What is the difference between norm of reaction and natural selection

Reaction norms are a means of conceptually, graphically, and mathematically describing this total variance and are a powerful tool for decomposing it into its constituent parts i.

A reaction norm is defined as the range of phenotypes expressed by a genotype along an environmental gradient. It is represented by a linear or nonlinear function which describes the value of a phenotypic trait for a particular genotype or group of genotypes in different environments. As such, it is closely related to the concept of phenotypic plasticity, which can be represented by a reaction norm with a non-zero slope i.

While the term which originated as Reaktionsnorm has been in use for over one hundred years, there has been some debate about the most appropriate way to describe it mathematically. Nonetheless, there is general consensus that a reaction norm has multiple properties, each of which can be the target of selection. Reaction norms are typically described as consisting of: 1 an intercept, elevation, or offset, which describes the mean trait value across all environments, 2 a slope, which quantifies the degree of trait plasticity, and 3 shape or curvature e.

Evidence that trait means and plasticities can evolve separately underscores the necessity of applying a reaction norm framework for studying ecological and evolutionary responses to the environment, because measuring phenotypes in a single environmental context does not necessarily reflect their relative values or diversities in a different context.

These contextual differences are particularly important in a world of rapid anthropogenic change and increasing environmental variability.

Therefore, in addition to being fundamental to ecological and evolutionary phenomena, reaction norm evolution is relevant for diverse biological fields, including behavior and psychology, conservation and natural resource management, global change biology, agriculture and breeding programs, and human health.

Given that evolutionary change is defined by genetic change, we focus this article on variation among reaction norms from different genotypes i. For an overview of the literature on plasticity itself keeping in mind that reaction norms need not be plastic , see the separate Oxford Bibliographies in Evolutionary Biology article Phenotypic Plasticity. There are currently no books dedicated exclusively to the topic of reaction norms or their evolution. However, there are several books on phenotypic plasticity or related evolutionary subfields that address reaction norms and provide a solid basis from which to pursue study on the topic.

A newcomer to the topic might wish to start with Schlichting and Pigliucci , which perhaps provides the most thorough introduction to reaction norm evolution, through the lens of phenotypic change in nature, and leaves the reader with the inspiring sense that much more remains to be discovered. There is some overlap between this book and Pigliucci , which was published shortly after. The latter provides a deeper look at the history of phenotypic plasticity research and is perhaps less balanced in tone, and therefore more likely to spark lively debate.

These books, as well as DeWitt and Scheiner , make clear that theoretical research on plasticity and reaction norms has long outpaced empirical work, leading to a deeper understanding of what might occur compared to what actually does occur in nature. Those wishing to delve deeper into the foundations of mathematical modeling of reaction norms should consult Levins Aside from this seminal work, West-Eberhard is the most important and widely cited contribution to our understanding of phenotypic plasticity and reaction norms on this list.

West-Eberhard pioneered the concept of genetic accommodation, which centres plasticity as a major force in evolution by enabling persistence of organisms in extreme or novel environments long enough to produce future generations and thereby the opportunity for evolutionary adaptation to occur i. West-Eberhard also proved to be highly influential in integrating developmental perspectives in evolutionary thinking at all levels of biological organization. Recent books apply this developmental approach— Gilbert and Epel , to evolutionary ecology eco-evo-devo and evolutionary medicine, and Sultan , to eco-devo, niche construction, and eco-evolutionary dynamics—using taxonomically diverse, modern examples.

The most recent addition by Hendry places the evolution of phenotypic plasticity into an eco-evolutionary context in an accessible way. DeWitt, T. Scheiner, eds. Phenotypic plasticity: Functional and conceptual approaches. Oxford: Oxford Univ. A broad survey of topics surrounding phenotypic plasticity, this edited volume ties in evolutionary theory throughout. Several chapters focus on the evolution of plasticity and reaction norms specifically, with more focus on theory and modeling and less on illustrative examples.

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Development , — Mitaka, Y. Caste-specific and sex-specific expression of chemoreceptor genes in a termite. We observe that the deviation from the optimal phenotype for both current and past environments decreased to zero, indicating optimal fit to all environments within the range experienced Fig 3A.

In addition, we observe less residual genetic variation compared to the case of slow coarse-grained environmental variability Fig 3B. This is also indicated by the narrow gap between the top and the mean performance curve in Fig 3A.

A Lack of fit see Evaluation of reaction norms in the current green line and past blue line environments. Orange line indicates the average slope of plasticity in the population, dashed orange line indicates optimal long-term adaptive plasticity.

Looking at the evolutionary trajectory of the population, we can see that while fitness to the current environment green line fluctuates, fitness to the whole environment set past environment; blue line gradually increases over time.

Moreover, we see no gap between performance in current and past environments. This indicates that increasing fitness to the current environments does not cause loss of fitness in past environments. Instead, the population accumulates responses that are adaptive for all previously experienced environments.

These results demonstrate that populations evolving in fast-changing environments produce adaptive plastic responses even when plasticity is costly and environmental change only occurs between generations. At this stage, we have merely confirmed well-known results e.

We now consider two explanations for the evolution of adaptive plasticity in coarse-grained environments. The standard interpretation is based on a lineage selection model, where faster environmental change will increase the odds that each allele is tested in more than one environment.

Adaptive plasticity can evolve since plastic alleles have greater mean fitness than non-plastic alleles when compared across multiple environments, even though the latter have higher fitness within each current environment. The learning theory interpretation instead is based on the prediction that decreasing the number of generations in each environment will decrease the genetic change accumulated within each environment i.

While both mechanisms cause a shift from short to long-term adaptation, each has distinct requirements: lineage selection relies on the transmission of genetic variants in order to compare the fitness of multiple alleles; learning theory requires that populations accumulate little genetic change in each environment, so that the system retains some information from the past. In contrast with lineage selection, learning theory does not require that past information is stored in separate lineages.

Rather, past information can also be stored in developmental parameters, such as the slope of plasticity. As long as plasticity does not revert to zero, the system retains some information about past adaptive plasticity and can be progressively improved after each environmental change, regardless of the presence of trans-generational genetic variation. In the next two sections, we make use of this key difference to determine which of the two processes can better explain the evolution of plasticity in coarse environments.

Under SSWM, the speed at which mutations arise is much slower compared to the speed at which they are fixed or lost, driving standing genetic variation to zero. Comparing the fitness of alleles across different environments is therefore impossible.

We model SSWM using a hill-climber algorithm: each evolutionary step produces only one mutation. If the new mutation is fitter than the previous one it is fixed, otherwise it is lost see Hill-climbing model. SSWM leads to a constant effective population size of 1 and makes lineage selection impossible. Therefore, if the lineage selection hypothesis is correct, we expect that adaptive plasticity will fail to evolve in all coarse-grained environments.

Contrary to the predictions of the lineage selection explanation, we find that the results from the above simulations are qualitatively and quantitatively similar to those obtained using a population size of , despite the SSWM selection regime Fig 4.

That is, populations fail to evolve plasticity when environments change every generations Fig 4A , and succeed in doing so when provided with either fine environmental grain Fig 4B or a rapid coarse-grained i.

Panels to the left show population performance see section Evaluation of reaction norms over time in current green line and past blue line environments. Panels to the right show the evolved reaction norm solid line compared to optimal reaction norm dashed line at the end of the evolutionary period.

Performance over time and evolved reaction norms are identical to weak selection scenarios. The evolutionary trajectory of populations under SSWM also remains remarkably similar to that of populations with standing genetic variation compare Fig 4 with Figs 1 , 2 and 3.

Populations evolving in fine-grained and fast coarse-grained environments both show a gradual increase in fitness to past environments, which remains comparable to fitness in the current environment. This indicates that they adapt to all previously seen environments rather than just the current one. Populations in slow coarse-grained environments instead perform consistently better in current environments compared to past ones, showing the repeated evolution of phenotypes adapted to current conditions, or adaptive tracking.

Their evolutionary trajectory also displays the same two-step cycle after each environmental change: fitness increase in both current and past environments phenotypic adaptation followed by fitness decrease in past environments only plasticity minimization Fig 4A.

Taken together, these findings demonstrate that both the final results and the evolutionary trajectories of our simulations are largely unaffected by the lack of standing genetic variation. Since standing genetic variation is required for adaptation via lineage selection, these results falsify the hypothesis that plasticity needs to evolve by averaging the fitness benefits of alternative variants across multiple environments.

In the next section, we make further predictions based on the learning theory explanation and try to falsify them. Using a learning theory framework, we can define the conditions that allow evolution in coarse-grained environments to approximate evolution in fine-grained ones. The two scenarios will produce the same outcome only as long as the average of evolutionary changes in coarse-grained environments is the same as the evolutionary changes that would happen in fine grained environments.

In our specific example, individuals selected in slow coarse-grained environments evolve non-plastic solutions after each environmental change. On average, evolutionary changes in slow coarse-grained environments decrease plasticity until it reaches zero. This is in contrast with fine-grained environments, which evolve plasticity towards the optimal adaptive slope.

Since the average change in plasticity in coarse-grained environments is different from the change in plasticity under fine-grained environments, the two scenarios have different outcomes. Conversely, individuals selected in fast coarse-grained environments retain some plasticity between environments. Furthermore, on average, the change in plasticity induced by each new environment points towards optimal adaptive plasticity: inherited maladaptive plasticity will be selected against, and inherited adaptive plasticity will be conserved.

Therefore, as long as plasticity does not reach zero before the environment changes, evolution in coarse-grained environments will follow the same direction as evolution in fine-grained environments. This is the reason why we expect lower learning rates to cause the evolution of adaptive plasticity in coarse-grained environments: lower learning rates ensure that the population does not find short-term, non-plastic optima before the next environmental change, which allows the averaging of plasticity across environments.

Since we define learning rates in biological systems as the amount of genetic change accumulated by the population in each new environment, they can be affected by several parameters other than rate of environmental change.

Stronger selective pressure will speed up the fixation of beneficial variants, and therefore also increase learning rates. If the learning rate explanation for the evolution of adaptive plasticity in coarse-grained environments is correct, these factors should be interchangeable with the rate of environmental change.

For example, small populations or populations with low mutation frequency should be able to find long-term plastic solutions even when environmental change is rare.

It is important to point out that decreasing population size or mutation frequency would instead hinder the action of lineage selection, which benefits from the maintenance of a large pool of genetic variants to select from. While a full exploration of all possible parameter space is beyond on the scope of this paper, we evaluate the learning theory explanation by testing the specific prediction that adaptively plastic responses can evolve even when environmental changes are slow, provided that mutation sizes are sufficiently small and hence learning rate is low.

This question can be answered using the same model, and in particular the case of slow coarse-grained environments environments change every generations with a population size of individuals. As shown above, adaptive plasticity fails to evolve under these conditions.

Learning theory explains this failure with the high learning rates in this population. As we can see in Fig 5B , the population eventually evolves an optimally adaptive plastic reaction norm, with negligible amounts of variation around both slope and intercept. Their evolutionary trajectories Fig 5A are also qualitatively similar to those of populations evolving in fast, coarse-grained environments. In both scenarios, fitness to the current environment green fluctuates around average fitness to past environments blue , indicating that the populations are not evolving phenotypes that increase current fitness at the expense of past adaptation.

The steady increase in average fitness to past environments instead indicates the evolution and retention of more general, plastic solutions. Orange lines indicate realized solid lines and optimal dashed lines adaptive plasticity. The population slowly evolves optimal adaptive plasticity.

While the two trajectories are similar in shape, the population experiencing slower environmental changes and smaller mutation rates takes a significantly longer to reach optimal plasticity. An increase in the number of generations required to find solutions is a known consequence of lower learning rates.

Intuitively, we can explain the longer time required to adapt as a consequence of the slower rate at which variants become available. While lineage selection is technically viable in this simulation, decreasing mutation sizes would also decrease the amount of available genetic variation, making it even less effective. A potential alternative explanation to our findings is that the reduced amount of genetic change per generation would enable multiple lineages to persist for longer, thus enabling the action of lineage selection.

The results are both qualitatively and quantitatively similar to those obtained in the previous simulation see Fig 6. Since our results are unaffected by the absence of lineages, we can rule out that the observed evolution of plasticity with smaller mutation rates is due to the longer persistence of multiple lineages. Taken together, our simulations provide falsifying evidence for a number of frequent assumptions on the requirements for the evolution of costly adaptive plasticity in coarse-grained environments, which we summarize in Table 1.

The solid orange lines indicates average population plalsticity, the dashed orange line optimal adaptive plasticity B Evolved reaction norms grey lines compared to optimal reaction norm dashed line at the end of the evolutionary period. The evolution of costly adaptive plasticity has often been framed as a necessity caused by environmental change outpacing the ability of natural selection to generate new adaptations [ 2 , 3 , 29 , 30 ], but the process by which organisms achieve plasticity in these conditions have seldom been clarified.

We demonstrate that neither individual nor lineage-level selection for adaptive plasticity are necessary for the evolution of adaptive plasticity. Rather, the speed of adaptation relative to environmental change modelled as learning rates is by itself a causal factor in the evolution of plastic responses that are adaptive across a range of coarse-grained environments.

High learning rates allow optimization of phenotypes in each current environment, at the expense of more general solutions that improve their fitness across all environments experienced.

Low learning rates instead make it impossible for phenotypes to chase short-term optima, yet allow individuals to reach long-term optimal plasticity despite the presence of short-term trade-offs. If approached from a purely adaptationist perspective, these results seem counter-intuitive: the conditions which allow natural selection to work most effectively high population sizes, high mutation rates, strong selective pressure and rare changes in the environment result in an evolutionary outcome adaptive tracking which has lower fitness than adaptive plasticity across all of our simulations see S1 Appendix.

Conversely, changes in the same parameters that decrease the ability of natural selection to effectively cause phenotypic change result in an evolutionary outcome adaptive plasticity which maximizes fitness of the population in the long-term. We explain these counter-intuitive findings by using learning rates, a core concept of learning theory. Specifically, we demonstrate that low learning rates prevent populations from reaching short-term optima before a new environmental change occurs.

This in turn allows evolved plastic reaction norms to be transferred across environments, so that they are effectively selected across multiple environments. The end result is that, as long as learning rates are sufficiently low, selection in coarse-grain environments converges on the same outcome as selection in fine-grained ones: adaptive plasticity.

In learning theory terms, the cumulative effect of testing models sequentially on each individual example online learning will be the same as testing them on the entire set at once batch learning only if learning rates are low enough to prevent overfitting to the last example seen [ 31 ].

While low learning rates are necessary to evolve general solutions in the presence of trade-offs in performance, none of the factors that affect learning rates is necessary by itself. This is because learning rate is a composite measure, so any given factor may be offset by the others.

We demonstrate this by showing that low mutation rate is sufficient to evolve costly adaptive plasticity even in slow, coarse-grained environments. Increasing population size and selection strength should instead decrease the odds of evolving costly adaptive plasticity, as both factors increase learning rates.

As a consequence, even populations with no measurable genetic variation in plasticity could evolve adaptive plastic responses as long as 1 new genetic variation can be produced over time and 2 short-term optima change before natural selection can reduce plasticity to zero. This observation reverses the suggested causal link between plasticity and the rate of genetic evolution.

Current theory proposes that plastic individuals experience weaker selection because they are able to cope with a wider range of environments [ 4 ]. Because of the reduced selective pressure, the amount of genetic change that accumulates in the population learning rate is also reduced. We instead suggest a low learning rate itself may skew populations towards evolving more general solutions, including plastic responses that are costly in current conditions but optimal across the entire set of previously experienced environments.

As such, weak selection could facilitate the evolution of plasticity. Since low learning rates promote the evolution of adaptive plastic responses by reducing the relative importance of minimizing plasticity costs, they are irrelevant to the evolution of inexpensive plastic responses.

When there are no costs of plasticity, every combination of slope and intercept that generates the optimal short-term phenotype is fitness equivalent within each environment. Because plastic and non-plastic solutions have the same short-term fitness, adaptive plasticity is selected for when the population moves towards the current phenotypic optimum and randomly drift after the optimal phenotype has been reached.

The population will thus inevitably find the optimum for all past environments, and learning rates will only determine the speed at which the population reaches the optimum. Learning rates are likewise irrelevant for the evolution of costly adaptive plasticity in fine-grained environments, which are sufficient but not necessary for the evolution of adaptive plasticity across all our simulations see S1 Fig.

Fine-grained environments allow natural selection to directly compare the fitness of phenotypes across multiple environments at the individual-level within each generation, so that adaptive plasticity is optimal even in the short-term.

Direct selection for plasticity is unsurprisingly sufficient to ensure the evolution of adaptive plasticity. Under those conditions, learning rates can only determine the speed of selective process rather than its outcome.

Our simulations consider the specific case of maintenance costs for plasticity. That is, we assume that plasticity directly decreases fitness, regardless of whether it is expressed. This assumption has a long history in modelling the evolution of plastic responses, but has been largely unsupported by empirical data which does not find costs of plasticity for the vast majority of traits analysed [ 32 , 33 ].

However, several alternative scenarios can create mathematically equivalent trade-offs between selection in current and past environments. A well-studied example is that of inaccurate cues, either due to imperfect perception or noise in the cues themselves [ 3 , 22 , 34 ].

Alternatively, the target phenotypes may not perfectly match with the best possible reaction norm. This scenario can happen for any reaction norm which is selected on a set of environments larger than its degrees of freedom 3 in the case of linear reaction norms [ 35 ] or if there are limits to the maximum amount of plastic changes that an organism can evolve [ 27 , 32 , 33 , 36 ].

In all of the above mentioned cases, optimal long-term plasticity would cause loss of fitness across current environments and consequently be selected against. Learning rates will thus be relevant for the evolution of plastic responses across all of them.

In our simulations, mutations that lead to adaptive plasticity are selected since they increase phenotypic fitness within current environments, eventually causing the evolution of adaptive long-term plasticity. This is in contrast with lineage selection models, in which mutations that cause adaptive plasticity are selected because of their long-term benefits, but are at best selectively neutral in current environments. Since the evolution of plasticity in our model is driven by a short-term rather than lineage selection process, we predict it to be both faster and more robust to the presence of trade-offs.

Similar dynamics apply to the evolution of modularity as a by-product of short-term phenotypic selection, and are proven to be scalable to arbitrarily complex systems [ 37 ]. In learning theory terms, organisms learn the regularities of the evolutionary problem, a process also known as generalization [ 31 ].

Therefore, as long as regularities remain the same, each individual will be able to produce adaptive phenotypes even in environments it has never experienced in its evolutionary history extrapolation , without the need for further adaptation. This ability to more rapidly evolve new adaptive phenotypes in response to new environments can instead considered as an increase in their evolvability.

Our demonstration that organisms can learn regularities between environments even when each organism only ever experiences a single environment opens up the possibility that evolved plastic responses may both prepare organisms for future, more extreme, environments via extrapolation and enable them to more rapidly evolve new adaptive solutions via evolvability.

This demonstrates that past evolution can shape evolutionary trajectories by biasing the phenotypic variants that are exposed to selection [ 24 , 40 ].

In summary, we use a simple reaction norm model to demonstrate that costly adaptive plasticity can evolve even when natural selection is unable to compare competing alleles over multiple environments i.

A learning theory framework helps us interpret this finding: Populations evolving in coarse-grained environments can evolve adaptive plasticity if the amount of adaptive change accumulated per environment—the learning rate—is low.

Populations with high learning rates evolve via repeated short-term adaptation even if this pattern is maladaptive in the long term. Low learning rates facilitate adaptation to the entire set of environments experienced over adaptation to just the current environment, favouring adaptive plasticity even in the presence of short-term functional trade-offs.

Thus, long-term adaptive plasticity can evolve even when it is not selected for at either the individual nor lineage level.

Whether a population evolves phenotypes that optimize fitness in the short or long term instead depends on the amount of adaptive changes it accumulates within each environment. For plasticity to evolve, the environment needs to fulfill two roles: determining the selective conditions selective role and providing information about those conditions constructive role [ 41 ]. We simulate the constructive role by assigning each target optima an environmental cue represented by a real number C sampled from a normal distribution with mean 1 and standard deviation 1.

Each of our simulations cycles between 10 short-term environments, which make up the long-term environment. Hence, the targets are directly proportional to the respective cue. This ensures that the relationship between selective environment and cues remains constant across environmental states.

We assume that the lifespan of the individuals is fixed and the same for all. As a result, environmental grain is solely determined by the parameter K. We choose small K values compared with the total number of generations in our simulations so that each population is able to evolve for multiple environmental cycles.

Our simulations were designed with temporal variation in mind, but the conclusions should be applicable to spatial variation as well.