Principle of Relatedness: Cross-Disciplinary Insights

• Principle of Relatedness is a cross-disciplinary concept defining how transitions or links between states depend on quantified relatedness in various contexts.
• In evolutionary and economic models, it informs cooperation thresholds and growth dynamics using metrics like genetic coefficients and co-location matrices.
• In computational fields, it underpins methods in graphical models and NLP by evaluating semantic proximity and network connectivity.

The principle of relatedness encompasses an array of technical concepts and operationalizations across evolutionary biology, economics, social psychology, natural language processing, and network science. Fundamentally, it states that the probability of a system, entity, or agent transitioning or linking to another state, trait, or activity depends critically on the degree to which the elements involved are “related” according to context-specific metrics. This principle manifests as statistical genetic association in evolutionary theory, as inter-industry compatibility in economic geography, as semantic/syntactic proximity in linguistics, and as graphical or probabilistic dependence in graphical models.

1. Evolutionary and Genetic Foundations

In evolutionary biology, the principle of relatedness is formalized via the coefficient of genetic relatedness, $r$, which quantifies the excess statistical association between a focal individual’s genotype and those of its social partners relative to background expectation. In kin-selection and social evolution models, $r$ enters analytic expressions, most classically Hamilton’s rule ($b/c > 1/r$), dictating the invasion condition for cooperation or altruism. Generalized frameworks demonstrate that relatedness interacts multiplicatively and additively with other parameters such as behavioral reciprocity ($\rho$) and payoff synergy ($d$), yielding threshold conditions such as: $\frac{b}{c} > \frac{1 + r \rho}{r + \rho}$ for the invasion of cooperative traits in two-player interactions. When synergistic effects are introduced, the cooperative threshold is further relaxed if $d > 0$ and exacerbated if $d < 0$, with the interaction term making relatedness, reciprocity, and synergy fundamentally non-reducible to a single index (Cleve et al., 2012). This multi-pathway synthesis underscores that relatedness, while always facilitating the spread of cooperation, must be evaluated alongside contextual ecological and behavioral feedbacks.

In higher-order scenarios (e.g., $n$-player games), relatedness is generalized to scaled coefficients (e.g., $\kappa$), which adjust for local competition and demographic structure. The inclusive fitness condition for the evolution of helping becomes: $G(z) = -C(z) + \kappa B(z) > 0$ with $G(z)$ capturing marginal effects and the invasion threshold determined by both direct and indirect (relatedness-weighted) gains (Peña et al., 2014). The interplay between relatedness and synergies of kind and scale can produce regimes of coexistence, bistability, or unique equilibria, with the relaxation or tightening of evolutionary dilemmas depending on both the magnitude and nature of $\kappa$, and the payoffs’ functional form.

2. Economic Geography and the Path-Dependence of Development

In economics and regional science, the principle of relatedness captures the empirical tendency of new economic activities (industries, products, technologies) to emerge and grow in regions where related activities already exist. This is formalized in density measures derived from prevalence matrices $V$ (e.g., employment or output statistics), with relatedness matrices $\Phi$ quantifying the statistical relatedness between industry pairs via metrics such as conditional probability, cosine similarity, or observed co-location frequency: $$d_{ir} = \frac{\sum_{j\neq i,\,j \in J_i} \phi_{ij} \nu_{jr}}{\sum_{j\neq i,\,j \in J_i} \phi_{ij}}$$ where $J_i$ is the set of industries most related to $i$. Out-of-sample prediction studies confirm that these density-based relatedness terms increase the accuracy of models forecasting industry presence and growth, with $R^2$ increments up to 16 percentage points in growth models (Li et al., 2022). However, such effects are generally stronger for predicting stationary distributions than dynamic growth, and the interpretability/predictive power tradeoff is shaped by aggregation level (city, firm, establishment, country) and prevalence metric.

Theoretical and empirical work highlights that relatedness is not simply a proxy for skill overlap or value-chain linkages; it encompasses labor market, supply-chain, regulatory, infrastructural, and institutional complementarities. Application to policy leverages relatedness for Smart Specialization strategies, anomaly detection, and growth diagnostics. For instance, regions with negative residuals in relatedness-based prediction models highlight missing industries that are “expected” by the logic of relatedness and may illuminate binding local constraints.

Recent machine learning extensions replace noisy pairwise co-location scores with many-body pattern extraction (e.g., via XGBoost or Random Forest models), resulting in Continuous Projection Space (CPS): an embedding where pairwise distances are informed by high-signal, high-dimensional predictive structure (Tacchella et al., 2021).

3. Semantics and Distributional Relatedness in Language

In computational linguistics and NLP, semantic relatedness is quantified both distributionally and ontologically. Distributional measures (cosine, PMI, Dice coefficient, KL divergence, Lin’s measure) score word pairs based on the overlap or divergence of context-word distributions in large corpora:

• Cosine similarity measures angle between context-vectors.
• PMI quantifies pointwise information-theoretic association.
• KLD and Jensen–Shannon divergences gauge distributional divergence.

These correlate with human judgments of semantic relatedness, but achieve higher fidelity when complemented by ontology-based measures (WordNet, taxonomic path distance). Hybrid models that integrate lexical overlap and semantic association (e.g., the Omiotis framework) implement a “principle of relatedness” at the text level, aligning with human similarity ratings across words, sentences, and paraphrastic pairs (Tsatsaronis et al., 2014, Mohammad et al., 2012).

4. Probabilistic Graphical Models and Network Connectivity

Formally, the principle of relatedness is realized in probabilistic graphical models as the correspondence between graphical connectivity and probabilistic relevance. Variables $x$ and $y$ are said to be related if and only if they are connected in every minimal Bayesian network consistent with the underlying dependency model. Stronger notions—mutual irrelevance, uncoupledness—are always sufficient for graphical unrelatedness, but only coincide in transitive graphoids (notably, regular Gaussians and strictly-positive binary distributions) (Geiger et al., 2016). This equivalence justifies the use of graph connectivity as a proxy for statistical dependence and undergirds the construction of similarity networks for modular knowledge elicitation.

5. Network Science and Entity Relatedness in Graphs

In network science, the principle of relatedness manifests as algorithmic solutions to the problem of explaining or quantifying why entities in a graph are deemed “related.” Approaches fall into two classes:

• Path-based explanations rank connection paths by structural features (importance, rarity, label diversity).
• Node-relevance–based explanations optimize subgraph goodness functions (e.g., via random-walk–induced relevance scores or minimum-cost spanning trees).

Formally, the explanation of relatedness becomes: $H^* = \arg\max_H g(H)$ where $g(H)$ aggregates node relevance or random-walk probabilities among query entities (Biagioni et al., 2018). These methods operationalize the principle that structural prominence, specificity, and informational novelty jointly define relatedness in graphs.

6. Relatedness in Psychology and Higher Education

In the psychological domain, particularly under Self-Determination Theory, relatedness represents an individual’s sense of connection and valued membership within a community. Empirical studies in STEM graduate education utilize Likert-scale instruments to quantify relatedness and demonstrate its role as a buffering mediator: high relatedness flattens the effect of sense of belonging on intent to persist, with a measured interaction $\Delta$-slope of –0.20 (Sarkar et al., 28 Aug 2025). Relatedness thus operates as a stabilizing, protective factor, underscoring the necessity of fostering meaningful interpersonal ties to sustain engagement.

7. Synthesis and Cross-Disciplinary Significance

Across domains, the principle of relatedness arises as a structuring force that shapes the transition probabilities, stability, and developmental trajectories of agents and activities. Its mathematical formalization differs—regression coefficients, co-location matrices, distributional distances, graphical connectivity, mediation paths—but its operational essence is invariant: transitions, growth, diffusion, or persistence are facilitated by the magnitude and structure of pre-existing related elements.

The principle further dictates that the magnitude and nature of “relatedness” often interact nonlinearly with other system parameters (e.g., reciprocity, synergy, local competition, social context), necessitating careful estimation and interpretation in both empirical and theoretical modeling. Its application and relevance persist in the design of statistical models, the construction of efficient algorithms, and the effective targeting of interventions and policies across economic, biological, social, and computational systems.