Gene–Culture Coevolution Models

• Gene–culture coevolution models are formal frameworks that quantify the dual influence of inherited genetic and cultural information on evolutionary trajectories.
• They combine replicator–mutator dynamics with cultural transmission kernels, highlighting rapid cultural changes versus slower genetic shifts.
• Agent-based and dual-store simulations reveal divergent selection regimes, including cumulative innovation and potential cultural suicide.

Gene–culture coevolution models formalize the mutual and recursive influence between biological evolution and cultural dynamics—where genetic and cultural inheritance systems jointly shape organismal fitness and population trajectories. These models capture the multilayered processes by which genes, learned behaviors, institutions, language, and ecological modifications interact over both short and evolutionary timescales. Implicit in such frameworks is the recognition that genes and culture can follow aligned or divergent adaptive trajectories, with consequences for cumulative cultural innovation, population demography, and the emergence of maladaptive "cultural attractors" such as celibacy or mass cultural suicide (Marriott et al., 2016, Maddamsetti et al., 2018).

1. Formal Modeling Structures and Mathematical Foundations

Core gene–culture coevolution models incorporate both classical population genetics and formal theories of cultural transmission. Traditional genetic evolution is often represented by replicator–mutator equations, in which genotype frequencies $x_i$ are updated each generation according to selection, mutation, and mean population fitness: $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$ where $W_j$ is the fitness of type $j$, $M_{j \rightarrow i}$ is the genetic mutation matrix, and $\overline{W}$ is the mean fitness (Maddamsetti et al., 2018).

Cultural evolutionary dynamics extend this framework to include transmission kernels for cultural traits. In vertically transmitted (parent-to-child) models, the update equation for frequency $y_k$ of cultural variant $k$ is: $y_k(t+1) = (1-\mu) f_k[y_1, ..., y_n] + \mu u_k$ where $f_k$ represents the fraction of children receiving trait $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$0, $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$1 is the innovation rate, and $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$2 describes de novo innovation (Maddamsetti et al., 2018).

Dual-inheritance models jointly evolve populations in the product space of genotype and "memotype" (cultural type), tracking joint frequencies $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$3 and updating them via: $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$4 where $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$5 factors the genetic and cultural phenotype into fitness; $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$6, $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$7 are genetic and cultural transmission matrices, often allowing horizontal and oblique learning (Maddamsetti et al., 2018). Extensions further incorporate epigenetic inheritance and multi-level ecological feedback (niche construction).

2. Agent-Based Dual-Store Models and Mechanistic Separation

Agent-based simulations provide a granular substrate for modeling gene–culture coevolution, particularly with respect to divergence between evolutionary trajectories of genes and culture. In the framework introduced by Marriott & Chebib (Marriott et al., 2016), each agent possesses two entirely distinct information stores:

• The genome $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$8 is an inert sequence determining inherited traits at birth and during sexual recombination, not directly altered during the agent's lifetime.
• The memome $$x_i(t+1) = \frac{\sum_j x_j(t) W_j M_{j \rightarrow i}}{\overline{W}}$$9 is an active set of "memeplexes" encoding daily behavioral strategies, capable of rapid intragenerational (individual learning) and horizontal (social learning) modification.

This strict separation is essential for divergent coevolution. Genetic evolution operates on the timescale of generations, whereas cultural information can respond and spread within a single lifetime, and propagate non-vertically (i.e., horizontally and obliquely). Memeplexes are constructed as contiguous subsequences of the genome that encode daily action plans under a fixed energy budget. Social learning entails swapping and mutating memeplexes between overlapping agents, strongly accelerating the spread and optimization of cultural solutions (Marriott et al., 2016).

3. Selection Modes, Transmission Pathways, and Divergence

Gene–culture coevolution models admit multiple selection regimes and transmission pathways, yielding sharply distinct evolutionary outcomes:

• Cooperative selection (rate divergence): Genes and culture optimize similar targets but at different rates. Cultural traits—subject to rapid horizontal experimentation and sharing—converge to near-optimal daily strategies far more quickly than the genome, as measured by declining wasted energy per memeplex versus genome (Marriott et al., 2016).
• Competitive selection (directional divergence): Cultural evolution can actively undermine biological fitness. For example, under strong horizontal social learning, memeplexes rapidly evolve to eliminate costly breeding actions, driving "cultural suicide", while the underlying genome retains or even increases investment in reproduction (Marriott et al., 2016).
• Cumulative cultural evolution: Horizontal and individual learning support indefinite accumulation of memeplex generations, enabling populations to transcend the adaptive envelope set by genes alone. In these models, purely vertically transmitted culture stagnates; only under dual-inheritance with horizontal transfer does memeplex generation scale linearly over time (Marriott et al., 2016).

The following table summarizes core evolutionary regimes:

Selection Type	Gene Trajectory	Culture Trajectory	Key Outcome
Cooperative (rate)	Slow Optimization	Rapid Optimization	Cultural acceleration
Competitive (directional)	Breeding persists	Breeding minimized	Potential for cultural suicide
Cumulative (horizontal)	Low memeplex gen.	High memeplex gen.	Open-ended cultural evolution

4. Parameter Regimes, Simulation Frameworks, and Calibration to Data

Model architectures span analytic (ODEs, replicator dynamics) and stochastic (agent-based, digital evolution) domains. Canonical frameworks include:

• Replicator–mutator equations (with multi-layer extensions for genetic, epigenetic, linguistic, and institutional states) (Maddamsetti et al., 2018).
• Agent-based models (ABMs) with explicit resources, energy budgeting, sexual mating, and layered transmission (vertical, oblique, horizontal) (Marriott et al., 2016).
• Digital evolution platforms (e.g., Avida), incorporating programmable niche construction, communication, and evolutionary trajectories (Maddamsetti et al., 2018).

Critical parameters include mutation rates ($W_j$0, $W_j$1), innovation rates ($W_j$2), population sizes ($W_j$3), social learning bias, network topology, and selection coefficients at both genetic and cultural layers.

Calibration of model parameters and validation against empirical data leverage large-scale datasets:

• Linguistic n-grams and textual corpora for fitting transmission bias and innovation rates.
• Genealogical/demographic records to estimate effective population sizes and timescales.
• Social network data for mapping imitation kernels and cultural cascade statistics (e.g., meme propagation depths).
• Ethnographic and cross-cultural survey indices for quantifying institutional variants and norm enforcement (Maddamsetti et al., 2018).

Model selection among purely genetic, purely cultural, or dual-inheritance regimes is accomplished via likelihood scoring (AIC/BIC, Bayes factors) on observed time series (Maddamsetti et al., 2018).

5. Empirical and Theoretical Implications: Divergence and Instabilities

Gene–culture coevolution models reveal several counterintuitive and empirically relevant phenomena:

• Cultural traits can evolve to reduce or eliminate biological fitness. In agent-based simulations, social learners often shed all reproductive behaviors from their memeplexes, resulting in lineages that self-extinguish—an analog to cultural suicide (Marriott et al., 2016).
• Population-level dynamics exhibit emergent age structure: With cumulative horizontal culture, reproductive duties shift to young agents (with genome-biased memomes), while older adults become vessels for highly optimized, non-breeding memeplexes—mirroring real-world pedagogical patterns observed in hunter–gatherers and social animals (Marriott et al., 2016).
• Separation of stores and horizontal transmission are necessary but not always sufficient for divergence; further work is required to map the phase boundaries of divergence under varying parameter regimes (e.g., mutation rates, social network topology) (Marriott et al., 2016).
• Niche construction effects: Inclusion of ecological feedback loops—where population activity directly modifies environmental variables—enables rich evolutionary dynamics such as ecological suicide phenomena and environmental coevolution (Maddamsetti et al., 2018).

6. Limitations, Extensions, and Directions for Research

Model limitations include restricted transmission types (e.g., absence of prestige or payoff bias), static or unchanging environments, and absence of migratory dynamics or environmental exogenous shocks. Analytical theory that generalizes agent-based findings—especially regarding transitions between cooperative and competitive divergence—remains an open area (Marriott et al., 2016).

Recent directions emphasize:

• Building multilayer joint state spaces bridging genotype, epigenotype, linguistics, and institutional behaviors (Maddamsetti et al., 2018).
• Implementation in both wet-lab (microbial, social animal) and in silico systems, enabling coupled empirical–computational experiments.
• Quantitative testing of hypotheses about cultural–genetic feedbacks using increasingly comprehensive real-time cultural and genetic datasets.

A plausible implication is that human and nonhuman populations may harbor "cultural parasites": behavioral traditions or institutions that perpetuate themselves despite (or because of) reducing host genetic fitness. This feature, highlighted in both empirical and simulation settings, underscores the profound independence and potential for divergence contained within dual-inheritance gene–culture systems (Marriott et al., 2016, Maddamsetti et al., 2018).