Solution (source code)

= Solution

<phenotypic plasticity> is the capacity of a <genotype> to produce different <phenotypes> in different environments. It can change an individual's performance within a generation, before any change in <allele frequency>. \b[<phenotypic plasticity> can buy time for evolutionary <adaptation> and generate new targets for selection, but an induced response is neither necessarily beneficial nor evidence of inherited evolutionary change.]

A <reaction norm> makes the distinction precise. Write an individual's <phenotypic trait> as $z=a+bC$, where $C$ is an environmental cue and the <genotype> helps determine the intercept $a$ and responsiveness $b$. Differences in $a$ represent different baseline <phenotypic traits>; differences in $b$ represent genetic variation in sensitivity, a form of <genotype-environment interaction>. If the <phenotype> maximizing <genotype fitness> in the later selective environment $E$ is $z^*=kE$, an informative cue can move individuals nearer that optimum immediately. Appropriate changes in developmental timing or physiology can therefore prevent demographic collapse and preserve the variation and numbers needed for subsequent <natural selection>.

The importance of cue reliability follows from a simple model. Suppose <genotype fitness> loss is proportional to squared mismatch, the cue and environment have finite second moments, and we ignore the costs of responding. Minimizing $\mathbb E[(a+bC-kE)^2]$ over $a,b$, with $\operatorname{Var}(C)>0$, gives
$$
\boxed{b^*=k\frac{\operatorname{Cov}(E,C)}{\operatorname{Var}(C)},\qquad
a^*=k\mathbb E[E]-b^*\mathbb E[C].}
$$
This is a model calculation, not a universal optimal <reaction norm>. It shows why reliable prediction of the selective environment can favor responsiveness, whereas an uninformative cue gives $b^*=0$. A response evolved under one cue–environment relation can become harmful when that relation changes. Temporal delays, irreversible <biological development>, limited response speed and energetic costs further constrain the advantage. Stress-induced loss of growth, for example, is not evidence of adaptive <phenotypic plasticity> unless it improves an appropriate measure of <genotype fitness> relative to a feasible alternative.

<phenotypic plasticity> can affect later <evolution> in several ways. It can expose previously unexpressed <genetic variation> when a novel environment changes developmental pathways. It can let a lineage enter a new habitat where <natural selection> then improves performance. It can also reduce the mismatch so effectively that <natural selection> on the underlying constitutive <phenotypic trait> weakens, slowing genetic change. Even maladaptive initial <phenotypic plasticity> can intensify <natural selection> for compensatory change, provided the <biological population> survives. Thus a rapid phenotypic response, rapid genetic <adaptation> and long-term diversification are three distinct outcomes, not interchangeable measures of success.

<genetic accommodation> is evolutionary change in an environmentally responsive <phenotypic trait> or its regulation. It can change the mean, threshold, magnitude or specificity of the response and can preserve or increase <phenotypic plasticity>. <genetic assimilation> is the particular case in which a formerly induced <phenotype> becomes expressed without the original inducing condition. Neither process requires the environment to write a beneficial change directly into the inherited <DNA>; <natural selection> or imposed breeding can sort existing and newly arising variation affecting the response. Assimilation need not occur when environments continue to fluctuate, because maintaining a responsive <reaction norm> may remain advantageous.

The classic experimental demonstration selected fruit flies for a wing-vein <phenotype> induced by heat treatment, eventually obtaining expression without that treatment.<Genetic assimilation of an acquired character by Conrad Hal Waddington>[Evolution 7, pp. 118–126; heat-induced crossveinless phenotype and selection for its expression]{ref} The key observation is the changed relation between environment and <phenotype> across selected generations. It demonstrates the feasibility of <genetic assimilation>, not that losing the vein was an adaptive response in nature, nor that acquired bodily modifications were directly copied into the <genome>. A modern replication should include heat-exposed unselected lines, untreated lines, replicated selection lines, controlled rearing and <genotype fitness> assays, and should distinguish segregating variation from a new major-effect <mutation>.

For diversification, <phenotypic plasticity> can permit use of several resources or produce alternative specialist forms. Repeated exposure to a new resource can increase the frequency with which one form is expressed, giving <natural selection> more opportunity to refine it. In spadefoot tadpoles, experiments compared the competitive performance of an induced carnivore form among <biological populations> differing in how often they produce it; the association between expression frequency and competitive refinement supports one prediction of plasticity-led <evolution>.<Plasticity-led evolution: evaluating the key prediction of frequency-dependent adaptation by Nicholas A. Levis and David W. Pfennig>[Proceedings of the Royal Society B 286, article 20182754; carnivore-frequency comparisons and competition experiments]{ref} Such comparisons do not directly observe the ancestor or establish that every difference arose after induction rather than from prior genetic divergence.

Alternative forms can lead to <ecological speciation> if specialization causes habitat-associated mating, divergent <natural selection>, and reduced <gene flow>. A mating preference coupled to the adopted habitat could help turn ecological divergence into <premating isolation>. But the opposite outcome is also plausible: one flexible <genotype> can succeed in both habitats, reducing divergent <natural selection> and maintaining <gene flow>. A difference in <reaction norms> is consequently not itself evidence of <speciation>. A plastic radiation can persist without producing new <species>, and a radiation can occur through ordinary heritable divergence with little contribution from <phenotypic plasticity>.

Testing the causal historical claim requires more than comparing present-day induced and constitutive forms. Use related lineages and explicit ancestral-state uncertainty, raise multiple <genotypes> in crossed environments, and measure both <reaction norms> and <genotype fitness>. Split-family rearing controls ancestry; cross-fostering and controlled generations help identify maternal carry-over; experimental manipulation of the cue separates induction from resource quality. Replicate <evolution> with and without access to the cue and quantify survival, subsequent genetic response and reproductive barriers. An extant sister lineage is an imperfect proxy for an ancestor, and correlations between <phenotypic plasticity> and <species> richness can reflect reverse causation or ecological opportunity. \b[<phenotypic plasticity> contributes most convincingly when a demonstrated cue-dependent <genotype fitness> benefit precedes heritable refinement, and any proposed diversification is independently connected to reduced <gene flow>.]