DenseLinearGenomicModel#

class pybrops.model.gmod.DenseLinearGenomicModel.DenseLinearGenomicModel(beta, u, trait=None, model_name=None, hyperparams=None, **kwargs)[source]#

Bases: LinearGenomicModel

The DenseLinearGenomicModel class represents a Multivariate Multiple Linear Regression model.

A Multivariate Multiple Linear Regression model is defined as:

\[Y = X \beta + Zu + e\]

Where:

\(Y\) is a matrix of response variables of shape (n,t).
\(X\) is a matrix of fixed effect predictors of shape (n,q).
\(\beta\) is a matrix of fixed effect regression coefficients of shape (q,t).
\(Z\) is a matrix of random effect predictors of shape (n,p).
\(u\) is a matrix of random effect regression coefficients of shape (p,t).
\(e\) is a matrix of error terms of shape (n,t).

Shape definitions:

n is the number of individuals
q is the number of fixed effect predictors (e.g. environments)
p is the number of random effect predictors (e.g. genomic markers)
t is the number of traits

Constructor for DenseLinearGenomicModel class.

Parameters:

beta (numpy.ndarray) –
A float64 fixed effect regression coefficient matrix of shape (q,t).

Where:
- q is the number of fixed effect predictors (e.g. environments).
- t is the number of individuals.
u (numpy.ndarray) –
A float64 random effect regression coefficient matrix of shape (p,t).

Where:
- p is the number of random effect predictors (e.g. genomic markers).
- t is the number of individuals.
trait (numpy.ndarray, None) –
An object_ array of shape (t,).

Where:
- t is the number of traits.
model_name (str, None) – Name of the model.
hyperparams (dict, None) – Model parameters.
kwargs (dict) – Used for cooperative inheritance. Dictionary passing unused arguments to the parent class constructor.

Methods

`bulmer`	Calculate the Bulmer effect.
`bulmer_numpy`	Calculate the Bulmer effect.
`copy`	Make a shallow copy of the GenomicModel.
`daavail`	Determine whether a deleterious allele is available in the present taxa.
`dacount`	Deleterious allele count across all taxa.
`dafixed`	Determine whether a deleterious allele is fixed across all taxa.
`dafreq`	Deleterious allele frequency across all taxa.
`dapoly`	Determine whether a deleterious allele is polymorphic across all taxa.
`deepcopy`	Make a deep copy of the GenomicModel.
`faavail`	Determine whether a favorable allele is available in the present taxa.
`facount`	Favorable allele count across all taxa.
`fafixed`	Determine whether a favorable allele is fixed across all taxa.
`fafreq`	Favorable allele frequency across all taxa.
`fapoly`	Determine whether a favorable allele is polymorphic across all taxa.
`fit`	Fit a dense, linear genomic model.
`fit_numpy`	Fit a dense, linear genomic model.
`from_csv_dict`	Read an object from a set of CSV files specified by values in a `dict`.
`from_hdf5`	Read `DenseLinearGenomicModel` from an HDF5 file.
`from_pandas_dict`	Read an object from a `dict` of `pandas.DataFrame`.
`gebv`	Calculate genomic estimated breeding values.
`gebv_numpy`	Calculate genomic estimated breeding values.
`gegv`	Calculate genomic estimated genotypic values.
`gegv_numpy`	Calculate genomic estimated genotypic values.
`lsl`	Calculate the lower selection limit for a population.
`lsl_numpy`	Calculate the lower selection limit for a population.
`nafixed`	Determine whether a neutral allele is fixed across all taxa.
`napoly`	Determine whether a neutral allele is polymorphic across all taxa.
`predict`	Predict breeding values.
`predict_numpy`	Predict breeding values.
`score`	Return the coefficient of determination R**2 of the prediction.
`score_numpy`	Return the coefficient of determination R**2 of the prediction.
`to_csv_dict`	Write an object to a set of CSV files specified by values in a `dict`.
`to_hdf5`	Write `DenseLinearGenomicModel` to an HDF5 file.
`to_pandas_dict`	Export an object to a `dict` of `pandas.DataFrame`.
`usl`	Calculate the upper selection limit for a population.
`usl_numpy`	Calculate the upper selection limit for a population.
`var_A`	Calculate the population additive genetic variance
`var_A_numpy`	Calculate the population additive genetic variance
`var_G`	Calculate the population genetic variance.
`var_G_numpy`	Calculate the population genetic variance.
`var_a`	Calculate the population additive genic variance
`var_a_numpy`	Calculate the population additive genic variance

Attributes

`beta`	Fixed effect regression coefficients.
`hyperparams`	Model parameters.
`model_name`	Name of the model.
`nexplan`	Number of explanatory variables required by the model.
`nexplan_beta`	Number of fixed effect explanatory variables required by the model.
`nexplan_u`	Number of random effect explanatory variables required by the model.
`nparam`	Number of model parameters.
`nparam_beta`	Number of fixed effect parameters.
`nparam_u`	Number of random effect parameters.
`ntrait`	Number of traits predicted by the model.
`trait`	Names of the traits predicted by the model.
`u`	Random effect regression coefficients.

property beta: ndarray#: Fixed effect regression coefficients.

bulmer(gtobj, ploidy=None, **kwargs)[source]#

Calculate the Bulmer effect.

Parameters:

gtobj (GenotypeMatrix, numpy.ndarray) – An object containing genotype data. Must be a matrix of genotype values.
ploidy (int) –
Ploidy of the species. If ploidy is None:
- If gtobj is a GenotypeMatrix, then get ploidy from GenotypeMatrix.
- If gtobj is a numpy.ndarray, then assumed to be 2 (diploid).
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population Bulmer effect statistics. In the event that additive genic variance is zero, NaN’s are produced.

Where:

t is the number of traits.

Return type:

numpy.ndarray

bulmer_numpy(Z, p, ploidy, **kwargs)[source]#

Calculate the Bulmer effect.

Parameters:

Z (numpy.ndarray) – A matrix of genotypes.
p (numpy.ndarray) – A vector of genotype allele frequencies of shape (p,).
ploidy (Integral) – Ploidy of the species.
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population Bulmer effect statistics. In the event that additive genic variance is zero, NaN’s are produced.

Where:

t is the number of traits.

Return type:

numpy.ndarray

abstract copy()#

Make a shallow copy of the GenomicModel.

Returns:: out – A shallow copy of the original GenomicModel
Return type:: GenomicModel

daavail(gmat, dtype=None, **kwargs)[source]#

Determine whether a deleterious allele is available in the present taxa.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to determine deleterious allele frequencies.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native boolean type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,t) containing whether a deleterious allele is available.

Return type:

numpy.ndarray

dacount(gmat, dtype=None, **kwargs)[source]#

Deleterious allele count across all taxa.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to count deleterious alleles.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,) containing allele counts of the deleterious allele.

Return type:

numpy.ndarray

dafixed(gmat, dtype=None, **kwargs)[source]#

Determine whether a deleterious allele is fixed across all taxa.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to determine deleterious allele frequencies.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,) containing whether a deleterious allele is fixed.

Return type:

numpy.ndarray

dafreq(gmat, dtype=None, **kwargs)[source]#

Deleterious allele frequency across all taxa.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to determine deleterious allele frequencies.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,) containing allele frequencies of the deleterious allele.

Return type:

numpy.ndarray

abstract dapoly(gmat, dtype, **kwargs)#

Determine whether a deleterious allele is polymorphic across all taxa.

An allele is considered deleterious if its effect is less than zero. Alleles with zero effect are not considered deleterious; they are considered neutral.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to determine deleterious allele frequencies.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,t) containing whether a deleterious allele is polymorphic.

Where:

p is the number of alleles.
t is the number of traits.

Return type:

numpy.ndarray

abstract deepcopy(memo)#

Make a deep copy of the GenomicModel.

Parameters:: memo (dict) – Dictionary of memo metadata.
Returns:: out – A deep copy of the original GenomicModel
Return type:: GenomicModel

faavail(gmat, dtype=None, **kwargs)[source]#

Determine whether a favorable allele is available in the present taxa.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to determine favorable allele frequencies.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,t) containing whether a favorable allele is available.

Return type:

numpy.ndarray

facount(gmat, dtype=None, **kwargs)[source]#

Favorable allele count across all taxa.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to count favorable alleles.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,t) containing allele counts of the favorable allele.

Return type:

numpy.ndarray

fafixed(gmat, dtype=None, **kwargs)[source]#

Determine whether a favorable allele is fixed across all taxa.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to determine favorable allele frequencies.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,t) containing whether a favorable allele is fixed.

Return type:

numpy.ndarray

fafreq(gmat, dtype=None, **kwargs)[source]#

Favorable allele frequency across all taxa.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to determine favorable allele frequencies.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,t) containing allele frequencies of the favorable allele.

Return type:

numpy.ndarray

abstract fapoly(gmat, dtype, **kwargs)#

Determine whether a favorable allele is polymorphic across all taxa.

An allele is considered favorable if its effect is greater than zero. Alleles with zero effect are not considered favorable; they are considered neutral.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to determine favorable allele frequencies.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,t) containing whether a favorable allele is polymorphic.

Where:

p is the number of alleles.
t is the number of traits.

Return type:

numpy.ndarray

fit(ptobj, cvobj, gtobj, **kwargs)[source]#

Fit a dense, linear genomic model.

Parameters:

ptobj (BreedingValueMatrix, pandas.DataFrame, numpy.ndarray) – An object containing phenotype data. Must be a matrix of breeding values or a phenotype data frame.
cvobj (numpy.ndarray) – An object containing covariate data.
gtobj (GenotypeMatrix, numpy.ndarray) – An object containing genotype data. Must be a matrix of genotype values.
trait (numpy.ndarray, None) – A trait name array of shape (t,).
kwargs (dict) – Additional keyword arguments.

Return type:

None

fit_numpy(Y, X, Z, **kwargs)[source]#

Fit a dense, linear genomic model.

Parameters:

Y (numpy.ndarray) – A phenotype matrix of shape (n,t).
X (numpy.ndarray) – A covariate matrix of shape (n,q).
Z (numpy.ndarray) – A genotypes matrix of shape (n,p).
trait (numpy.ndarray) – A trait name array of shape (t,).
kwargs (dict) – Additional keyword arguments.

Return type:

None

abstract classmethod from_csv_dict(filenames, **kwargs)#

Read an object from a set of CSV files specified by values in a dict.

Parameters:

filenames (str) – Dictionary of CSV file names from which to read.
kwargs (dict) – Additional keyword arguments to use for dictating importing from a CSV.

Returns:

out – An object read from a set of CSV files.

Return type:

CSVDictInputOutput

classmethod from_hdf5(filename, groupname=None)[source]#

Read DenseLinearGenomicModel from an HDF5 file.

Parameters:

filename (str, Path, h5py.File) – If str or Path, an HDF5 file name from which to read. File is closed after reading. If h5py.File, an opened HDF5 file from which to read. File is not closed after reading.
groupname (str, None) – If str, an HDF5 group name under which DenseLinearGenomicModel data is stored. If None, DenseLinearGenomicModel is read from base HDF5 group.

Returns:

gmat – A genotype matrix read from file.

Return type:

DenseLinearGenomicModel

abstract classmethod from_pandas_dict(dic, **kwargs)#

Read an object from a dict of pandas.DataFrame.

Parameters:

dic (dict) – Python dictionary containing pandas.DataFrame from which to read.
kwargs (dict) – Additional keyword arguments to use for dictating importing from a dict of pandas.DataFrame.

Returns:

out – An object read from a dict of pandas.DataFrame.

Return type:

PandasDictInputOutput

gebv(gtobj, **kwargs)[source]#

Calculate genomic estimated breeding values.

Remark: The difference between ‘predict’ and ‘gebv’ is that ‘predict’ can incorporate other factors (e.g., fixed effects) to provide prediction estimates.

Parameters:

gtobj (GenotypeMatrix) – An object containing genotype data. Must be a matrix of genotype values.
kwargs (dict) – Additional keyword arguments.

Returns:

out – Genomic estimated breeding values matrix.

Return type:

BreedingValueMatrix

gebv_numpy(Z, **kwargs)[source]#

Calculate genomic estimated breeding values.

Remark: The difference between ‘predict_numpy’ and ‘gebv_numpy’ is that ‘predict_numpy’ can incorporate other factors (e.g., fixed effects) to provide prediction estimates.

Parameters:

Z (numpy.ndarray) – A matrix of genotype values.
kwargs (dict) – Additional keyword arguments.

Returns:

gebv_hat – A matrix of genomic estimated breeding values.

Return type:

numpy.ndarray

abstract gegv(gtobj, **kwargs)#

Calculate genomic estimated genotypic values.

Parameters:

Z (numpy.ndarray) – A matrix of genotypic markers.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A matrix of genomic estimated genotypic values.

Return type:

numpy.ndarray

abstract gegv_numpy(Z, **kwargs)#

Calculate genomic estimated genotypic values.

Parameters:

Z (numpy.ndarray) – A matrix of genotypic markers.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A matrix of genomic estimated genotypic values.

Return type:

numpy.ndarray

property hyperparams: dict#: Model parameters.

lsl(gtobj, ploidy=None, **kwargs)[source]#

Calculate the lower selection limit for a population.

Parameters:

gtobj (GenotypeMatrix) – An object containing genotype data. Must be a matrix of genotype values.
ploidy (int) – Ploidy of the species.
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population lower selection limit statistics.

Where:

t is the number of traits.

Return type:

numpy.ndarray

lsl_numpy(p, ploidy, **kwargs)[source]#

Calculate the lower selection limit for a population.

Parameters:

p (numpy.ndarray) – A vector of genotype allele frequencies of shape (p,).
ploidy (int) – Ploidy of the species.
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population lower selection limit statistics.

Where:

t is the number of traits.

Return type:

numpy.ndarray

property model_name: str#: Name of the model.

abstract nafixed(gmat, dtype, **kwargs)#

Determine whether a neutral allele is fixed across all taxa.

An allele is considered neutral if its effect is equal to zero.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to determine neutral allele frequencies.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,t) containing whether a neutral allele is fixed.

Where:

p is the number of alleles.
t is the number of traits.

Return type:

numpy.ndarray

abstract napoly(gmat, dtype, **kwargs)#

Determine whether a neutral allele is polymorphic across all taxa.

An allele is considered neutral if its effect is equal to zero.

Parameters:

gmat (GenotypeMatrix) – Genotype matrix for which to determine neutral allele frequencies.
dtype (numpy.dtype, None) – Datatype of the returned array. If None, use the native type.
kwargs (dict) – Additional keyword arguments.

Returns:

out – A numpy.ndarray of shape (p,t) containing whether a neutral allele is polymorphic.

Where:

p is the number of alleles.
t is the number of traits.

Return type:

numpy.ndarray

abstract property nexplan: Integral#: Number of explanatory variables required by the model.

abstract property nexplan_beta: Integral#: Number of fixed effect explanatory variables required by the model.

abstract property nexplan_u: Integral#: Number of random effect explanatory variables required by the model.

abstract property nparam: Integral#: Number of model parameters.

property nparam_beta: Integral#: Number of fixed effect parameters.

property nparam_u: Integral#: Number of random effect parameters.

property ntrait: int#: Number of traits predicted by the model.

predict(cvobj, gtobj, **kwargs)[source]#

Predict breeding values.

Remark: The difference between ‘predict’ and ‘gebv’ is that ‘predict’ can incorporate other factors (e.g., fixed effects) to provide prediction estimates.

Parameters:

cvobj (numpy.ndarray) – An object containing covariate data.
gtobj (GenotypeMatrix,) – An object containing genotype data. Must be a matrix of genotype values.
kwargs (dict) – Additional keyword arguments.

Returns:

out – Estimated breeding values matrix.

Return type:

BreedingValueMatrix

predict_numpy(X, Z, **kwargs)[source]#

Predict breeding values.

Remark: The difference between ‘predict_numpy’ and ‘gebv_numpy’ is that ‘predict_numpy’ can incorporate other factors (e.g., fixed effects) to provide prediction estimates.

Parameters:

X (numpy.ndarray) – A matrix of covariates.
Z (numpy.ndarray) – A matrix of genotype values.
kwargs (dict) – Additional keyword arguments.

Returns:

Y_hat – A matrix of estimated breeding values.

Return type:

numpy.ndarray

score(ptobj, cvobj, gtobj, **kwargs)[source]#

Return the coefficient of determination R**2 of the prediction.

Parameters:

ptobj (BreedingValueMatrix, pandas.DataFrame, numpy.ndarray) – An object containing phenotype data. Must be a matrix of breeding values or a phenotype data frame.
cvobj (numpy.ndarray) – An object containing covariate data.
gtobj (GenotypeMatrix, numpy.ndarray) – An object containing genotype data. Must be a matrix of genotype values.
kwargs (dict) – Additional keyword arguments.

Returns:

Rsq – A coefficient of determination array of shape (t,).

Where:

t is the number of traits.

Return type:

numpy.ndarray

score_numpy(Y, X, Z, **kwargs)[source]#

Return the coefficient of determination R**2 of the prediction.

Parameters:

Y (numpy.ndarray) – A matrix of phenotypes.
X (numpy.ndarray) – A matrix of covariates.
Z (numpy.ndarray) – A matrix of genotypes.
kwargs (dict) – Additional keyword arguments.

Returns:

Rsq – A coefficient of determination array of shape (t,).

Where:

t is the number of traits.

Return type:

numpy.ndarray

abstract to_csv_dict(filenames, **kwargs)#

Write an object to a set of CSV files specified by values in a dict.

Parameters:

filenames (dict) – Dictionary of CSV file names to which to write.
kwargs (dict) – Additional keyword arguments to use for dictating export to a CSV.

Return type:

None

to_hdf5(filename, groupname=None, overwrite=True)[source]#

Write DenseLinearGenomicModel to an HDF5 file.

Parameters:

filename (str, Path, h5py.File) – If str, an HDF5 file name to which to write. File is closed after writing. If h5py.File, an opened HDF5 file to which to write. File is not closed after writing.
groupname (str, None) – If str, an HDF5 group name under which DenseLinearGenomicModel data is stored. If None, DenseLinearGenomicModel is written to the base HDF5 group.
overwrite (bool) – Whether to overwrite data fields if they are present in the HDF5 file.

Return type:

None

abstract to_pandas_dict(**kwargs)#

Export an object to a dict of pandas.DataFrame.

Parameters:: kwargs (dict) – Additional keyword arguments to use for dictating export to a dict of pandas.DataFrame.
Returns:: out – An output dataframe.
Return type:: dict

property trait: ndarray | None#: Names of the traits predicted by the model.

property u: ndarray#: Random effect regression coefficients.

usl(gtobj, ploidy=None, **kwargs)[source]#

Calculate the upper selection limit for a population.

Parameters:

gtobj (GenotypeMatrix) – An object containing genotype data. Must be a matrix of genotype values.
ploidy (int) – Ploidy of the species.
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population upper selection limit statistics.

Where:

t is the number of traits.

Return type:

numpy.ndarray

usl_numpy(p, ploidy, **kwargs)[source]#

Calculate the upper selection limit for a population.

Parameters:

p (numpy.ndarray) – A vector of genotype allele frequencies of shape (p,).
ploidy (int) – Ploidy of the species.
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population upper selection limit statistics.

Where:

t is the number of traits.

Return type:

numpy.ndarray

var_A(gtobj, **kwargs)[source]#

Calculate the population additive genetic variance

Parameters:

gtobj (GenotypeMatrix) – An object containing genotype data. Must be a matrix of genotype values.
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population additive genetic variances.

Where:

t is the number of traits.

Return type:

numpy.ndarray

var_A_numpy(Z, **kwargs)[source]#

Calculate the population additive genetic variance

Parameters:

Z (numpy.ndarray) – A matrix of genotypes.
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population additive genetic variances.

Where:

t is the number of traits.

Return type:

numpy.ndarray

var_G(gtobj, **kwargs)[source]#

Calculate the population genetic variance.

Parameters:

gtobj (GenotypeMatrix, numpy.ndarray) – An object containing genotype data. Must be a matrix of genotype values.
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population genetic variances.

Where:

t is the number of traits.

Return type:

numpy.ndarray

var_G_numpy(Z, **kwargs)[source]#

Calculate the population genetic variance.

Parameters:

Z (numpy.ndarray) – A matrix of genotypes.
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population genetic variances.

Where:

t is the number of traits.

Return type:

numpy.ndarray

var_a(gtobj, ploidy=None, **kwargs)[source]#

Calculate the population additive genic variance

Parameters:

gtobj (GenotypeMatrix, numpy.ndarray) – An object containing genotype data. Must be a matrix of genotype values.
ploidy (int) –
Ploidy of the species.

If ploidy is None:
- If gtobj is a GenotypeMatrix, then get ploidy from GenotypeMatrix.
- If gtobj is a numpy.ndarray, then assumed to be 2 (diploid).
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population additive genic variances.

Where:

t is the number of traits.

Return type:

numpy.ndarray

var_a_numpy(p, ploidy, **kwargs)[source]#

Calculate the population additive genic variance

Parameters:

p (numpy.ndarray) – A vector of genotype allele frequencies of shape (p,).
ploidy (Integral) – Ploidy of the species.
kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing population additive genic variances.

Where:

t is the number of traits.

Return type:

numpy.ndarray