Environment-Mediated Selection

• Environment-mediated selection is a theory describing how persistent and dynamic environmental conditions interact with genetic variation to shape adaptation.
• Population genetic models demonstrate that transient environmental shocks, gradients, and fluctuations can induce rapid allele frequency changes and stable polymorphism.
• Ecosystem and spatial models reveal that biotic and abiotic feedbacks jointly regulate selection pressures, enhancing resilience and driving adaptive branching.

Environment-mediated selection refers to evolutionary dynamics and system-level feedbacks in which the fitness landscape and trajectory of adaptation are governed not solely by heritable genetic variation or internal behavioral programs, but by persistent and dynamic environmental conditions or constraints that interact with, select for, and are modified by organismal traits. This concept extends classical models of selection to include transient, stochastic, cyclical, or structural environmental variation—ranging from physiological phenotypes under stabilizing selection facing fluctuating environments to ecological systems where selection pressure is exerted exclusively through the viability induced by resource limitation.

1. Foundational Models of Environment-Mediated Selection

Environment-mediated selection is most precisely formalized in population genetic models where fitness depends jointly on genotype and time-varying environmental effects. In additive-locus models for quantitative traits, the phenotype $Y_k = G_k + E_k$ combines a polygenic effect $G_k = \sum_{i=1}^L x_{k,i}\alpha_i$ and environmental deviation $E_k$ with variance $V_E$ (Harpak et al., 2020). Stabilizing selection acts on the phenotype, with fitness given by:

$$W(z, E_t) = \exp\left[-\frac{(z + E_t - \theta)^2}{2V_s}\right]$$

where $\theta$ is a fixed optimum and $E_t$ models shifting mean environmental effects. Environmental shocks ($E_t\neq 0$) instantaneously alter directional selection on all contributing loci, prompting transient pulses of allele-frequency change—even when the trait optimum remains static. Thus, the environmental variance and its autocorrelation time serve as critical modulators of genetic turnover, explicitly quantifying the rate and spectrum of polygenic adaptation generated purely by environmental fluctuation.

2. Fluctuating Selection, Genetic Drift, and Fixation Dynamics

Temporal and spatial environmental fluctuations fundamentally reshape classic genetic drift and selection models. In fluctuating populations with environmental volatility (e.g., variable carrying capacity), the effective strength of selection and drift are computed via linear superposition of phase-specific coefficients (Meyer et al., 2019), yielding compact formulae for fixation probabilities, absorption times, and effective population sizes:

$$N_{\rm eff} = N\;\frac{4\,r\,\tau}{(1+r)\,\bigl(2\,\tau +1-r\bigr)}, \qquad s_{\rm eff} = s + \frac{s_g(1-r)}{2\tau} + \frac{s_d}{2\tau}$$

As a result, the fate of mutants—and the genome-wide rate of adaptation—are determined by aggregated contributions of environmental histories, rather than by static parameters.

In one-sided random environments, rare but strong environmental events induce abrupt increases in the frequency of fit types. The large-$N$ limit produces a Wright-Fisher diffusion with superposed jump processes, where the generator incorporates both Brownian diffusion (genetic drift) and Poissonian jumps (selection bursts induced by environmental peaks) (Cordero et al., 2019). These models demonstrate that environment-mediated selection cannot always be reduced to an "effective fitness;" instead, the full environmental jump distribution modulates both forward-time frequencies and ancestral genealogies.

3. Spatial Structure, Heterogeneity, and Amplification Regimes

Environment-mediated selection is further modulated by spatial structure and heterogeneity. In graph-structured populations, strong environmental gradients (e.g., nutrients, drug concentrations) across partially isolated demes can amplify natural selection—yielding both accelerated fixation of advantageous mutants and reduced mean fixation/extinction times (Fruet et al., 31 Jul 2025). Key amplification occurs when mutant advantage is concentrated in "upstream" demes with high migration outflow, or in refugia demes under rare migration. The fixation probability is

$$\rho = \frac{1}{D} \sum_{i=1}^D a_i (st) - \frac{1}{2D} \sum_{i=1}^D b_i (st)^2 + O((st)^3)$$

where coefficients $a_i, b_i$ arise from environment-graph interactions. Under circulation symmetry, environmental heterogeneity exerts no first-order effect, but second-order terms increase fixation probability when variance in local advantage is high.

In classical Moran processes with environmental fitness heterogeneity, mean reproductive rate determines selection only in large populations, but variance in fitness among mutants suppresses fixation relative to residents, especially when the mutant's advantage is unevenly distributed (Kaveh et al., 2017).

4. Coevolutionary and Ecological System Feedbacks

The Tangled Nature Model (TNM) formalism demonstrates environment-mediated selection at the community and ecosystem scale. Here, both biotic and abiotic components enter the fitness function, and global habitability $E = -\sum_{i,j} n_i K_{ij} n_j$ is shaped and regulated by the traits of resident species (Arthur et al., 2019). Three layered mechanisms are identified:

1. Selection by Survival: Only those community configurations that incidentally generate a surviving, habitable environment persist.
2. Sequential Selection: Repeated community resets promote feedback assemblies with active environment regulation.
3. Entropic Hierarchy: Mutation-driven diversity endows the system with memory, supporting upward ratchets in biomass, complexity, and stability.

This iterative environment-mediated selection results in emergent system-level homeostasis, increased resilience, and long-run entropic growth—mechanistically underpinning the "Gaia" hypothesis as a natural statistical outcome of organism-environment coevolution.

5. Environment-Mediated Selection and Polymorphism

Fluctuating environmental selection can generate stable genetic polymorphism even when classical models predict monomorphism. In rapidly varying, cyclic environments, time-averaged replicator equations acquire non-linear, multi-partite fitness terms. These non-linearities, arising from population tracking of environmental cycles, open new parameter regions where protected polymorphism is induced—with possible trade-off of decreased mean population fitness (Allahverdyan et al., 2019). For example, in two-morph systems, a rapid cyclic environment can create a stable interior equilibrium even when one allele is favored on average; in multi-morph games (e.g., rock-paper-scissors), tracking introduces new polymorphic centers and limit cycles. Environmental mediation thus extends and complicates classic predictions about diversity and adaptive branching.

6. General Analytical Frameworks for Adaptive Polymorphism

A unified quantitative criterion for adaptive branching under spatio-temporally heterogeneous environments is given by the sum of spatial variance, temporal variance (weighted by generation overlap), permanent spatial differentiation (amplified by limited dispersal), and local temporal autocorrelations (Svardal et al., 2014). In the generalized island model, the condition for disruptive selection is:

$$E_T[ \text{Var}_S[\partial s] ] + \gamma\, \text{Var}_T[ E_S[\partial s] ] + 2\,\frac{1-m}{m}\text{Var}_S[ E_T[\partial s] ] + \mathcal{C}[\partial s] > - E_T[ E_S[ \partial^2 s ] ]$$

This criterion unifies prior results (island, lottery, Levene models) and demonstrates how environment-mediated selection—via mean, variance, dispersal rates, and autocorrelation structure—predisposes diversification and polymorphism.

7. Resource-Limited Adaptive Dynamics and Viability Selection

In systems where environmental selection is implemented as real-world viability under resource constraints (e.g., storage space or renewable energy), adaptation proceeds through differential survival, not via explicit fitness or reward proxies. For instance, in self-training autonomous systems, only those behaviors which persistently increase available environmental resources (e.g., freeing disk space) are propagated, with all other proxy or semantic rewards rendered evolutionarily unstable (Dodgson et al., 18 Jan 2026). Negative-space learning (NSL) prunes non-viable strategies, consolidating effective behavioral repertoire by preservation, not by external signal. Environmental mediation can thus yield sustainable self-improvement and reward-hacking immunity in open-ended machine learning frameworks.

8. Macroevolutionary Consequences and Interpretive Caveats

Environment-mediated selection produces genome-wide, recurrent adaptation, even when trait optima or fitness landscapes remain unchanged. In practical terms, this necessitates strong caution when interpreting observed between-group differences in polygenic scores or allele frequencies. Without explicit control or modeling of environmental distributions, polygenic adaptation signals may reflect environmental compensation rather than true divergent optima (Harpak et al., 2020). Moreover, neglected factors such as gene-environment interaction, linkage disequilibrium, and demographic history can further decouple genetic effects across environments and complicate inference.

A general implication is that environment-mediated selection bridges microevolutionary and macroevolutionary dynamics, driving punctuated equilibrium, competitive exclusion, altruistic behavior, and speciation via resource limitation and energy flows (Abadi et al., 2020). Variation in environment and its autocorrelation structure become primary determinants of genetic diversity and system resilience.

Table: Key Mathematical Formalisms in Environment-Mediated Selection

Model/Equation	Description	Paper/Section
$W(z, E_t) = \exp[-(z + E_t - \theta)^2/2V_s]$	Stabilizing selection with fluctuating environment	(Harpak et al., 2020) §2
$N_{\rm eff}, s_{\rm eff}$ formulas	Diffusion approximation for variable population/environment	(Meyer et al., 2019) §2
$dX(t) = ... + \int X(1-X)u\,\widetilde N(dt,du)$	Wright-Fisher diffusion with environmental jumps	(Cordero et al., 2019)
General branching condition	Adaptive polymorphism in spatio-temporal environments	(Svardal et al., 2014) Eq.(14,15)
$\rho_\infty =$ arithmetic mean rule	Fixation in Moran process under environmental heterogeneity	(Kaveh et al., 2017) §3
Resource-limited viability	Survival-based selection in autonomous learning systems	(Dodgson et al., 18 Jan 2026) §2

Environment-mediated selection is thus a pervasive, foundational paradigm in evolutionary theory, ecology, and autonomous systems. It rigorously accounts for transient, persistent, and structured environmental modulation of selection pressures, and generates both classical and emergent evolutionary patterns through mechanisms grounded in environmental dynamics rather than static fitness landscapes.