Genetic Informed Trees (GIT*) Overview

• Genetic Informed Trees (GIT*) are probabilistic frameworks that integrate domain-specific information with tree-based models for applications in genomics, epidemiology, and robotic planning.
• GIT* employs statistical techniques such as MCMC, SMC, and genetic programming to infer genealogical structures, transmission chains, and optimal navigation paths from complex datasets.
• These frameworks enhance model accuracy and interpretability by combining biological priors, dynamic feedback, and environmental data across varied applications.

Genetic Informed Trees (GIT) encompass a family of probabilistic frameworks for modeling and inferring branching structures—trees or tree-like graphs—in contexts where genetic or environmental information plays a central role in guiding inference or search. Originating in genomics and epidemiology, and more recently adapted to computational path planning, the GIT philosophy is to combine tree-based structure with rich, domain-specific information, utilizing statistical or machine-learning methods to enhance accuracy, tractability, and interpretability (Worby et al., 2014, Zhang et al., 28 Aug 2025, Deng et al., 5 Dec 2025).

1. Theoretical Foundations of GIT*

Genetic Informed Trees unify probabilistic graphical modeling and domain-specific principles to describe ancestry, path, and transmission processes. In genomics, the essential construct is the latent tree or ancestral recombination graph (ARG), where observed genomic data $S$ are linked to unobserved genealogical structures $T$ and parameters $\Theta$ under a hierarchical generative model:

$$P(T, \Theta | S) \propto P(S | T, \Theta_\text{sub}) \cdot P(T | \Theta_\text{demo}, \rho) \cdot P(\Theta)$$

Here, $P(T | \Theta_\text{demo}, \rho)$ encodes biological priors: Kingman’s coalescent, birth-death models, or ARGs with recombination at rate $\rho$; $P(S | T, \Theta_\text{sub})$ expresses mutation or substitution likelihoods, typically via rate matrices. In epidemic modeling, GIT* further imposes mechanistic constraints on transmission routes, colonization dynamics, and group structure, with measurement models accounting for genetic distances (e.g., geometric distributions on SNP differences) and screening test sensitivities (Worby et al., 2014, Deng et al., 5 Dec 2025).

In robotics and planning, GIT* designates a class of informed, tree-based planners whose heuristics are "genetically" evolved or tuned using environmental and dynamic data. The core insight is to encode search heuristics as symbolic "genotypes," evolving them through genetic programming guided by reinforcement-like feedback, with the resultant "G-heuristics" steering bidirectional trees towards optimal paths (Zhang et al., 28 Aug 2025).

2. Statistical Models and Heuristic Construction

In pathogen genomics and population genetics, GIT* treats the evolutionary history as a hidden tree-like structure, integrating known and latent variables within an explicit probabilistic model. The statistical backbone is a joint factorization over genealogies $T$, observed sequences $S$, substitution parameters $\Theta_\text{sub}$, demography $\Theta_\text{demo}$, and, if appropriate, recombination rates $\rho$ (Deng et al., 5 Dec 2025). Likelihoods in genomic GIT* take the form

$$P(S | T, \Theta_\text{sub}) = \prod_{l=1}^M \prod_{i=1}^{L_l} P(S_{i}^{(l)} | T, Q)$$

with classical Felsenstein pruning or barcoding-mutation recursions. In transmission-chain inference, latent colonization times and sources are modeled stochastically, with transmission likelihoods and pairwise genetic distances informed either by transmission chain length (model A) or latent groups (model B) (Worby et al., 2014).

For robotic planning, the GIT* construction generalizes linear-combination heuristics from predecessors such as EIT*. Here, the learned key for sorting tree edges combines multiple primitives: reverse-tree cost-to-go $\widehat g(\mathbf{x}_t)$, effort estimates, artificial potential field (APF) energies $U[\mathbf{x}]$, and a dynamic importance $w_\text{dyn}[\mathbf{x}_t]$ that penalizes over-explored nodes. The heuristic is evolved as a symbolic tree via reinforced genetic programming, with operators $\{ +, -, \times, \log, \sqrt{\cdot}, |\cdot| \}$ and terminals drawn from environmental measurements. An example form is

$$\mathrm{key}_{\mathcal{R}}^{\mathrm{GIT*}}(\mathbf{x}_s,\mathbf{x}_t) = (\widehat g(\mathbf{x}_t)-\pi) \cdot \frac{\log(1+|U[\mathbf{x}_t]-U[\mathbf{x}_s]|)}{1+w_\mathrm{dyn}[\mathbf{x}_t]} + \sqrt{\overline{e}(\mathbf{x}_s)+\overline{e}(\mathbf{x}_s,\mathbf{x}_t)} \cdot \log(\overline{d}(\mathbf{x}_t))$$

(Zhang et al., 28 Aug 2025).

3. Inference Algorithms and Data Integration

GIT* frameworks employ Markov Chain Monte Carlo (MCMC), Sequential Monte Carlo (SMC), Hidden Markov Models (HMM), and genetic programming (GP) as their principal computational engines.

• Genomics and Transmission: Data-augmented MCMC algorithms sample latent genealogical or transmission parameters, integrating over unobserved colonization times, sources, group labels, and missing genotypes. Acceptance ratios are computed from joint posterior densities, balancing likelihoods for genetic, epidemiological, and screening data (Worby et al., 2014, Deng et al., 5 Dec 2025). SMC and SMC’ HMMs (Sequentially Markov Coalescent) provide scalable alternatives for ARG inference, reducing complexity and enabling marginal inference per block or locus.
• Planning/Control: Reinforced genetic programming (RGP) evolves heuristics by benchmarking planner performance against state-of-the-art baselines (e.g., EIT*), using a scalar reward that combines solution time, quality, and success rate. Crossover, mutation, and tournament selection are employed at each GP generation, with fitness functions penalizing complexity and promoting parsimony (Zhang et al., 28 Aug 2025).
• Data Modalities: GIT* models are constructed to support temporal and spatial calibration (branch lengths in time/divisions, diffusion models for spatial structure), and recombination (ARGs for genomes, gene conversion hotspots). Genetic data are integrated via explicit mutation models; for environments, auxiliary sensor data feed into learned tree heuristics.

4. Validation, Simulation, and Performance Metrics

GIT* frameworks are validated through forward simulation and empirical benchmarking:

• Genomics/Epidemics: Outbreak simulation proceeds by drawing importations, simulating acquisition hazards, and generating pathogen sequences according to model parameters. Inference accuracy is quantified by the ROC curve (sensitivity vs. 1-specificity) and the area under the curve (AUC), with high mutation rates and low transmissibility yielding optimal discrimination (Worby et al., 2014). Resolution is determined by expected genetic distance contrasts—$E[d|\text{linked}] \ll E[d|\text{unlinked}]$ increases clarity of tree inference.
• Path Planning: GIT* planners are evaluated on an array of simulated and real-world benchmarks—dividing-walls, random-rectangle, and goal-enclosure environments in up to $\mathbb{R}^{16}$, as well as robotic manipulation tasks. Key metrics include time to initial solution, initial/final path cost, and success rate. Empirical results show consistent reductions in solution time (20–85%) and success rate improvements relative to EIT* and other baseline planners (Zhang et al., 28 Aug 2025).

Domain	Core Validation Strategy	Main Metrics
Genomics/Epidemiology	Forward simulation + ROC analysis	AUC, sensitivity/specificity
Robotic Path Planning	Empirical benchmarks (sim/real)	$t_\text{init}$, $c_\text{init}$, success

5. Domain Applications and Parallels

GIT* principles apply across cellular, population, and species-genomic scales, as well as computational planning:

• Cell Lineages: In phylogenetic barcoding, GIT* infers binary/multistate cell-division trees, with barcoding mutation matrices replacing traditional molecular substitutions (Deng et al., 5 Dec 2025).
• Population Genetics: The framework is used for ARG-based demographic inference, with recombination and mutation dynamics determining genealogical patterns at genome scale.
• Species Phylogenetics: GIT* leverages multispecies coalescent models, gene-tree–species-tree reconciliation, and evolutionary rate heterogeneity (Deng et al., 5 Dec 2025).
• Transmission Chain Reconstruction: GIT* enables joint inference of who-infected-whom, introduction events, and within-host diversity, handling unobserved infection times and forward-simulation validation (Worby et al., 2014).
• Motion Planning: In robotics, GIT* denotes heuristically-guided, sampling-based planners whose learned keys incorporate environmental and dynamic structure, outperforming conventional approaches on speed and success metrics (Zhang et al., 28 Aug 2025).

6. Mathematical Properties and Scalability

Identifiability and computational tractability are domain-dependent within GIT*:

• Identifiability: For four taxa, species-tree topology is identifiable from unrooted gene-tree distributions under the multispecies coalescent (Deng et al., 5 Dec 2025).
• Consistency: Sequentially Markov coalescent (SMC’) converges to the full ARG as $\rho \to 0$; local tree correlation errors scale as $O(\rho^2)$ (Deng et al., 5 Dec 2025).
• Complexity: Maximum-likelihood phylogeny inference is NP-hard in the number of taxa; ARG inference scales exponentially without SMC approximations. In planning, nearest-neighbor queries and heuristic evaluation are the computational bottlenecks, but the online cost after G-heuristic training is $O(1)$ per edge. Tree-sequence storage approaches (e.g., tskit) enable efficient O(1) per-step updates in large-scale genealogy traversals.

7. Limitations, Extensions, and Future Directions

GIT* frameworks must be specialized for the scale and modality of the application, with limits arising from intractable posterior inference in high dimensions, and context-specificity of learned heuristics or priors:

• In path planning, RGP-learned G-heuristics require retraining for new classes of environments; generalization is limited to the benchmark distribution seen during evolution (Zhang et al., 28 Aug 2025). Future extensions may combine symbolic heuristics with neural networks or integrate human demonstration data.
• In genomics, GIT* abstracts over differences in data type and prior structure by adjusting $\Theta_\text{demo}$ and $\Theta_\text{sub}$, retaining a shared statistical skeleton (Deng et al., 5 Dec 2025). Limitations remain in handling large sample sizes, highly recombining regions, and model misspecification.
• In epidemic modeling, the approach provides explicit support for unobserved events and within-host diversity, but performance may hinge on the contrast in genetic distances between linked and unlinked chains (Worby et al., 2014).

A plausible implication is that the GIT* paradigm, by explicitly integrating genetic, environmental, or process-informed structure into tree-based modeling, provides a modular and unifying framework across disciplines, while maintaining the flexibility to accommodate advances in algorithms and domain-knowledge incorporation.