The evolution of reaction norms: simple models for age and size at maturity

This paper presents a simple model for the evolution of reaction norms for age and size at maturity that predicts reaction norms with a variety of shapes. Using realistic parameter values the model predicts reaction norms close to those observed in Drosophila. The major assumptions of the model are: 1) that net reproductive rate is maximized, 2) that growth is determinate, and 3) that mortality rates are independent of age and size at maturity. If, additionally, juvenile mortality is uncorrelated with a growth coefficient, k, the model predicts that selection favors maturation later at a smaller size when k is reduced by environmental factors and that decreased juvenile mortality leads to delayed maturity. These two predictions conform with those found by previous models using other measures of fitness. Correlations between k and juvenile mortality can change the shape of the predicted reaction norm. Depending on the precise form of the correlation, the model can predict done- or bowl-shaped reaction norms and can predict delayed or earlier maturity as k decreases. These shapes are qualitatively different from those predicted by previous models that used different fitness measures. Systematic estimates of the parameter values for this and for related models are required to determine the appropriate fitness measure for models of reaction norms.     

THE EVOLUTION OF PHENOTYPIC PLASTICITY IN LIFE-HISTORY TRAITS: PREDICTIONS OF REACTION NORMS FOR AGE AND SIZE AT MATURITY

We used life-history theory to predict reaction norms for age and size at maturation. We assumed that fecundity increases with size and that juvenile mortality rates of offspring decrease as ages-at-maturity of parents increase, then calculated the reaction norm by varying growth rate and calculating an optimal age at maturity for each growth rate. The reaction norm for maturation should take one of at least four shapes that depend on specific relations between changes in growth rates and changes in adult mortality rates, juvenile mortality rates, or both. Most organisms should mature neither at a fixed size nor at a fixed age, but along an age-size trajectory. The model makes possible a clear distinction between the genetic and phenotypic components of variation. The evolved response to selection is reflected in the shape and position of the reaction norm. The phenotypic response of a single organism to rapid or slow growth is defined by the location of its maturation event as a point on the reaction norm. A quantitative test with data from 19 populations and species of fish showed that predictions were in good agreement with observations (r = 0.93, P < 0.0001). The predictions of the model also agreed qualitatively with observed phenotypic variation in age and size at maturity in humans, platyfish, fruit flies, and red deer. This preliminary success suggests that experiments designed to test the predictions directly will be worthwhile.     

General Classification of Maturation Reaction-Norm Shape from Size-based Processes

Phenotypic plasticity of size at maturation is commonly described using size–age maturation reaction norms (MRNs). MRNs for age and size at maturation are analyzed and classified into three general categories related to different size scalings of growth and mortality. The underlying model for growth and mortality is based on processes at the level of the individual, and is motivated by the energy budget of fish. MRN shape is a balance between opposing factors and depends on subtle details of size dependence of growth and mortality. MRNs with both positive and negative slopes are predicted, and for certain mortality conditions also a lower critical spawning mass. The model is applied to predict a generic fishery-induced evolutionary response and allows assessment of climate change impact on MRNs. Our work stresses the importance of using realistic size dependence of mortality and growth, since this strongly influences the predicted MRNs and sensitivity to harvest pressure.     

Probabilistic maturation reaction norms assessed from mark–recaptures of wild fish in their natural habitat

Reaction norms are a valuable tool in evolutionary biology. Lately, the probabilistic maturation reaction norm approach, describing probabilities of maturing at combinations of age and body size, has been much applied for testing whether phenotypic changes in exploited populations of fish are mainly plastic or involving an evolutionary component. However, due to typical field data limitations, with imperfect knowledge about individual life histories, this demographic method still needs to be assessed. Using 13 years of direct mark–recapture observations on individual growth and maturation in an intensively sampled population of brown trout (Salmo trutta), we show that the probabilistic maturation reaction norm approach may perform well even if the assumption of equal survival of juvenile and maturing fish does not hold. Earlier studies have pointed out that growth effects may confound the interpretation of shifts in maturation reaction norms, because this method in its basic form deals with body size rather than growth. In our case, however, we found that juvenile body size, rather than annual growth, was more strongly associated with maturation. Viewed against earlier studies, our results also underscore the challenges of generalizing life‐history patterns among species and populations.     

Growth and survival effects on maturation pattern in populations of grayling with recent common ancestors

Mortality and growth rates were shown to influence maturation patterns in five populations of grayling ( Thymallus thymallus ) in central Norway. The populations share recent common ancestors as they derive from introductions performed in 1910, and they inhabit lakes with different environmental conditions (i.e. length of growth season, lake area and fishing pressure). Mortality rate (range of Z -values: 0.36–0.77) and growth pattern varied strongly among the populations. Mortality rates were negatively associated with population mean age at maturity ( r _sp=−0.90), supporting life-history theory which predicts early maturation to be favoured under conditions with high adult mortalities. Maturation reaction norms differed significantly among the populations. Individuals from one population showed no maturation plasticity (all individuals matured at age three), whereas rapid growers were found to mature earlier than slow growers in the remaining four populations. Life-history theory is again supported as it predicts rapid growers to mature early due to high age-specific fecundity and short generation times. Given low mortality risks, slow growers are predicted to delay maturation in order to gain high first-time fecundity. In high-mortality systems all individuals are predicted to mature early. This theory is supported by the present data as populationwise maturation plasticity increased with decreasing mortality rates. In the population with no maturation plasticity the corresponding high mortality rates were probably due to high fishing pressures.     

Unexpected discontinuities in life-history evolution under size-dependent mortality

In many organisms survival depends on body size. We investigate the implications of size-selective mortality on life-history evolution by introducing and analysing a new and particularly flexible life-history model with the following key features: the lengths of growth and reproductive periods in successive reproductive cycles can vary evolutionarily, the model does not constrain evolution to patterns of either determinate or indeterminate growth, and lifetime number and sizes of broods are the outcomes of evolutionarily optimal life-history decisions. We find that small changes in environmental conditions can lead to abrupt transitions in optimal life histories when size-dependent mortality is sufficiently strong. Such discontinuous switching results from antagonistic selection pressures and occurs between strategies of early maturation with short reproductive periods and late maturation with long reproductive cycles. When mortality is size-selective and the size-independent component is not too high, selection favours prolonged juvenile growth, thereby allowing individuals to reach a mortality refuge at large body size before the onset of reproduction. When either component of mortality is then increased, the mortality refuge first becomes unattractive and eventually closes up altogether, resulting in short juvenile growth and frequent reproduction. Our results suggest a new mechanism for the evolution of life-history dimorphisms.     

Assessing evolutionary consequences of size-selective recreational fishing on multiple life-history traits,with an application to northern pike (<Emphasis Type="Italic">Esox lucius</Emphasis>)

Despite mounting recognition of the importance of fishing-induced evolution, methods for quantifying selection pressures on multiple adaptive traits affected by size-selective harvesting are still scarce. We study selection differentials on three life-history traits—reproductive investment, size at maturation, and growth capacity—under size-selective exploitation of northern pike (Esox lucius L.) with recreational-fishing gear. An age-structured population model is presented that accounts for the eco-evolutionary feedback arising from density-dependent and frequency-dependent selection. By introducing minimum-length limits, maximum-length limits, and combinations of such limits (resulting in harvestable-slot length limits) into the model, we examine the potential of simple management tools for mitigating selection pressures induced by recreational fishing. With regard to annual reproductive investment, we find that size-selective fishing mortality exerts relatively small positive selection differentials. By contrast, selection differentials on size at maturation are large and consistently negative. Selection differentials on growth capacity are often large and positive, but become negative when a certain range of minimum-length limits are applied. In general, the strength of selection is reduced by implementing more stringent management policies, but each life-history trait responds differently to the introduction of specific harvest regulations. Based on a simple genetic inheritance model, we examine mid- and long-term evolutionary changes of the three life-history traits and their impacts on the size spectrum and yield of pike. Fishing-induced evolution often reduces sizes and yields, but details depend on a variety of factors such as the specific regulation in place. We find no regulation that is successful in reducing to zero all selection pressures on life-history traits induced by recreational fishing. Accordingly, we must expect that inducing some degree of evolution through recreational fishing is inevitable.     

Adaptive changes in harvested populations: plasticity and evolution of age and size at maturation

We investigate harvest-induced adaptive changes in age and size at maturation by modelling both plastic variation and evolutionary trajectories. Harvesting mature individuals displaces the reaction norm for age and size at maturation toward older ages and larger sizes and rotates it clockwise, whereas harvesting immature individuals has the reverse qualitative effect. If both immature and mature individuals are harvested, the net effect has approximately the same trend as when harvesting immature individuals only. This stems from the sensitivity of the evolutionary response, which depends on the maturity state of harvested individuals, but also on the type of harvest mortality (negatively or positively density dependent, density independent) and the value of three life-history parameters (natural mortality, growth rate and the trade-off between growth and reproduction). Evolutionary changes in the maturation reaction norm have strong repercussions for the mean size and the density of harvested individuals that, in most cases, result in the reduction of biomass--a response that population dynamical models would overlook. These results highlight the importance of accounting for evolutionary trends in the long-term management of exploited living resources and give qualitative insights into how to minimize the detrimental consequences of harvest-induced evolutionary changes in maturation reaction norms.     

Temperature, growth rate, and body size in ectotherms: fitting pieces of a life-history puzzle

The majority of ectotherms grow slower but mature at a larger body size in colder environments. This phenomenon has puzzled biologists because classic theories of life-history evolution predict smaller sizes at maturity in environments that retard growth. During the last decade, intensive theoretical and empirical research has generated some plausible explanations based on nonadaptive or adaptive plasticity. Nonadaptive plasticity of body size is hypothesized to result from thermal constraints on cellular growth that cause smaller cells at higher temperatures, but the generality of this theory is poorly supported. Adaptive plasticity is hypothesized to result from greater benefits or lesser costs of delayed maturation in colder environments. These theories seem to apply well to some species but not others. Thus, no single theory has been able to explain the generality of temperature-size relationships in ectotherms. We recommend a multivariate theory that focuses on the coevolution of thermal reaction norms for growth rate and size at maturity. Such a theory should incorporate functional constraints on thermal reaction norms, as well as the natural covariation between temperature and other environmental variables.     

Age and size at maturity: A quantitative review of diet‐induced reaction norms in insects

Optimality models predict that diet‐induced bivariate reaction norms for age and size at maturity can have diverse shapes, with the slope varying from negative to positive. To evaluate these predictions, we perform a quantitative review of relevant data, using a literature‐derived database of body sizes and development times for over 200 insect species. We show that bivariate reaction norms with a negative slope prevail in nearly all taxonomic and ecological categories of insects as well as in some other ectotherm taxa with comparable life histories (arachnids and amphibians). In insects, positive slopes are largely limited to species, which feed on discrete resource items, parasitoids in particular. By contrast, with virtually no meaningful exceptions, herbivorous and predatory insects display reaction norms with a negative slope. This is consistent with the idea that predictable resource depletion, a scenario selecting for positively sloped reaction norms, is not frequent for these insects. Another source of such selection—a positive correlation between resource levels and juvenile mortality rates—should similarly be rare among insects. Positive slopes can also be predicted by models which integrate life‐history evolution and population dynamics. As bottom‐up regulation is not common in most insect groups, such models may not be most appropriate for insects.     

Adaptation to spatially heterogeneous modifying and adaptive environments

The development of an individual's phenotype is influenced by environmental factors (the modifying environment) which may differ from those factors (the adaptive environment) that decide on the adaptational value of the developed phenotype. The shapes of adaptationally optimal norms of reaction are therefore essentially determined by associations between these two environmental components together with the degree of adaptational sensitivity of the developed phenotypes. Two complementary aspects of optimality are accounted for: (a) environments can be optimal for a given norm of reaction and (b) norms of reaction can be optimal for a given environment. The results are obtained for random distribution of genotypes over environmental conditions and under the physiologically reasonable premise that fitness is a function of the costs of modification and adaptation. It turned out that the associations of adaptive and modifying environments are the primary sources of adaptational optimization. More specifically, it is shown that (i) independence between the two environmental components constitutes an adaptationally optimal environment only for norms of reaction in which all phenotypes are adaptively insensitive; (ii) if costs of modification do not depend on the environment, and if the two environmental components are not associated, adaptationally optimal norms of reaction can always be realized through phenogenetic invariance; (iii) as a rule, adaptively sensitive phenotypes developed under strong environmental associations necessitate phenogenetic plasticity for the optimal norm of reaction; (iv) a norm of reaction which is adaptationally optimal in its adaptationally optimal environment can always be realized through phenogenetic invariance, if costs of modification do not vary with the environment. These results reveal an important role of patterns of adaptive sensitivity of phenotypes, which may even surpass that of shapes of norms of reaction in adaptational processes.     

Size-dependent predation and correlated life history traits alter eco-evolutionary dynamics and selection for faster individual growth

Age at maturation is a key life history trait influencing individual fitness, population age structure, and ecological interactions. We investigated the evolution of age at maturity through changes in the von Bertalanffy growth constant for organisms with a simple juvenile-adult life history. We used Gillespie eco-evolutionary models to uncover the role of predation in driving the evolution of the growth constant when eco-evolutionary dynamics are present. We incorporated both size-independent and size-dependent predation into our models to generate differences in selection and dynamics in the system. Our results generally support the idea that faster ontogenetic growth is beneficial when populations are growing but that predation tends to have little effect on age at maturity unless there are trade-offs with other life history traits. In particular, if faster ontogenetic growth comes at the cost of fecundity, our results suggest that predation selects for intermediate levels of growth and fecundity. Eco-evolutionary dynamics influenced the nature of selection only when growth was linked to fecundity. We also found that predators that increasingly consume larger prey tend to have higher population sizes due to the greater energy intake from larger prey, but the growth rate-fecundity trade-off reversed this pattern. Overall, our results suggest an important role for interactions between size-dependent foraging and life-history trade-offs in generating varying selection on age at maturity through underlying growth traits.     

A Systematic Overview of Harvesting-Induced Maturation Evolution in Predator–Prey Systems with Three Different Life-History Tradeoffs

There are concerns that anthropogenic harvesting may cause phenotypic adaptive changes in exploited wild populations, in particular maturation at a smaller size and younger age. In this paper, we study the evolutionarily stable size at maturation of prey subjected to size-selective harvesting in a simple predator?Cprey model, taking into account three recognized life-history costs of early maturation, namely reduced fecundity, reduced growth, and increased mortality. Our analysis shows that harvesting large individuals favors maturation at smaller size compared to the unharvested system, independent of life-history tradeoff and the predator??s prey-size preference. In general, however, the evolutionarily stable maturation size can either increase or decrease relative to the unharvested system, depending on the harvesting regime, the life-history tradeoff, and the predator??s preferred size of prey. Furthermore, we examine how the predator population size changes in response to adaptive change in size at maturation of the prey. Surprisingly, in some situations, we find that the evolutionarily stable maturation size under harvesting is associated with an increased predator population size. This occurs, in particular, when early maturation trades off with growth rate. In total, we determine the evolutionarily stable size at maturation and associated predator population size for a total of forty-five different combinations of tradeoff, harvest regime, and predated size class.     

Density-dependent processes in the life history of fishes: evidence from laboratory populations of zebrafish Danio rerio

Population regulation is fundamental to the long-term persistence of populations and their responses to harvesting, habitat modification, and exposure to toxic chemicals. In fish and other organisms with complex life histories, regulation may involve density dependence in different life-stages and vital rates. We studied density dependence in body growth and mortality through the life-cycle of laboratory populations of zebrafish Danio rerio. When feed input was held constant at population-level (leading to resource limitation), body growth was strongly density-dependent in the late juvenile and adult phases of the life-cycle. Density dependence in mortality was strong during the early juvenile phase but declined thereafter and virtually ceased prior to maturation. Provision of feed in proportion to individual requirements (easing resource limitation) removed density dependence in growth and substantially reduced density dependence in mortality, thus indicating that 'bottom-up' effects act on growth as well as mortality, but most strongly on growth. Both growth and mortality played an important role in population regulation, with density-dependent growth having the greater impact on population biomass while mortality had the greatest impact on numbers. We demonstrate a clear ontogenic pattern of change in density-dependent processes within populations of a very small (maximum length 5 mm) fish, maintained in constant homogeneous laboratory conditions. The patterns are consistent with those distilled from studies on wild fish populations, indicating the presence of broad ontogenic patterns in density-dependent processes that are invariant to maximum body size and hold in homogeneous laboratory, as well as complex natural environments.     

Disparate maturation adaptations to size-dependent mortality

Body size is an important determinant of resource use, fecundity and mortality risk. Evolution of maturation size in response to size-dependent selection is thus a fundamental part of life-history theory. Increased mortality among small individuals has previously been predicted to cause larger maturation size, whereas increased mortality among large individuals is expected to have the opposite effect. Here we use a continuously size-structured model to demonstrate that, contrary to these widespread expectations, increased mortality among small individuals can have three alternative effects: maturation size may increase, decrease or become evolutionarily bistable. We show that such complex responses must be reckoned with whenever mortality is size-dependent, growth is indeterminate, reproduction impairs growth and fecundity increases with size. Predicting adaptive responses to altered size-dependent mortality is thus inherently difficult, since, as demonstrated here, such mortality cannot only reverse the direction of adaptation, but also cause abrupt shifts in evolutionarily stable maturation sizes.     

Reduction of Delia radicum attack in field brassicas using a vertical barrier

According to life‐history theory, longer development time may result in bigger adults. However, reaction norms describing age and size at maturity often follow an L‐shaped form. This relationship is attributable to the simple notion that slowly growing individuals may not lengthen their development excessively after the maturation decision has been made, for example, when development is time limited in seasonal environments. In arthropods, growth occurs within instars, and thus the optimal growth strategy might be mediated by the phenotypic adjustment of instar numbers. We studied the relationship between age and size at maturity of a lichen‐feeding moth, Eilema depressum (Esper) (Lepidoptera: Arctiidae: Lithosiinae), and the variability of instar numbers in relation to achieved adult body mass and time used for maturation. A positive relationship between age and size at maturity was found across developmental pathways and a negative one within the developmental pathways. Directly developing larvae had higher growth rates, attained smaller pupal mass, and passed fewer instars than larvae maturing after overwintering. Host quality did not affect whether larvae matured during the remaining or the next season. High variation in the number of instars together with variable growth rates indicates high plasticity in adaptation to varying environmental conditions. Our results also confirm previous results that instar number variability may be a key characteristic mediating age and size at maturity in insects.     

Measuring probabilistic reaction norms for age and size at maturation

We present a new probabilistic concept of reaction norms for age and size at maturation that is applicable when observations are carried out at discrete time intervals. This approach can also be used to estimate reaction norms for age and size at metamorphosis or at other ontogenetic transitions. Such estimations are critical for understanding phenotypic plasticity and life-history changes in variable environments, assessing genetic changes in the presence of phenotypic plasticity, and calibrating size- and age-structured population models. We show that previous approaches to this problem, based on regressing size against age at maturation, give results that are systematically biased when compared to the probabilistic reaction norms. The bias can be substantial and is likely to lead to qualitatively incorrect conclusions; it is caused by failing to account for the probabilistic nature of the maturation process. We explain why, instead, robust estimations of maturation reaction norms should be based on logistic regression or on other statistical models that treat the probability of maturing as a dependent variable. We demonstrate the utility of our approach with two examples. First, the analysis of data generated for a known reaction norm highlights some crucial limitations of previous approaches. Second, application to the northeast arctic cod (Gadus morhua) illustrates how our approach can be used to shed new light on existing real-world data.     

Evolutionary responses to harvesting in ungulates

1. We investigate the evolutionary responses to harvesting in ungulates using a state-dependent, stochastic, density-dependent individual-based model of red deer Cervus elaphus (L.) females subject to different harvesting regimes. 2. The population's mean weight at first reproduction shifts towards light weights as harvesting increases, and its distribution changes from a single peak distribution under very low or high harvest rates, to a bimodal distribution under intermediate harvest rates. 3. These results suggest that, consistent with previous studies on aquatic species, harvesting-induced mortality may drive adaptive responses in ungulates by reducing the fitness benefits from adult survival and growth in favour of early and lightweight reproduction. 4. Selective harvesting for heavy animals has no additional effect on the evolutionarily stable strategy, suggesting that harvest rate is more important than the degree of selectivity in driving adaptive responses. However, selective harvesting of light females is positively associated with maturation weights even higher than those of a nonharvested population, probably due to the reduction in the fitness value of the offspring. 5. The average number of weight at maturation strategies in the population declines but the total number of strategies across all simulations increases with harvest rate, suggesting that harvesting-induced selection on weight at maturity overcomes the increase in strategy diversity expected from density-dependent release. 6. Yield initially increases with harvesting due to enhanced productivity of light females experiencing density-dependent release. However, it crashes under intense harvesting resulting in a population skewed to light, young and, therefore, less reproductive animals.     

DOES SIZE MATTER MOST? THE EFFECT OF GROWTH HISTORY ON PROBABILISTIC REACTION NORM FOR SALMON MATURATION

Body size is widely believed to affect the occurrence of sexual maturation. Recent studies have used changes in the age-specific body size at which the probability of maturing is 50%, a feature of probabilistic reaction norms, to quantify purported evolution of life histories. However, body size results from a combination of growth rates during successive developmental stages. Therefore, to understand the evolution of the maturation schedule, it is necessary to comprehend the relationships among body size, growth history, and maturation schedule. We examined the relationships among body size, previous growth history, and maturation probability in chum salmon (Oncorhynchus keta). In this study, previous growth history was estimated from yearly specific growth increments that provide information describing body size. Previous growth history was found to be more closely linked to maturation probability than body size. The most recent growth condition was the most important factor affecting whether a fish matured during the subsequent breeding season. Because individuals of similar body size and same age can have different growth histories, the relationship between body size and maturation probability could be plastically modified by growth history. This may violate an assumption required to infer evolution, namely that size-related maturation trends in probabilistic reaction norms are immune to growth history.     

A new demographic function maximized by life-history evolution

A goal of life-history theory has been to understand what combination of demographic traits is maximized by natural selection. In practice, researchers usually choose either density-independent population growth rate, lambda, or lifetime reproductive success, R0 (expected number of offspring produced in a lifetime). Others have shown that the maxima of density-independent lambda and R0 are evolutionarily stable strategies under specific density-dependent conditions: population regulation by equal density dependence among all age classes for lambda and by density dependence on a single age class for R0. Here I extend these connections between density-independent optimization models and density-dependent invasion function models in two ways. First, I derive a new demographic function for which a maximum corresponds to attainability of the equilibrium strategy or stability of the mean rather than stability of the variance of the strategy distribution. Second, I show explicitly a continuous range of cases with maxima between those for the lambda and R0. Graphical and biological interpretations are given for an example model. Finally, exceptions to a putative life-history generality (from lambda and R0 models), that high early-life mortality selects for high iteroparity, are shown.