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Take selection for darker coats as the premise of the hypothetical example, rather than an established prediction about polar bears. The course of an adaptive walk depends on the available variation, its inheritance, fitness effects and ecological context. Warming alone does not specify a pigmentation mechanism, the strength of selection or whether dark coloration would improve total reproductive success.

The initial response can use standing genetic variation. If darker phenotypes already segregate and have an additive heritable component, a response can begin without waiting for a new mutation. The breeder's equation $R=h^{2}S$ describes a short-term one-trait expectation under its assumptions. Here $S$ is the difference between the mean phenotype of successful parents and the population mean, while $h^2$ is narrow-sense heritability in the relevant environment. Environmental darkening without inherited differences does not supply the same response.

If useful variants are absent, arrival can limit adaptation. In a diploid population with census size $N$ and per-haploid-genome beneficial mutation rate $U_b$, the approximate number of new beneficial copies is $2N{U}_b$ per generation. Most rare variants are lost initially. In a suitable large-population, weak-selection model, an allele whose heterozygote has advantage $s$ has establishment probability of approximately $2s$; this is not a general formula for every dominance relation or bottleneck. The mutation supply depends on actual reproductive numbers, while effective population size controls much of the drift and inheritance history. Long generation times can make a short walk in generations slow in calendar years.

The genetic architecture matters. A change in pigment production, hair structure or the spatial regulation of a developmental pathway can have different pleiotropic consequences. A large-effect allele may be hidden when recessive, constrained by costs in another trait, or beneficial only after a change at another locus. Under sign epistasis, the sign of a step depends on the starting genotype; under diminishing returns, later favourable steps tend to have smaller benefits on an already adapted background. One-step-at-a-time fixation is only an approximation for a sexual, potentially polygenic population.

Recombination can assemble favourable variants inherited from different parents, but can also break favourable combinations. Gene flow can introduce useful alleles or oppose local adaptation if migrants come from a differently selected population. Population bottlenecks can remove rare variants and strengthen drift. Spatial differences in substrate, prey, mate choice or thermal conditions can maintain more than one coat phenotype instead of producing uniform dark fixation.

Finally, the fitness landscape can move while the population responds. Selection on survival, reproduction, energetic balance and correlated traits must be considered jointly. If demographic decline is faster than adaptive change, the existence of an accessible darker phenotype does not guarantee evolutionary rescue. No particular number of substitutions, waiting time or final shade follows from the premise alone. One would need measurements of inherited variation, population structure, generation time and the fitness of alternative phenotypes in the changing environment.

Rapid artificial selection is often measured over a short interval during which breeders impose a consistent objective on a population containing useful inherited variation. Evolution in nature is not intrinsically incapable of comparable speed. The contrast arises from the strength and consistency of selection, accessible variation, competing fitness demands and the timescale on which change is measured.

In the one-trait breeder's equation, $R=h^{2}S$. Breeders can choose an extreme fraction of parents each generation, giving a large and consistently signed selection differential. They may also supply favourable food and protection that reduce viability costs of the selected trait. In nature, reproductive success integrates survival, mating and fecundity, so an improvement in the measured trait can be offset by a cost elsewhere.

For multiple traits, the short-term response is summarized by Lande's equationThe additive genetic covariance matrix $\mathbf{G}$ can deflect the response away from the direction of the selection gradient $\mathbf{\beta }$. There may be little inherited variation along the direction that selection currently favours, even when each individual trait is heritable. Correlated responses and antagonistic pleiotropy can therefore slow change in one focal character without eliminating evolution altogether.

Natural selection also fluctuates through time and space. A drought can favour one phenotype and a later environment another; repeated changes partly cancel in the long-term net displacement. Peter R. Grant and B. Rosemary Grant documented changing directions and outcomes in a long-term study of Darwin's finches. Such observations show that a small endpoint difference can conceal substantial intervening evolution, rather than demonstrating persistent evolutionary inactivity.^[ref]

Gene flow can oppose local selection, and density or frequency dependence can move the optimum as a trait becomes common. An organism may already be near an ecological optimum, so stabilizing selection removes deviations that a breeder might deliberately amplify. Plasticity can buffer a new environment and reduce immediate selection on the underlying genetic trait. Alternatively, plasticity can expose new variation; its effect is not invariably to slow evolution.

Initial experimental responses can exploit standing variation and linkage disequilibrium that later disappear. Sustained change may then depend on mutation, recombination or a new environment. Artificially selected lines can reach plateaus, suffer inbreeding or show costs outside the selected environment. Comparing their first few generations with a natural lineage averaged over thousands of generations consequently exaggerates the general difference. Calendar time also matters: a species with a long generation interval has fewer opportunities for inherited change per year.

Finally, measured phenotypic change is not necessarily genetic evolution. Environmental trends can make wild populations change quickly without an inherited response, or conceal a genetic response by changing development in the opposite direction. Common-garden, pedigree or genomic evidence is needed to separate these effects. Strong short-term response under controlled selection and modest long-term net change in nature are compatible with the same inheritance and selection principles.