sexy_yeast

A repository containing code for a simulation of evolution in a sexually reproducing yeast culture.

Overview of the Program

This program simulates adaptive evolution of a population modeled using a Sherrington-Kirkpatrick (SK) spin-glass model from physics. It introduces genome evolution as a series of mutation events, where each mutation can either increase or decrease the fitness of the genome. x The program uses concepts like:

• Spin systems (σ) to represent the state of each genome site.
• Fitness landscape, defined by external fields (h) and coupling interactions (J).
• Fitness optimization via a mutation process where each mutation either improves or maintains fitness until the optimal state is reached.

The goal is to simulate the optimization of a genome (represented by spins ±1) through beneficial mutations and track how fitness evolves until a fitness peak is reached.

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Key Concepts

1. Spin System (σ)

   • Each gene (or spin) is represented as +1 or -1.
   • The configuration of all spins is the state of the genome.

2. Fitness Calculation

   • Fitness is a function of external fields (h) and interactions between spins (J).
   • Mutations flip individual spins, potentially improving fitness.
   • Fitness is maximized through a series of beneficial mutations (Sequential Selection with Weak Mutation, or SSWM regime).

3. Optimization

   • The main function, relax_sk, implements the optimization loop that continuously selects beneficial mutations until no further improvements are possible.

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Program Breakdown

1. Initialization
   • The size of the genome (N = 1000) and parameters for sparsity (ρ = 0.25) and epistatic strength (β = 0.5) are defined.
   • These parameters control how strongly genome sites interact and how many of the interaction terms (J) are non-zero.

sig_0 = cmn.init_sigma(N)
h = cmn.init_h(N, beta)
J = cmn.init_J(N, beta, rho)

• init_sigma(N): Randomly initializes the genome configuration (+1 or -1) for all sites.
• init_h(N, beta): Generates external fields that affect each site’s fitness.
• init_J(N, beta, rho): Initializes a sparse symmetric matrix representing interactions between genome sites.

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2. Compute Initial Fitness

F_off = cmn.calc_F_off(sig_0, h, J)
init_fit = cmn.compute_fit_slow(sig_0, h, J, F_off)

• calc_F_off: Calculates a fitness offset to normalize fitness values.
• compute_fit_slow: Calculates the fitness of a given configuration using external fields (h) and interaction matrix (J).

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3. Optimization Loop

flip_seq = cmn.relax_sk(sig_0, h, J)

• relax_sk is the main optimization function:
  • It continuously selects beneficial mutations using SSWM until no more beneficial mutations are possible.
  • It returns a sequence of indices representing the sites that were mutated.

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4. Reconstruct Final Genome State

sig_final = cmn.compute_sigma_from_hist(sig_0, flip_seq, num_of_muts)
final_fit = cmn.compute_fit_slow(sig_final, h, J, F_off)

• compute_sigma_from_hist reconstructs the genome configuration at any point in the mutation history.
• compute_fit_slow calculates the fitness of the final configuration.

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5. Distribution of Fitness Effects (DFE)

dfe = cmn.calc_dfe(sig_final, h, J)

• calc_dfe calculates the distribution of fitness effects for all possible single-site mutations in the final genome state.
• The DFE shows whether most mutations are beneficial, neutral, or deleterious.

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Logging Results

The program logs all the important steps:

• Initial and final genome states (sig_0, sig_final)
• Parameters (N, rho, beta)
• Fitness values at each step
• Mutation sequence (flip_seq)
• The distribution of fitness effects (dfe)

Example log output:

N: 1000
rho: 0.25
beta: 0.5
init_fit: 1.0
num_of_muts: 300
final_fit: 1.45
dfe: [-0.2, 0.1, -0.5, 0.3, ...]

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Functions Explained

1. Fitness Calculation

   • calc_basic_lfs: Computes the local fitness fields for each site.
   • calc_energies: Calculates how much each site contributes to the overall fitness.
   • compute_fit_slow: Computes the total fitness of a configuration by summing contributions from h and J.

2. Mutation Process

   • calc_bdfe: Calculates the beneficial distribution of fitness effects.
   • sswm_flip: Chooses a beneficial mutation based on probabilities derived from the fitness effect of each possible mutation.

3. Optimization

   • relax_sk: Implements the SSWM regime, continuously flipping spins until no beneficial mutations remain.
   • compute_sigma_from_hist: Reconstructs the genome state from the mutation history.

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Flow of the Program

1. Initialization

   • Randomly initialize genome (σ), external fields (h), and interactions (J).

2. Compute Initial Fitness

   • Calculate fitness for the initial genome state.

3. Optimize Genome

   • Run the optimization loop (relax_sk), flipping beneficial spins until fitness is maximized.

4. Analyze Results

   • Compute the final fitness and the distribution of fitness effects (dfe).

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Main Goals of the Program

1. Simulate how a genome evolves by accumulating beneficial mutations.
2. Track how fitness changes during this process.
3. Analyze the distribution of fitness effects (DFE) to understand evolutionary dynamics.

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Real-World Applications

This model can be used in evolutionary biology to:

• Study adaptive evolution in complex fitness landscapes.
• Model epistasis (interactions between genes).
• Investigate the role of sparse gene interactions in evolutionary dynamics.

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Explain on the claculstion contrabotion of beta abd rho in the sumilation

Epistasis and Fitness Landscape Complexity The parameters beta and rho in your interaction matrix (J) and external fields (h) control how fitness is calculated. These can significantly affect inheritance and mutation effects.

Epistasis (beta) High beta (close to 1): Strong epistatic interactions — fitness depends heavily on combinations of multiple mutations. Low beta (close to 0): Weak epistasis — fitness is more additive, with each mutation affecting fitness independently. Sparsity (rho) High rho: More connections between sites — mutations affect many other sites (more complex fitness landscape). Low rho: Fewer connections — simpler fitness landscape. To simulate different modes of inheritance related to epistasis:

Use high beta for strongly epistatic traits (like metabolic networks). Use low beta for additive traits (like polygenic inheritance).