and fix any (even deleterious) alleles. Here, previous analyses are extended by concentrating on the critical balance between forward and reverse migration rates that still allows phase III to proceed. It is shown that selective advantage, dominance, recombination rate, and the number of loci all affect the ability of a genotype to invade and become fixed in a new subpopulation, but it is unlikely that phase III will occur in the absence of differential migration unless the invading genotype consists of a few dominant loci with a large selection advantage, spreading into a few populations of lower fitness. Therefore, as was envisioned by Wright, differential migration from more to less fit populations will be necessary for phase III to occur under most circumstances.     

VARIANCE-INDUCED PEAK SHIFTS

The increase in phenotypic variance that occurs in some populations as a result of bottlenecks and founder events can cause a dramatic increase in the probability of a peak shift from one adaptive state to another. Periods of small population size allow drift in the amount of phenotypic variance. Increases in phenotypic variance, coupled with a constant individual fitness function with multiple peaks, can cause the mean fitness landscape to change from bimodal to unimodal, thereby allowing the population's mean phenotype to change deterministically by selection. As the amount of phenotypic variance is returned to an equilibrium state, the multiple peaks reemerge, but the population has moved from one stable state to another. These variance-induced peak shifts allow punctuational evolution from one peak to another at a rate that can be much higher than that predicted by Wright's shifting-balance process alone.     

Population structure and evolutionary progress

Wright's shifting-balance theory is discussed as an example of a process that can cause species to evolve combinations of characters that could not evolve under natural selection alone. A review of the existing theory of peak shifts indicates that the conditions of extreme isolation that are necessary to permit genetic drift to alter the outcome of natural selection in local populations would make gene flow too weak to spread a new combination of genes to other populations in a reasonable time. Instead, it seems likely that major demographic changes must occur in a species for the shifting-balance process to work. A discussion of direct and indirect studies of gene flow in natural populations suggests that the current genetic structure of many species is likely to reflect past demographic events rather than ongoing gene flow. It is possible then that demographic processes could be responsible for spreading new traits in a species, but that would be true whether those new traits evolved only owing to natural selection or owing in addition to genetic drift and other forces.     

Population and evolutionary dynamics in spatially structured seasonally varying environments

Increasingly imperative objectives in ecology are to understand and forecast population dynamic and evolutionary responses to seasonal environmental variation and change. Such population and evolutionary dynamics result from immediate and lagged responses of all key life‐history traits, and resulting demographic rates that affect population growth rate, to seasonal environmental conditions and population density. However, existing population dynamic and eco‐evolutionary theory and models have not yet fully encompassed within‐individual and among‐individual variation, covariation, structure and heterogeneity, and ongoing evolution, in a critical life‐history trait that allows individuals to respond to seasonal environmental conditions: seasonal migration. Meanwhile, empirical studies aided by new animal‐tracking technologies are increasingly demonstrating substantial within‐population variation in the occurrence and form of migration versus year‐round residence, generating diverse forms of ‘partial migration’ spanning diverse species, habitats and spatial scales. Such partially migratory systems form a continuum between the extreme scenarios of full migration and full year‐round residence, and are commonplace in nature. Here, we first review basic scenarios of partial migration and associated models designed to identify conditions that facilitate the maintenance of migratory polymorphism. We highlight that such models have been fundamental to the development of partial migration theory, but are spatially and demographically simplistic compared to the rich bodies of population dynamic theory and models that consider spatially structured populations with dispersal but no migration, or consider populations experiencing strong seasonality and full obligate migration. Second, to provide an overarching conceptual framework for spatio‐temporal population dynamics, we define a ‘partially migratory meta‐population’ system as a spatially structured set of locations that can be occupied by different sets of resident and migrant individuals in different seasons, and where locations that can support reproduction can also be linked by dispersal. We outline key forms of within‐individual and among‐individual variation and structure in migration that could arise within such systems and interact with variation in individual survival, reproduction and dispersal to create complex population dynamics and evolutionary responses across locations, seasons, years and generations. Third, we review approaches by which population dynamic and eco‐evolutionary models could be developed to test hypotheses regarding the dynamics and persistence of partially migratory meta‐populations given diverse forms of seasonal environmental variation and change, and to forecast system‐specific dynamics. To demonstrate one such approach, we use an evolutionary individual‐based model to illustrate that multiple forms of partial migration can readily co‐exist in a simple spatially structured landscape. Finally, we summarise recent empirical studies that demonstrate key components of demographic structure in partial migration, and demonstrate diverse associations with reproduction and survival. We thereby identify key theoretical and empirical knowledge gaps that remain, and consider multiple complementary approaches by which these gaps can be filled in order to elucidate population dynamic and eco‐evolutionary responses to spatio‐temporal seasonal environmental variation and change.     

On using integral projection models to generate demographically driven predictions of species' distributions: development and validation using sparse data

Knowledge of species' geographic distributions is critical for understanding and forecasting population dynamics, responses to environmental change, biodiversity patterns, and conservation planning. While many suggestive correlative occurrence models have been used to these ends, progress lies in understanding the underlying population biology that generates patterns of range dynamics. Here, we show how to use a limited quantity of demographic data to produce demographic distribution models (DDMs) using integral projection models for size‐structured populations. By modeling survival, growth, and fecundity using regression, integral projection models can interpolate across missing size data and environmental conditions to compensate for limited data. To accommodate the uncertainty associated with limited data and model assumptions, we use Bayesian models to propagate uncertainty through all stages of model development to predictions. DDMs have a number of strengths: 1) DDMs allow a mechanistic understanding of spatial occurrence patterns; 2) DDMs can predict spatial and temporal variation in local population dynamics; 3) DDMs can facilitate extrapolation under altered environmental conditions because one can evaluate the consequences for individual vital rates. To illustrate these features, we construct DDMs for an overstory perennial shrub in the Proteaceae family in the Cape Floristic Region of South Africa. We find that the species' population growth rate is limited most strongly by adult survival throughout the range and by individual growth in higher rainfall regions. While the models predict higher population growth rates in the core of the range under projected climates for 2050, they also suggest that the species faces a threat along arid range margins from the interaction of more frequent fire and drying climate. The results (and uncertainties) are helpful for prioritizing additional sampling of particular demographic parameters along these gradients to iteratively refine projections. In the appendices, we provide fully functional R code to perform all analyses.     

Primate DNA suggests long‐term stability of an African rainforest

Red colobus monkeys, due to their sensitivity to environmental change, are indicator species of the overall health of their tropical rainforest habitats. As a result of habitat loss and overhunting, they are among the most endangered primates in the world, with very few viable populations remaining. Traditionally, extant indicator species have been used to signify the conditions of their current habitats, but they have also been employed to track past environmental conditions by detecting previous population fluctuations. Kibale National Park (KNP) in Uganda harbors the only remaining unthreatened large population of red colobus. We used microsatellite DNA to evaluate the historical demography of these red colobus and, therefore, the long‐term stability of their habitat. We find that the red colobus population throughout KNP has been stable for at least ~40,000 years. We interpret this result as evidence of long‐term forest stability because a change in the available habitat or population movement would have elicited a corresponding change in population size. We conclude that the forest of what is now Kibale National Park may have served as a Late Pleistocene refuge for many East African species.     

Necessary and sufficient conditions for evolutionary suicide

Evolutionary suicide is an evolutionary process where a viable population adapts in such a way that it can no longer persist. It has already been found that a discontinuous transition to extinction is a necessary condition for suicide. Here we present necessary and sufficient conditions, concerning the bifurcation point, for suicide to occur. Evolutionary suicide has been found in structured metapopulation models. Here we show that suicide can occur also in unstructured population models. Moreover, a structured model does not guarantee the possibility of suicide: we show that suicide cannot occur in age-structured population models of the Gurtin-MacCamy type. The point is that the mutant’s fitness must explicitly depend not only on the environmental interaction variable, but also on the resident strategy.     

ON PHASE THREE OF THE SHIFTING-BALANCE THEORY

A common conclusion in several recent publications devoted to the deterministic analysis of the third phase of Wright's shifting-balance theory is that under reasonable conditions phase three should proceed easily. I argue that the mathematical equations analyzed in these papers do not correspond to the biological situation they were meant to describe. I present a more appropriate study of the third phase of the shifting balance. My results show that the third phase can proceed only under much more restricted conditions than the previous studies suggested. Migration should be neither too strong not too weak relative to selection. The higher peak should be sufficiently dominant over the lower peak. Recombination can greatly reduce the plausibility of this phase or completely preclude peak shifts. A very important determinant of the ultimate outcome of the competition between different peaks is the topological structure of the network of demes. Peak shifts in two-dimensional networks of demes are more difficult than in one-dimensional networks. Phase three can be accomplished easiest if it is initiated in one of the peripheral demes.     

Anecdotal,Historical and Critical Commentaries on Genetics: Wright and Fisher on Inbreeding and Random Drift

Sewall Wright and R. A. Fisher often differed, including on the meaning of inbreeding and random gene frequency drift. Fisher regarded them as quite distinct processes, whereas Wright thought that because his inbreeding coefficient measured both they should be regarded as the same. Since the effective population numbers for inbreeding and random drift are different, this would argue for the Fisher view.SEWALL Wright and R. A. Fisher were central figures in mathematical population genetics; along with J. B. S. Haldane they effectively invented the field and dominated it for many years. On most issues the three were in agreement. In particular, all favored a neo-Darwinian gradualist approach and believed in the importance of a mathematical theory for understanding the evolutionary process. Yet on a few questions Fisher and Wright differed profoundly and argued vehemently. Fisher was contentious and was often involved in controversy, frequently attacking his opponents mercilessly. Wright, in contrast, was very gentle to most people. But there were a few exceptions and Fisher was one. Haldane mostly stayed out of the arguments between them.One question on which the two disagreed was the importance of random gene frequency drift and its role in Wright''s shifting-balance theory of evolution. Wright thought that a structured population with many partially isolated subpopulations, within which there was random drift and among which there was an appropriate amount of migration, offered the greatest chance for evolutionary novelty and could greatly increase the speed of evolution. Fisher thought that a large panmictic population offered the best chance for advantageous genes and gene combinations to spread through the population, unimpeded by random processes. They also disagreed on dominance, Fisher believing that it evolved by selection of dominance modifiers and Wright that it was a consequence of the nature of gene action. These differences were widely argued by population geneticists in the middle third of the twentieth century, and the interested community divided into two camps. Although the issues are not settled, Wright''s shifting-balance theory has less support than it formerly had. As for dominance, there is general quantitative disagreement with Fisher''s explanation of modifiers, but other mechanisms (e.g., selection for more active alleles) have to some extent replaced it. Wright''s theory remains popular and has been generalized and extended (Kacser and Burns 1973).     

Regulation of developmental transitions

Plants undergo a series of profound developmental changes throughout their lifetimes in response to both external environmental factors and internal intrinsic ones. When these changes are abrupt and dramatic, the process is referred to as phase change. Recently, several genes have been discovered that play a role in these developmental transitions. Their sequence and expression patterns shed new light on the mechanisms of phase change, and provide a link between the external and internal factors that control them. Examples of these transitions include changes from juvenile to adult leaf formation, vegetative to inflorescence meristem development, and inflorescence to floral meristem initiation.     

Cumulative weather effects can impact across the whole life cycle

Predicting how species will be affected by future climatic change requires the underlying environmental drivers to be identified. As vital rates vary over the lifecycle, structured population models derived from statistical environment–demography relationships are often used to inform such predictions. Environmental drivers are typically identified independently for different vital rates and demographic classes. However, these rates often exhibit positive temporal covariance, suggesting that vital rates respond to common environmental drivers. Additionally, models often only incorporate average weather conditions during a single, a priori chosen time window (e.g. monthly means). Mismatches between these windows and the period when the vital rates are sensitive to variation in climate decrease the predictive performance of such approaches. We used a demographic structural equation model (SEM) to demonstrate that a single axis of environmental variation drives the majority of the (co)variation in survival, reproduction, and twinning across six age–sex classes in a Soay sheep population. This axis provides a simple target for the complex task of identifying the drivers of vital rate variation. We used functional linear models (FLMs) to determine the critical windows of three local climatic drivers, allowing the magnitude and direction of the climate effects to differ over time. Previously unidentified lagged climatic effects were detected in this well‐studied population. The FLMs had a better predictive performance than selecting a critical window a priori, but not than a large‐scale climate index. Positive covariance amongst vital rates and temporal variation in the effects of environmental drivers are common, suggesting our SEM–FLM approach is a widely applicable tool for exploring the joint responses of vital rates to environmental change.     

The dynamics of climate-induced range shifting; perspectives from simulation modelling

Predicted future climate change will alter species' distributions as they attempt to track the most suitable 'climate window'. Climate envelope models indicate the direction of likely range changes but do not incorporate population dynamics, therefore observed responses may differ greatly from these projections. We use simulation modelling to explore the consequences of a period of environmental change for a species structured across an environmental gradient. Results indicate that a species' range may lag behind its climate envelope and demonstrate that the rate of movement of a range can accelerate during a period of climate change. We conclude that the inclusion of both population dynamics and spatial environmental variability is vital to develop models that can both predict, and be used to manage, the impact of changing climate on species' biogeography.     

Behaviourally structured populations persist longer under harsh environmental conditions

The factors and mechanisms that enhance population persistence in a fragmented habitat and/or under harsh environmental conditions are of significant current interest. We consider the dynamics of a population in an isolated habitat surrounded by an unfavourable environment subject to different behavioural responses between the individuals. We assume that there are two responses available: one of them is aggression in its extreme form, the other is its contrary when an individual takes flight in order to avoid any contact with its conspecific. We show that a behaviourally structured population consisting of individuals with fixed behavioural responses is intrinsically less prone to extinction under harsh environmental condition than a population where the individuals can ‘choose’ between the two given behaviours. We also show that, contrary to an intuitively expected negative impact of aggression on population persistence, the optimal conditions for population persistence are reached when a considerable proportion of the individuals exhibit aggressive behaviour.     

Density-structured models for plant population dynamics

Density-structured models are structured population models in which the state variable is the proportion of populations or sites in a small number of discrete density states. Although such models have rarely been used, they have the advantage that they are straightforward to parameterize, make few assumptions about population dynamics, and permit rapid data collection using coarse density assessment. In this article, we highlight their use in relating population dynamics to environmental variation and their robustness to measurement error. We show that density-structured models are able to accurately represent population dynamics under a wide range of conditions. We look at the effects of including a persistent seedbank and describe numerical approximations for the mean and variance of population size. For simulated data, we determine the extent to which the underlying continuous process may be inferred from density-structured data. Finally, we discuss issues of parameter estimation and applications for which these types of models may be useful.     

Causes and consequences of animal dispersal strategies: relating individual behaviour to spatial dynamics

Knowledge of the ecological and evolutionary causes of dispersal can be crucial in understanding the behaviour of spatially structured populations, and predicting how species respond to environmental change. Despite the focus of much theoretical research, simplistic assumptions regarding the dispersal process are still made. Dispersal is usually regarded as an unconditional process although in many cases fitness gains of dispersal are dependent on environmental factors and individual state. Condition-dependent dispersal strategies will often be superior to unconditional, fixed strategies. In addition, dispersal is often collapsed into a single parameter, despite it being a process composed of three interdependent stages: emigration, inter-patch movement and immigration, each of which may display different condition dependencies. Empirical studies have investigated correlates of these stages, emigration in particular, providing evidence for the prevalence of conditional dispersal strategies. Ill-defined use of the term 'dispersal', for movement across many different spatial scales, further hinders making general conclusions and relating movement correlates to consequences at the population level. Logistical difficulties preclude a detailed study of dispersal for many species, however incorporating unrealistic dispersal assumptions in spatial population models may yield inaccurate and costly predictions. Further studies are necessary to explore the importance of incorporating specific condition-dependent dispersal strategies for evolutionary and population dynamic predictions.     

Stationary phase mutagenesis: mechanisms that accelerate adaptation of microbial populations under environmental stress

Microorganisms are exposed to constantly changing environmental conditions. In a growth-restricting environment (e.g. during starvation), mutants arise that are able to take over the population by a process known as stationary phase mutation. Genetic adaptation of a microbial population under environmental stress involves mechanisms that lead to an elevated mutation rate. Under stressful conditions, DNA synthesis may become more erroneous because of the induction of error-prone DNA polymerases, resulting in a situation in which DNA repair systems are unable to cope with increasing amounts of DNA lesions. Transposition may also increase genetic variation. One may ask whether the rate of mutation under stressful conditions is elevated as a result of malfunctioning of systems responsible for accuracy or are there specific mechanisms that regulate the rate of mutations under stress. Evidence for the presence of mutagenic pathways that have probably been evolved to control the mutation rate in a cell will be discussed.     

Long- and short-term influence of environment on recruitment in a species with highly delayed maturity

Short-term effects of environmental perturbations on various life history traits are reasonably well documented in birds and mammals. But, in the present context of global climate change, there is a need to consider potential long-term effects of natal conditions to better understand and predict the consequences of these changes on population dynamics. The environmental conditions affecting offspring during their early development may determine their lifetime reproductive performance, and therefore the number of recruits produced by a cohort. In this study, we attempted to link recruitment to natal and recent (previous year) conditions in the long-lived black-browed albatross (Thalassarche melanophrys) at Kerguelen Islands. The environmental variability was described using both climatic variables over breeding (sea surface temperature anomaly) and non-breeding grounds (Southern Oscillation index), and variables related to the colony (breeding success and colony size). Immature survival was linked to the breeding success of the colony in the year of birth, which was expected to reflect the average seasonal parental investment. At the cohort level, this initial mortality event may act as a selective filter shaping the number, and presumably the quality (breeding frequency, breeding success probability), of the individuals that recruit into the breeding population. The decision to start breeding was strongly structured by the age of the individuals and adjusted according to recent conditions. An effect of natal conditions was not detected on this parameter, supporting the selection hypothesis. Recruitment, as a whole, was thus influenced by a combination of long- and short-term environmental impacts. Our results highlight the complexity of the influence of environmental factors on such long-lived species, due to the time-lag (associated with a delayed maturity) between the impact of natal conditions on individuals and their repercussion on the breeding population.     

EPISTASIS AND THE INCREASE IN ADDITIVE GENETIC VARIANCE: IMPLICATIONS FOR PHASE 1 OF WRIGHT'S SHIFTING-BALANCE PROCESS

Central to Wright's shifting-balance theory is the idea that genetic drift and selection in systems with gene interaction can lead to the formation of “adaptive gene complexes.” The theory of genetic drift has been well developed over the last 60 years; however, nearly all of this theory is based on the assumption that only additive gene effects are acting. Wright's theory was developed recognizing that there was a “universality of interaction effects,” which implies that additive theory may not be adequate to describe the process of differentiation that Wright was considering. The concept of an adaptive gene complex implies that an allele that is favored by individual selection in one deme may be removed by selection in another deme. In quantitative genetic terms, the average effects of an allele relative to other alleles changes from deme to deme. The model presented here examines the variance in local breeding values (LBVs) of a single individual and the covariance in the LBVs of a pair of individuals mated in the same deme relative to when they are mated in different demes. Local breeding value is a measure of the average effects of the alleles that make up that individual in a particular deme. I show that when there are only additive effects the covariance between the LBVs of individuals equals the variance in the LBV of an individual. As the amount of epistasis in the ancestral population increases, the variance in the LBV of an individual increases and the covariance between the LBVs of a pair of individuals decreases. The divergence in these two values is a measure of the extent to which the LBV of an individual varies independently of the LBVs of other individuals. When this value is large, it means that the relative ordering of the average effects of alleles will change from deme to deme. These results confirm an important component of Wright's shifting-balance theory: When there is gene interaction, genetic drift can lead to the reordering of the average effects of alleles and when coupled with selection this will lead to the formation of the adaptive gene complexes.