model

fitness_normal(R̲̲::Matrix{Int64}, n̲ₜ::Vector{Int64}, n_neutral::Int, n_bc::Int; kwargs...)

Defines a model to estimate fitness effects in a competitive fitness experiment across growth-dilution cycles.

Model summary

• Prior on population mean fitness at time t, π(sₜ)

sₜ ~ Normal(params=s_pop_prior)

• Prior on population log mean fitness associated error at time t, π(logσₜ)

logσₜ ~ Normal(params=logσ_pop_prior)

• Prior on non-neutral relative fitness for barcoe m, π(s⁽ᵐ⁾)

s⁽ᵐ⁾ ~ Normal(params=s_bc_prior)

• Prior on non-neutral log relative fitness associated error for barcode m π(logσ⁽ᵐ⁾)

logσ⁽ᵐ⁾ ~ Normal(params=logσ_bc_prior)

• Prior on log Poisson distribtion parameters for barcode m at time t , π(logλₜᵣ⁽ᵐ⁾)

logλₜ⁽ᵐ⁾ ~ Normal(params=logλ_prior)

• Probability of total number of barcodes read given the Poisson distribution parameters at time t π(nₜ | logλ̲ₜ)

nₜ ~ Poisson(∑ₘ exp(λₜ⁽ᵐ⁾))

• Barcode j frequency at time t (deterministic relationship from the Poisson parameters)

fₜ⁽ʲ⁾ = λₜ⁽ʲ⁾ / ∑ₖ λₜ⁽ᵏ⁾

• log frequency ratio for barcode j at time t (deterministic relationship from barcode frequencies)

logγₜ⁽ʲ⁾ = log(f₍ₜ₊₁₎⁽ʲ⁾ / fₜ⁽ʲ⁾)

• Probability of number of reads at time t for all barcodes given the total number of reads and the barcode frequencies π(r̲ₜ | nₜ, f̲ₜ)

r̲ₜ ~ Multinomial(nₜ, f̲ₜ)

• Probability of neutral barcodes frequency ratio for barcode n at time t π(logγₜ⁽ⁿ⁾| sₜ, σₜ)

logγₜ⁽ⁿ⁾ ~ Normal(μ = -sₜ, σ = exp(logσₜ))

• Probability of non-neutral barcodes frequency ratio for barcode m at time t π(logγₜ⁽ᵐ⁾| s⁽ᵐ⁾, σ⁽ᵐ⁾, sₜ)

logγₜ⁽ᵐ⁾ ~ Normal(μ = s⁽ᵐ⁾ - sₜ, σ = exp(logσ⁽ᵐ⁾))

Arguments

• R̲̲::Matrix{Int64}: T × B matrix–split into a vector of vectors for computational efficiency–where T is the number of time points in the data set and B is the number of barcodes. Each column represents the barcode count trajectory for a single lineage.
• n̲ₜ::Vector{Int64}: Vector with the total number of barcode counts for each time point. NOTE: This vector must be equivalent to computing vec(sum(R̲̲, dims=2)).
• n_neutral::Int: Number of neutral lineages in dataset.
• n_bc::Int: Number of mutant lineages in dataset.

Optional Keyword Arguments

• s_pop_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_pop_prior[1] = mean, s_pop_prior[2] = standard deviation, Matrix: s_pop_prior[:, 1] = mean, s_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness values. If typeof(s_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of adjacent time points in dataset.
• logσ_pop_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_pop_prior[1] = mean, logσ_pop_prior[2] = standard deviation, Matrix: σ_pop_prior[:, 1] = mean, logσ_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness log-error utilized in the log-likelihood function. If typeof(logσ_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of adjacent time points in dataset.
• s_bc_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_bc_prior[1] = mean, s_bc_prior[2] = standard deviation, Matrix: s_bc_prior[:, 1] = mean, s_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness values. If typeof(s_bc_prior) <: Matrix, there should be as many rows in the matrix as mutant lineages × number of unique environments in the dataset.
• logσ_bc_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_bc_prior[1] = mean, logσ_bc_prior[2] = standard deviation, Matrix: logσ_bc_prior[:, 1] = mean, logσ_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness log-error utilized in the log-likelihood function. If typeof(logσ_bc_prior) <: Matrix, there should be as many rows in the matrix as mutant lineages × number of unique environments in the dataset.
• logλ_prior::VecOrMat{Float64}=[3.0, 3.0]: Vector or Matrix with the corresponding parameters (Vector: logλ_prior[1] = mean, logλ_prior[2] = standard deviation, Matrix: logλ_prior[:, 1] = mean, logλ_prior[:, 2] = standard deviation) for a Normal prior on the log of the λ parameter in the Poisson distribution. The λ parameter can be interpreted as the mean number of barcode counts since we assume any barcode count n⁽ᵇ⁾ ~ Poisson(λ⁽ᵇ⁾). If typeof(λ_prior) <: Matrix, there should be as many rows in the matrix as number of barcodes × number of time points in the dataset.

Latent Variables

• Population mean fitness per timepoint.
• Mutant fitness effects.
• λ dispersion parameters per barcode and timepoint.

Notes

• Models fitness effects as normally distributed.
• Utilizes a Poisson observation model for barcode counts.
• Setting informative priors is recommended for stable convergence.

multienv_fitness_normal(R̲̲::Matrix{Int64}, n̲ₜ::Vector{Int64}, n_neutral::Int, n_bc::Int; kwargs...)

Defines a model to estimate fitness effects in a competitive fitness experiment with different environments across growth-dilution cycles.

Model summary

• Prior on population mean fitness at time t, π(sₜ)

sₜ ~ Normal(params=s_pop_prior)

• Prior on population log mean fitness associated error at time t, π(logσₜ)

logσₜ ~ Normal(params=logσ_pop_prior)

• Prior on non-neutral relative fitness for barcode m in environment i π(sᵢ⁽ᵐ⁾)

sᵢ⁽ᵐ⁾ ~ Normal(params=s_bc_prior)

• Prior on non-neutral log relative fitness associated error for barcode m in environment i π(logσᵢ⁽ᵐ⁾)

logσᵢ⁽ᵐ⁾ ~ Normal(params=logσ_bc_prior)

• Prior on log Poisson distribtion parameters for barcode m at time t , π(logλₜᵣ⁽ᵐ⁾)

logλₜ⁽ᵐ⁾ ~ Normal(params=logλ_prior)

• Probability of total number of barcodes read given the Poisson distribution parameters at time t π(nₜ | logλ̲ₜ)

nₜ ~ Poisson(∑ₘ exp(λₜ⁽ᵐ⁾))

• Barcode j frequency at time t (deterministic relationship from the Poisson parameters)

fₜ⁽ʲ⁾ = λₜ⁽ʲ⁾ / ∑ₖ λₜ⁽ᵏ⁾

• log frequency ratio for barcode j at time t (deterministic relationship from barcode frequencies)

logγₜ⁽ʲ⁾ = log(f₍ₜ₊₁₎⁽ʲ⁾ / fₜ⁽ʲ⁾)

• Probability of number of reads at time t for all barcodes given the total number of reads and the barcode frequencies π(r̲ₜ | nₜ, f̲ₜ)

r̲ₜ ~ Multinomial(nₜ, f̲ₜ)

• Probability of neutral barcodes frequency ratio for barcode n at time t π(logγₜ⁽ⁿ⁾| sₜ, logσₜ)

logγₜ⁽ⁿ⁾ ~ Normal(μ = -sₜ, σ = exp(logσₜ))

• Probability of non-neutral barcodes frequency ratios π(logγₜ⁽ᵐ⁾| s⁽ᵐ⁾, logσ⁽ᵐ⁾, sₜ). Note: This is done grouping by corresponding environment such that if time t is associated with environment i, sᵢ⁽ᵐ⁾ is used as the fitness value.

logγₜ⁽ᵐ⁾ ~ Normal(μ = sᵢ⁽ᵐ⁾ - sₜ, σ = exp(σ⁽ᵐ⁾))

Arguments

• R̲̲::Matrix{Int64}:: T × B matrix–split into a vector of vectors for computational efficiency–where T is the number of time points in the data set and B is the number of barcodes. Each column represents the barcode count trajectory for a single lineage.
• n̲ₜ::Vector{Int64}: Vector with the total number of barcode counts for each time point. NOTE: This vector must be equivalent to computing vec(sum(R̲̲, dims=2)).
• n_neutral::Int: Number of neutral lineages in dataset.
• n_bc::Int: Number of mutant lineages in dataset.

Keyword Arguments

• envs::Vector{<:Any}: List of environments for each time point in dataset. NOTE: The length must be equal to that of n̲t to have one environment per time point.

Optional Keyword Arguments

• s_pop_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_pop_prior[1] = mean, s_pop_prior[2] = standard deviation, Matrix: s_pop_prior[:, 1] = mean, s_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness values. If typeof(s_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of adjacent time points in dataset.
• logσ_pop_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_pop_prior[1] = mean, logσ_pop_prior[2] = standard deviation, Matrix: σ_pop_prior[:, 1] = mean, logσ_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness log-error utilized in the log-likelihood function. If typeof(logσ_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of adjacent time points in dataset.
• s_bc_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_bc_prior[1] = mean, s_bc_prior[2] = standard deviation, Matrix: s_bc_prior[:, 1] = mean, s_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness values. If typeof(s_bc_prior) <: Matrix, there should be as many rows in the matrix as mutant lineages × number of unique environments in the dataset.
• logσ_bc_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_bc_prior[1] = mean, logσ_bc_prior[2] = standard deviation, Matrix: logσ_bc_prior[:, 1] = mean, logσ_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness log-error utilized in the log-likelihood function. If typeof(logσ_bc_prior) <: Matrix, there should be as many rows in the matrix as mutant lineages × number of unique environments in the dataset.
• logλ_prior::VecOrMat{Float64}=[3.0, 3.0]: Vector or Matrix with the corresponding parameters (Vector: logλ_prior[1] = mean, logλ_prior[2] = standard deviation, Matrix: logλ_prior[:, 1] = mean, logλ_prior[:, 2] = standard deviation) for a Normal prior on the log of the λ parameter in the Poisson distribution. The λ parameter can be interpreted as the mean number of barcode counts since we assume any barcode count n⁽ᵇ⁾ ~ Poisson(λ⁽ᵇ⁾). If typeof(λ_prior) <: Matrix, there should be as many rows in the matrix as number of barcodes × number of time points in the dataset.

Latent Variables

• Population mean fitness per timepoint
• Mutant fitness effects per environment
• λ dispersion parameters per barcode and timepoint

Notes

• Models fitness effects as normally distributed.
• Utilizes a Poisson observation model for barcode counts.
• Can estimate time-varying and environment-specific fitness effects.
• Setting informative priors is recommended for stable convergence.

genotype_fitness_normal(R̲̲::Vector{Matrix{Int64}}, n̲ₜ::Vector{Vector{Int64}}, n_neutral::Int, n_bc::Int; kwargs...)

Defines a hierarchical model to estimate fitness effects in a competitive fitness experiment where multiple barcodes belong to a specific "genotype." This means that different barcodes are grouped together through a fitness hyperparameter where each barcode samples from the distribution of this hyperparameter.

Model summary

• Prior on population mean fitness at time t, π(sₜ)

sₜ ~ Normal(params=s_pop_prior)

• Prior on population log mean fitness associated error π(logσₜ)

logσₜ ~ Normal(params=logσ_pop_prior)

• Prior on non-neutral relative hyper-fitness for genotype i π(θᵢ)

θᵢ ~ Normal(params=s_bc_prior)

• prior on non-centered samples that allow local fitness to vary in the positive and negative direction for genotype i π(θ̃ᵢ⁽ᵐ⁾). Note, this is a standard normal with mean zero and standard deviation one.

θ̃ᵢ⁽ᵐ⁾ ~ Normal(μ = 0, σ = 1)

• prior on log deviations of local fitness of barcode m from hyper-fitness for genotype i π(logτᵢ⁽ᵐ⁾)

logτᵢ⁽ᵐ⁾ ~ Normal(params=logτ_prior)

• local relative fitness for non-neutral barcode m with genotype i (deterministic relationship from hyper-priors)

sᵢ⁽ᵐ⁾ = θᵢ + θ̃ᵢ⁽ᵐ⁾ * exp(logτᵢ⁽ᵐ⁾)

• Prior on non-neutral log relative fitness associated error for non-neutral barcode m with genotype i, π(logσᵢ⁽ᵐ⁾)

logσᵢ⁽ᵐ⁾ ~ Normal(params=logσ_bc_prior)

• Prior on log Poisson distribtion parameters for barcode m at time t in replicate r, π(logλₜᵣ⁽ᵐ⁾)

logλₜᵣ⁽ᵐ⁾ ~ Normal(params=logλ_prior)

• Probability of total number of barcodes read given the Poisson distribution parameters π(nₜ | logλ̲ₜ)

nₜ ~ Poisson(∑ₖ exp(λₜ⁽ᵏ⁾))

• Barcode j frequency at time t (deterministic relationship from the Poisson parameters)

fₜ⁽ʲ⁾ = λₜ⁽ʲ⁾ / ∑ₖ λₜ⁽ᵏ⁾

• • log frequency ratio for barcode j at time t (deterministic relationship from barcode frequencies)

logγₜ⁽ʲ⁾ = log(fₜ₊₁⁽ʲ⁾ / fₜ⁽ʲ⁾)

• Probability of number of reads at time t for all barcodes given the total number of reads and the barcode frequencies π(r̲ₜ | nₜ, f̲ₜ)

r̲ₜ ~ Multinomial(nₜ, f̲ₜ)

• Probability of neutral barcodes n frequency ratio at time t π(logγₜ⁽ⁿ⁾| sₜ, logσₜ)

logγₜ⁽ⁿ⁾ ~ Normal(μ = -sₜ, σ = exp(logσₜ))

• Probability of non-neutral barcode m with genotype i frequency ratio at time t π(logγₜ⁽ᵐ⁾| sᵢ⁽ᵐ⁾, logσᵢ⁽ᵐ⁾, sₜ)

logγₜ⁽ᵐ⁾ ~ Normal(μ = sᵢ⁽ᵐ⁾ - sₜ, σ = exp(logσᵢ⁽ᵐ⁾))

Arguments

• R̲̲::Vector{Matrix{Int64}}:: Length R vector wth T × B matrices where T is the number of time points in the data set, B is the number of barcodes, and R is the number of experimental replicates. For each matrix in the vector, each column represents the barcode count trajectory for a single lineage.
• n̲ₜ::Vector{Vector{Int64}}: Vector of vectors with the total number of barcode counts for each time point on each replicate. NOTE: This vector must be equivalent to computing vec.(sum.(R̲̲, dims=2)).
• n_neutral::Int: Number of neutral lineages in dataset.
• n_bc::Int: Number of mutant lineages in dataset.

Keyword Arguments

• genotypes::Vector{Vector{<:Any}}: Vector with the list of genotypes for each non-neutral barcode.

Optional Keyword Arguments

• s_pop_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_pop_prior[1] = mean, s_pop_prior[2] = standard deviation, Matrix: s_pop_prior[:, 1] = mean, s_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness values. If typeof(s_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of time adjacent time points in dataset.
• logσ_pop_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_pop_prior[1] = mean, logσ_pop_prior[2] = standard deviation, Matrix: logσ_pop_prior[:, 1] = mean, logσ_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness error utilized in the log-likelihood function. If typeof(logσ_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of time adjacent time points × number of replicates in dataset.
• s_bc_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_bc_prior[1] = mean, s_bc_prior[2] = standard deviation, Matrix: s_bc_prior[:, 1] = mean, s_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness values. If typeof(s_bc_prior) <: Matrix, there should be as many rows in the matrix as number of mutant lineages × number of replicates in the dataset.
• logσ_bc_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_bc_prior[1] = mean, logσ_bc_prior[2] = standard deviation, Matrix: logσ_bc_prior[:, 1] = mean, logσ_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness error utilized in the log-likelihood function. If typeof(logσ_bc_prior) <: Matrix, there should be as many rows in the matrix as mutant lineages × number of replicates in the dataset.
• logλ_prior::VecOrMat{Float64}=[3.0, 3.0]: Vector or Matrix with the corresponding parameters (Vector: logλ_prior[1] = mean, logλ_prior[2] = standard deviation, Matrix: logλ_prior[:, 1] = mean, logλ_prior[:, 2] = standard deviation) for a Normal prior on the λ parameter in the Poisson distribution. The λ parameter can be interpreted as the mean number of barcode counts since we assume any barcode count n⁽ᵇ⁾ ~ Poisson(λ⁽ᵇ⁾). If typeof(logλ_prior) <: Matrix, there should be as many rows in the matrix as number of barcodes × number of time points × number of replicates in the dataset.

Latent Variables

• Population mean fitness per timepoint.
• Genotype hyper-fitness effects.
• Non-centered samples for each of the non-neutral barcodes.
• Deviations from the hyper parameter value for each non-neutral barcode.
• λ dispersion parameters per barcode and timepoint.

Notes

• Models hyper-fitness effects as normally distributed.
• Models fitness effects as normally distributed.
• Utilizes a Poisson observation model for barcode counts.
• Setting informative priors is recommended for stable convergence.

replicate_fitness_normal(R̲̲::Array{Int64,3}, n̲ₜ::Matrix{Int64}, n_neutral::Int, n_bc::Int; kwargs...)

Defines a hierarchical model to estimate fitness effects in a competitive fitness experiment across growth-dilution cycles over multiple experimental replicates.

Model summary

• Prior on population mean fitness at time t in replicate r, π(sₜᵣ)

sₜᵣ ~ Normal(params=s_pop_prior)

• Prior on population log mean fitness associated error at time t in replicate r, π(logσₜ)

logσₜᵣ ~ Normal(params=logσ_pop_prior)

• Prior on non-neutral relative hyper-fitness for barcode m π(θ⁽ᵐ⁾)

θ⁽ᵐ⁾ ~ Normal(params=s_bc_prior)

• Prior on non-centered samples that allow local fitness to vary in the positive and negative direction for barcode m in experimental replicate r π(θ̃ᵣ⁽ᵐ⁾). Note, this is a standard normal with mean zero and standard deviation one.

θ̃ᵣ⁽ᵐ⁾ ~ Normal(μ = 0, σ = 1)

• Prior on log deviations of local fitness from hyper-fitness for barcode m in replicate r π(logτᵣ⁽ᵐ⁾)

logτᵣ⁽ᵐ⁾ ~ Normal(params=logτ_prior)

• Local relative fitness for non-neutral barcode m in replicate r (deterministic relationship from hyper-priors)

sᵣ⁽ᵐ⁾ = θ⁽ᵐ⁾ + θ̃ᵣ⁽ᵐ⁾ * exp(logτᵣ⁽ᵐ⁾)

• Prior on non-neutral log relative fitness associated error for non-neutral barcode m in replcate r, π(logσᵣ⁽ᵐ⁾)

logσᵣ⁽ᵐ⁾ ~ Normal(params=logσ_bc_prior)

• Prior on log Poisson distribtion parameters for barcode m at time t in replicate r, π(logλₜᵣ⁽ᵐ⁾)

logλₜᵣ⁽ᵐ⁾ ~ Normal(params=logλ_prior)

• Probability of total number of barcodes read given the Poisson distribution parameters at time t in replicate r π(nₜᵣ | logλ̲ₜᵣ)

nₜᵣ ~ Poisson(∑ₘ exp(λₜᵣ⁽ᵐ⁾))

• Barcode j frequency at time t in replciate r (deterministic relationship from the Poisson parameters)

fₜᵣ⁽ʲ⁾ = λₜᵣ⁽ʲ⁾ / ∑ₖ λₜᵣ⁽ᵏ⁾

• Log frequency ratio for barcode j at time t in replicate r (deterministic relationship from barcode frequencies)

logγₜᵣ⁽ʲ⁾ = log(f₍ₜ₊₁₎ᵣ⁽ʲ⁾ / fₜᵣ⁽ʲ⁾)

• Probability of number of reads at time t for all barcodes in replicate r given the total number of reads and the barcode frequencies π(r̲ₜᵣ | nₜᵣ, f̲ₜᵣ)

r̲ₜᵣ ~ Multinomial(nₜᵣ, f̲ₜᵣ)

• Probability of neutral barcodes n frequency ratio at time t in replicate r, π(logγₜᵣ⁽ⁿ⁾| sₜᵣ, logσₜᵣ)

logγₜᵣ⁽ⁿ⁾ ~ Normal(μ = -sₜᵣ, σ = exp(logσₜᵣ))

• Probability of non-neutral barcode m frequency ratio at time t in replicate r π(logγₜᵣ⁽ᵐ⁾| sᵣ⁽ᵐ⁾, logσᵣ⁽ᵐ⁾, sₜᵣ)

logγₜ⁽ᵐ⁾ ~ Normal(μ = sᵣ⁽ᵐ⁾ - sₜᵣ, σ = exp(logσᵣ⁽ᵐ⁾))

Arguments

• R̲̲::Array{Int64, 3}:: T × B × R where T is the number of time points in the data set, B is the number of barcodes, and R is the number of experimental replicates. For each slice in the R axis, each column represents the barcode count trajectory for a single lineage.
• n̲ₜ::Matrix{Int64}: Matrix with the total number of barcode counts for each time point on each replicate. NOTE: This matrix must be equivalent to computing vec(sum(R̲̲, dims=2)).
• n_neutral::Int: Number of neutral lineages in dataset.
• n_bc::Int: Number of mutant lineages in dataset.

Optional Keyword Arguments

• s_pop_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_pop_prior[1] = mean, s_pop_prior[2] = standard deviation, Matrix: s_pop_prior[:, 1] = mean, s_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness values. If typeof(s_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of time adjacent time points in dataset.
• logσ_pop_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_pop_prior[1] = mean, logσ_pop_prior[2] = standard deviation, Matrix: logσ_pop_prior[:, 1] = mean, logσ_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness error utilized in the log-likelihood function. If typeof(logσ_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of time adjacent time points × number of replicates in dataset.
• s_bc_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_bc_prior[1] = mean, s_bc_prior[2] = standard deviation, Matrix: s_bc_prior[:, 1] = mean, s_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness values. If typeof(s_bc_prior) <: Matrix, there should be as many rows in the matrix as number of mutant lineages × number of replicates in the dataset.
• logσ_bc_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: s_bc_prior[1] = mean, s_bc_prior[2] = standard deviation, Matrix: s_bc_prior[:, 1] = mean, s_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness error utilized in the log-likelihood function. If typeof(logσ_bc_prior) <: Matrix, there should be as many rows in the matrix as mutant lineages × number of replicates in the dataset.
• logλ_prior::VecOrMat{Float64}=[3.0, 3.0]: Vector or Matrix with the corresponding parameters (Vector: logλ_prior[1] = mean, logλ_prior[2] = standard deviation, Matrix: logλ_prior[:, 1] = mean, logλ_prior[:, 2] = standard deviation) for a Normal prior on the λ parameter in the Poisson distribution. The λ parameter can be interpreted as the mean number of barcode counts since we assume any barcode count n⁽ᵇ⁾ ~ Poisson(λ⁽ᵇ⁾). If typeof(logλ_prior) <: Matrix, there should be as many rows in the matrix as number of barcodes × number of time points × number of replicates in the dataset.

Latent Variables

• Population mean fitness per timepoint.
• Mutant hyper-fitness effects.
• Mutant fitness effects per experimental replicate.
• λ dispersion parameters per barcode and timepoint.

Notes

• Models hyper-fitness effects as normally distributed.
• Models fitness effects as normally distributed.
• Utilizes a Poisson observation model for barcode counts.
• Setting informative priors is recommended for stable convergence.

replicatefitnessnormal(R̲̲::Vector{Matrix{Int64}}, n̲ₜ::Vector{Vector{Int64}}, nneutral::Int, nbc::Int; kwargs...)

Defines a hierarchical model to estimate fitness effects in a competitive fitness experiment across growth-dilution cycles over multiple experimental replicates.

Arguments

• R̲̲::Vector{Matrix{Int64}}:: Length R vector wth T × B matrices where T is the number of time points in the data set, B is the number of barcodes, and R is the number of experimental replicates. For each matrix in the vector, each column represents the barcode count trajectory for a single lineage.
• n̲ₜ::Vector{Vector{Int64}}: Vector of vectors with the total number of barcode counts for each time point on each replicate. NOTE: This vector must be equivalent to computing vec.(sum.(R̲̲, dims=2)).
• n_neutral::Int: Number of neutral lineages in dataset.
• n_bc::Int: Number of mutant lineages in dataset.

Optional Keyword Arguments

• s_pop_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_pop_prior[1] = mean, s_pop_prior[2] = standard deviation, Matrix: s_pop_prior[:, 1] = mean, s_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness values. If typeof(s_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of time adjacent time points in dataset.
• logσ_pop_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_pop_prior[1] = mean, logσ_pop_prior[2] = standard deviation, Matrix: logσ_pop_prior[:, 1] = mean, logσ_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness error utilized in the log-likelihood function. If typeof(logσ_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of time adjacent time points × number of replicates in dataset.
• s_bc_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_bc_prior[1] = mean, s_bc_prior[2] = standard deviation, Matrix: s_bc_prior[:, 1] = mean, s_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness values. If typeof(s_bc_prior) <: Matrix, there should be as many rows in the matrix as number of mutant lineages × number of replicates in the dataset.
• logσ_bc_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: s_bc_prior[1] = mean, s_bc_prior[2] = standard deviation, Matrix: s_bc_prior[:, 1] = mean, s_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness error utilized in the log-likelihood function. If typeof(logσ_bc_prior) <: Matrix, there should be as many rows in the matrix as mutant lineages × number of replicates in the dataset.
• logλ_prior::VecOrMat{Float64}=[3.0, 3.0]: Vector or Matrix with the corresponding parameters (Vector: logλ_prior[1] = mean, logλ_prior[2] = standard deviation, Matrix: logλ_prior[:, 1] = mean, logλ_prior[:, 2] = standard deviation) for a Normal prior on the λ parameter in the Poisson distribution. The λ parameter can be interpreted as the mean number of barcode counts since we assume any barcode count n⁽ᵇ⁾ ~ Poisson(λ⁽ᵇ⁾). If typeof(logλ_prior) <: Matrix, there should be as many rows in the matrix as number of barcodes × number of time points × number of replicates in the dataset.

Latent Variables

• Population mean fitness per timepoint.
• Mutant hyper-fitness effects.
• Mutant fitness effects per experimental replicate.
• λ dispersion parameters per barcode and timepoint.

Notes

• Models hyper-fitness effects as normally distributed.
• Models fitness effects as normally distributed.
• Utilizes a Poisson observation model for barcode counts.
• Setting informative priors is recommended for stable convergence.

multienv_replicate_fitness_normal(R̲̲::Matrix{Int64}, n̲ₜ::Vector{Int64}, n_neutral::Int, n_bc::Int; kwargs...)

Defines a hierarchical model to estimate fitness effects in a competitive fitness experiment with different environments across growth-dilution cycles over multiple experimental replicates.

Model summary

• Prior on population mean fitness at time t in replicate r, π(sₜᵣ)

sₜᵣ ~ Normal(params=s_pop_prior)

• Prior on population log mean fitness associated error at time t in replicate r, π(logσₜ)

logσₜᵣ ~ Normal(params=logσ_pop_prior)

• Prior on non-neutral relative hyper-fitness for barcode m in environment i π(θᵢ⁽ᵐ⁾)

θᵢ⁽ᵐ⁾ ~ Normal(params=s_bc_prior)

• Prior on non-centered samples that allow local fitness to vary in the positive and negative direction for barcode m in experimental replicate r in environment i π(θ̃ᵣᵢ⁽ᵐ⁾). Note, this is a standard normal with mean zero and standard deviation one.

θ̃ᵣᵢ⁽ᵐ⁾ ~ Normal(μ = 0, σ = 1)

• Prior on log deviations of local fitness from hyper-fitness for barcode m in replicate r in environment i π(logτᵣᵢ⁽ᵐ⁾)

logτᵣᵢ⁽ᵐ⁾ ~ Normal(params=logτ_prior)

• Local relative fitness for non-neutral barcode m in replicate r in environment i (deterministic relationship from hyper-priors)

sᵣᵢ⁽ᵐ⁾ = θᵢ⁽ᵐ⁾ + θ̃ᵣᵢ⁽ᵐ⁾ * exp(logτᵣᵢ⁽ᵐ⁾)

• Prior on non-neutral log relative fitness associated error for non-neutral barcode m in replcate r in environment i, π(logσᵣᵢ⁽ᵐ⁾)

logσᵣᵢ⁽ᵐ⁾ ~ Normal(params=logσ_bc_prior)

• Prior on log Poisson distribtion parameters for barcode m at time t in replicate r, π(logλₜᵣ⁽ᵐ⁾)

logλₜᵣ⁽ᵐ⁾ ~ Normal(params=logλ_prior)

• Probability of total number of barcodes read given the Poisson distribution parameters at time t in replicate r π(nₜᵣ | logλ̲ₜᵣ)

nₜᵣ ~ Poisson(∑ₘ exp(λₜᵣ⁽ᵐ⁾))

• Barcode j frequency at time t in replicate r (deterministic relationship from the Poisson parameters)

fₜᵣ⁽ʲ⁾ = λₜᵣ⁽ʲ⁾ / ∑ₖ λₜᵣ⁽ᵏ⁾

• Log frequency ratio for barcode j at time t in replicate r (deterministic relationship from barcode frequencies)

logγₜᵣ⁽ʲ⁾ = log(f₍ₜ₊₁₎ᵣ⁽ʲ⁾ / fₜᵣ⁽ʲ⁾)

• Probability of number of reads at time t for all barcodes in replicate r given the total number of reads and the barcode frequencies π(r̲ₜᵣ | nₜᵣ, f̲ₜᵣ)

r̲ₜᵣ ~ Multinomial(nₜᵣ, f̲ₜᵣ)

• Probability of neutral barcodes n frequency ratio at time t in replicate r, π(logγₜᵣ⁽ⁿ⁾| sₜᵣ, logσₜᵣ)

logγₜᵣ⁽ⁿ⁾ ~ Normal(μ = -sₜᵣ, σ = exp(logσₜᵣ))

• Probability of non-neutral barcodes frequency ratio for barcode m in replicate r π(logγₜᵣ⁽ᵐ⁾| sᵣ⁽ᵐ⁾, logσᵣ⁽ᵐ⁾, sₜᵣ). Note: This is done grouping by corresponding environment such that if time t is associated with environment i, sᵣᵢ⁽ᵐ⁾ is used as the fitness value.

logγₜᵣ⁽ᵐ⁾ ~ Normal(μ = sᵣᵢ⁽ᵐ⁾ - sₜᵣ, σ = exp(logσᵣᵢ⁽ᵐ⁾))

Arguments

• R̲̲::Array{Int64, 3}:: T × B × R where T is the number of time points in the data set, B is the number of barcodes, and R is the number of experimental replicates. For each slice in the R axis, each column represents the barcode count trajectory for a single lineage.
• n̲ₜ::Matrix{Int64}: Matrix with the total number of barcode counts for each time point on each replicate. NOTE: This matrix must be equivalent to computing vec(sum(R̲̲, dims=2)).
• n_neutral::Int: Number of neutral lineages in dataset.
• n_bc::Int: Number of mutant lineages in dataset.

Keyword Arguments

• envs::Vector{<:Any}: List of environments for each time point in dataset. NOTE: The length must be equal to that of the number of rows in n̲t to have one environment per time point.

Optional Keyword Arguments

• s_pop_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_pop_prior[1] = mean, s_pop_prior[2] = standard deviation, Matrix: s_pop_prior[:, 1] = mean, s_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness values. If typeof(s_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of time adjacent time points in dataset.
• logσ_pop_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_pop_prior[1] = mean, logσ_pop_prior[2] = standard deviation, Matrix: logσ_pop_prior[:, 1] = mean, logσ_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness error utilized in the log-likelihood function. If typeof(logσ_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of time adjacent time points × number of replicates in dataset.
• s_bc_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_bc_prior[1] = mean, s_bc_prior[2] = standard deviation, Matrix: s_bc_prior[:, 1] = mean, s_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness values. If typeof(s_bc_prior) <: Matrix, there should be as many rows in the matrix as number of mutant lineages × number of replicates in the dataset.
• logσ_bc_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_bc_prior[1] = mean, logσ_bc_prior[2] = standard deviation, Matrix: logσ_bc_prior[:, 1] = mean, logσ_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness error utilized in the log-likelihood function. If typeof(logσ_bc_prior) <: Matrix, there should be as many rows in the matrix as mutant lineages × number of replicates in the dataset.
• logλ_prior::VecOrMat{Float64}=[3.0, 3.0]: Vector or Matrix with the corresponding parameters (Vector: logλ_prior[1] = mean, logλ_prior[2] = standard deviation, Matrix: logλ_prior[:, 1] = mean, logλ_prior[:, 2] = standard deviation) for a Normal prior on the λ parameter in the Poisson distribution. The λ parameter can be interpreted as the mean number of barcode counts since we assume any barcode count n⁽ᵇ⁾ ~ Poisson(λ⁽ᵇ⁾). If typeof(logλ_prior) <: Matrix, there should be as many rows in the matrix as number of barcodes × number of time points × number of replicates in the dataset.

Latent Variables

• Population mean fitness per timepoint.
• Mutant hyper-fitness effects per environment.
• Non-centered samples for each of the experimental replicates.
• Deviations from the hyper parameter value for each experimental replicate.
• λ dispersion parameters per barcode and timepoint.

Notes

• All barcodes must be included in all replicates.
• Models hyper-fitness effects as normally distributed.
• Models fitness effects as normally distributed.
• Utilizes a Poisson observation model for barcode counts.
• Can estimate time-varying and environment-specific fitness effects.
• Setting informative priors is recommended for stable convergence.

multienvreplicatefitnessnormal(R̲̲::Vector{Matrix{Int64}}, n̲ₜ::Vector{Vector{Int64}}, nneutral::Int, n_bc::Int; kwargs...)

Defines a hierarchical model to estimate fitness effects in a competitive fitness experiment with different environments across growth-dilution cycles over multiple experimental replicates.

Arguments

• R̲̲::Vector{Matrix{Int64}}:: Length R vector wth T × B matrices where T is the number of time points in the data set, B is the number of barcodes, and R is the number of experimental replicates. For each matrix in the vector, each column represents the barcode count trajectory for a single lineage.
• n̲ₜ::Vector{Vector{Int64}}: Vector of vectors with the total number of barcode counts for each time point on each replicate. NOTE: This vector must be equivalent to computing vec.(sum.(R̲̲, dims=2)).
• n_neutral::Int: Number of neutral lineages in dataset.
• n_bc::Int: Number of mutant lineages in dataset.

Keyword Arguments

• envs::Vector{Vector{<:Any}}: Length R vector with the list of environments for each time point in each replicate. NOTE: The length must be equal to that of the number of rows in n̲ₜ to have one environment per time point.

Optional Keyword Arguments

• s_pop_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_pop_prior[1] = mean, s_pop_prior[2] = standard deviation, Matrix: s_pop_prior[:, 1] = mean, s_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness values. If typeof(s_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of time adjacent time points in dataset.
• logσ_pop_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_pop_prior[1] = mean, logσ_pop_prior[2] = standard deviation, Matrix: logσ_pop_prior[:, 1] = mean, logσ_pop_prior[:, 2] = standard deviation) for a Normal prior on the population mean fitness error utilized in the log-likelihood function. If typeof(logσ_pop_prior) <: Matrix, there should be as many rows in the matrix as pairs of time adjacent time points × number of replicates in dataset.
• s_bc_prior::VecOrMat{Float64}=[0.0, 2.0]: Vector or Matrix with the corresponding parameters (Vector: s_bc_prior[1] = mean, s_bc_prior[2] = standard deviation, Matrix: s_bc_prior[:, 1] = mean, s_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness values. If typeof(s_bc_prior) <: Matrix, there should be as many rows in the matrix as number of mutant lineages × number of replicates in the dataset.
• logσ_bc_prior::VecOrMat{Float64}=[0.0, 1.0]: Vector or Matrix with the corresponding parameters (Vector: logσ_bc_prior[1] = mean, logσ_bc_prior[2] = standard deviation, Matrix: logσ_bc_prior[:, 1] = mean, logσ_bc_prior[:, 2] = standard deviation) for a Normal prior on the mutant fitness error utilized in the log-likelihood function. If typeof(logσ_bc_prior) <: Matrix, there should be as many rows in the matrix as mutant lineages × number of replicates in the dataset.
• logλ_prior::VecOrMat{Float64}=[3.0, 3.0]: Vector or Matrix with the corresponding parameters (Vector: logλ_prior[1] = mean, logλ_prior[2] = standard deviation, Matrix: logλ_prior[:, 1] = mean, logλ_prior[:, 2] = standard deviation) for a Normal prior on the λ parameter in the Poisson distribution. The λ parameter can be interpreted as the mean number of barcode counts since we assume any barcode count n⁽ᵇ⁾ ~ Poisson(λ⁽ᵇ⁾). If typeof(logλ_prior) <: Matrix, there should be as many rows in the matrix as number of barcodes × number of time points × number of replicates in the dataset.

Latent Variables

• Population mean fitness per timepoint.
• Mutant hyper-fitness effects per environment.
• Non-centered samples for each of the experimental replicates.
• Deviations from the hyper parameter value for each experimental replicate.
• λ dispersion parameters per barcode and timepoint.

Notes

• All barcodes must be included in all replicates.
• All environments must appear at least once on each replicate.
• Models hyper-fitness effects as normally distributed.
• Models fitness effects as normally distributed.
• Utilizes a Poisson observation model for barcode counts.
• Can estimate time-varying and environment-specific fitness effects.
• Setting informative priors is recommended for stable convergence.