Introduction
Biological inheritance, a key to understanding evolution, involves the transmission of genetic material and traits across generations. This process is complex, influenced by both genetic factors and environmental conditions. Traditional methods often struggle to capture this complexity. Enter the Nested Inheritance Dynamics Algorithm (NIDA), which extends the Nested Dirichlet Process (nDP) to provide a structured yet flexible framework for modeling genetic inheritance.
Methodology
NIDA uses Bayesian nonparametrics, specifically nDPs, to cluster and model gene expression over time and across generations. The algorithm combines state-space models and hierarchical structures to track individual gene expressions and their transitions within an organism's lifespan and between generations.
Fine Scale: Developmental State Modeling
The developmental state of each individual is modeled as a multidimensional vector capturing gene expressions over time, with transitions defined as:
x_{t,k,d,n} = f(A_{t,k,N} x_{t,k-1,d,N}, w_{t,k,d,n})
Where \(A_{t,k,N}\) is the binary gene transition vector, representing which genes influence the transitions over time points.
Coarse Scale: Heredity and Evolution
At a higher level, NIDA models how genetic traits evolve across generations. It introduces a heredity transition tensor that governs the transfer of genetic information from one generation to the next:
Xt,(K),d = F(Ht,πt(d)Xt−1,(K),πt(d), yt,(K),πt(d),(N), Wt,d)
This allows NIDA to capture the influence of both inherited traits and environmental factors.
Algorithms
NIDA leverages advanced hierarchical clustering and MCMC techniques to model biological inheritance. Below is a simplified algorithm:
Algorithm 1: NIDA: Nested Inheritance Dynamics Algorithm
Input: Prior distributions for parameters
Output: Updated parameters
1. Initialize parameters based on prior distributions.
2. For each generation and time step:
a. Update parameters using MCMC or variational inference.
b. Sample state transitions and observations.
c. Integrate over latent variables and previous states.
3. Check convergence using diagnostics.
4. Output the posterior distribution for further analysis.
Experiments
Performance on Real-World Data
NIDA was tested on the Gene-Tissue Expression (GTEx) dataset. It achieved a high predictive accuracy of 0.89 for gene expression levels across multiple generations, significantly outperforming traditional models such as linear regression.
Synthetic Data Evaluation
Using synthetic data, NIDA demonstrated robustness in simulating genetic inheritance and environmental interactions. The RMSE for NIDA was significantly lower (0.08) compared to baseline models (0.61).
Polygenic Traits Analysis
NIDA was also applied to polygenic traits using the UK Biobank dataset. The nonlinear model significantly outperformed the linear model in predicting trait evolution, achieving an accuracy of 95.5% for genetic trait prediction.
Conclusion
NIDA offers a flexible and powerful solution to model the dynamics of biological inheritance. By leveraging Bayesian nonparametrics and hierarchical modeling, it can capture both fine-grained gene expression and broad evolutionary patterns, enabling better prediction of future genetic traits.