Visualizing Modes of Adaptation in a Changing World

A key challenge in biology is to understand how the process of development shapes the phenotypic variation that natural selection can act upon. One powerful approach is to represent development as a dynamical system to reveal the underlying logic of how this variation is generated (Milocco and Uller, 2024). This in-silico experiment provides a dynamic visualization of these principles by exploring a critical question: how does the pace of environmental change affect a population’s mode of adaptation?

The Simulation: Genetic Assimilation vs. Plasticity

The script uses a population-based genetic algorithm where a Gene Regulatory Network (GRN) must adapt to a moving environmental optimum. This setup allows us to explore how a population copes with different rates of environmental change.

The animations below show a direct comparison between two scenarios. We can observe three key elements:

• The Optimum (red ‘x’): The ideal phenotype dictated by the environment at each generation.
• The Average Reference Phenotype (green square): The population’s genetically determined state in a neutral environment. Its movement represents genetic adaptation.
• The Average Expressed Phenotype (blue circle): The population’s actual state under environmental influence. The vector between the green square and blue circle is the plastic response.

Mathematical Foundation

The simulation is grounded in two core mathematical components: the GRN’s developmental dynamics and the evolutionary fitness model.

1. GRN Dynamics: Development is modeled as a dynamical system where the change in gene expression (\(\dot{x}_i\)) for each gene is a function of regulatory inputs from other genes (\(\theta_{ij}\)) and the environment (\(u_j\)). The script numerically integrates the following differential equation to find the steady-state phenotype: \(\dot{x}_{i}=\frac{r(b_{i})}{K_{i}+r(b_{i})}-\mu_{i}x_{i}; \quad b_{i}=\sum_{j=1}^{n}\theta_{ij}x_{j}+u_{j}\)

2. Evolutionary Fitness: Selection is modeled using a Gaussian fitness function. An individual’s fitness (\(w\)) decreases exponentially with the squared Euclidean distance (\(d^2\)) between its phenotype and the moving optimum. Individuals are selected as parents for the next generation with a probability proportional to their fitness. \(w = e^{-k \cdot d^2}\)

Discussion

This comparative simulation provides a powerful, visual demonstration of how the rate of environmental change dictates a population’s adaptive strategy (Uller et al., 2024). Under slow, predictable change, the population relies on genetic assimilation, where its underlying genetics gradually evolve to match the environment. Under rapid change, however, this process is too slow. Survival depends on leveraging existing phenotypic plasticity as a short-term solution to keep pace.

This visually reinforces the concept that plasticity can “take the lead” in adaptive evolution, serving as a crucial first step that allows a population to persist in a new environment while slower genetic changes follow.

//=========================================================================
// ALGORITHM: GRN Adaptation to a Moving Optimum
//=========================================================================

// --- 1. System Initialization ---
params <- Load_Configuration_Data()
founder_genotype <- Initialize_Founder_GRN()
initial_population <- Create_Initial_Population(founder_genotype, params.n_pop)

// --- 2. Pre-calculate Environmental Trajectories ---
// For each scenario (e.g., slow_speed, fast_speed):
optimum_path <- Generate_Optimum_Trajectory(params.speed, params.n_generations)
environmental_inputs <- Generate_Environmental_Inputs(optimum_path)

// --- 3. Run Evolutionary Scenarios ---
// For each scenario to be run:
    Run_Scenario(scenario_name, initial_population, optimum_path, environmental_inputs)

// --- Core Evolutionary Function: Evolve_One_Generation ---
FUNCTION Evolve_Population(population, optimum_path, environmental_inputs)
    FOR gen = 1 TO params.n_generations
        current_optimum <- optimum_path[gen]
        current_env_input <- environmental_inputs[gen]
        
        // --- 3A. Calculate Fitness ---
        FOR each individual IN population
            // Calculate phenotype with environmental influence (plastic)
            expressed_phenotype <- Find_Steady_State(individual.genotype, current_env_input)
            
            // Calculate phenotype without environmental influence (genetic)
            reference_phenotype <- Find_Steady_State(individual.genotype, neutral_input)
            
            distance_to_optimum <- Euclidean_Distance(expressed_phenotype, current_optimum)
            individual.fitness <- Calculate_Gaussian_Fitness(distance_to_optimum)
            
            // Store results for this generation
            history.expressed_phenotypes[individual] <- expressed_phenotype
            history.reference_phenotypes[individual] <- reference_phenotype
        END FOR
        
        // --- 3B. Reproduction ---
        selected_parents <- Select_Parents_By_Fitness(population)
        new_population <- Create_Offspring(selected_parents, params.mutation_rate)
        population <- new_population
        
        // --- 3C. Visualization & Logging ---
        Update_Animation_Frame(history, gen)
        Save_GIF_Frame()
        
    END FOR
    RETURN population, history
END FUNCTION

//=========================================================================

References

Milocco, L., and Uller, T. (2024). Utilizing developmental dynamics for evolutionary prediction and control. PNAS, 121(14).

Uller, T., Milocco, L., Isanta-Navarro, J., Cornwallis, C. K., and Feiner, N. (2024). Twenty years on from Developmental Plasticity and Evolution: middle-range theories and how to test them. Journal of Experimental Biology, 227.