AdditiveDominanceLinearGenomicModel

class pybrops.model.gmod.AdditiveDominanceLinearGenomicModel.AdditiveDominanceLinearGenomicModel

Bases: AdditiveLinearGenomicModel

The AdditiveDominanceLinearGenomicModel class represents an interface for a Multivariate Multiple Linear Regression model.

A Multivariate Multiple Linear Regression model is defined as:

\[\mathbf{Y} = \mathbf{XB} + \mathbf{ZU} + \mathbf{E}\]

Where:

• \(\mathbf{Y}\) is a matrix of response variables of shape (n,t).

• \(\mathbf{X}\) is a matrix of fixed effect predictors of shape (n,q).

• \(\mathbf{B}\) is a matrix of fixed effect regression coefficients of shape (q,t).

• \(\mathbf{Z}\) is a matrix of random effect predictors of shape (n,p).

• \(\mathbf{U}\) is a matrix of random effect regression coefficients of shape (p,t).

• \(\mathbf{E}\) is a matrix of error terms of shape (n,t).

Block matrix modifications to :

\(\mathbf{Z}\) and \(\mathbf{U}\) can be decomposed into block matrices pertaining to different sets of effects:

\[\mathbf{Z} = \begin{bmatrix} \mathbf{Z_{misc}} & \mathbf{Z_{a} & \mathbf{Z_{d}} \end{bmatrix}\]

Where:

• \(\mathbf{Z_{misc}}\) is a matrix of miscellaneous random effect predictors of shape (n,p_misc)

• \(\mathbf{Z_{a}}\) is a matrix of additive genomic marker predictors of shape (n,p_a)

• \(\mathbf{Z_{d}}\) is a matrix of dominance genomic marker predictors of shape (n,p_d)

\[\begin{split}\mathbf{U} = \begin{bmatrix} \mathbf{U_{misc}} \\ \mathbf{U_{a}} \\ \mathbf{U_{d}} \end{bmatrix}\end{split}\]

Where:

• \(\mathbf{U_{misc}}\) is a matrix of miscellaneous random effects of shape (p_misc,t)

• \(\mathbf{U_{a}}\) is a matrix of additive genomic marker effects of shape (p_a,t)

• \(\mathbf{U_{d}}\) is a matrix of dominance genomic marker effects of shape (p_d,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.

• p_misc is the number of miscellaneous random effect predictors.

• p_a is the number of additive genomic marker predictors.

• p_d is the number of dominance genomic marker predictors.

• The sum of p_misc, p_a, and p_d equals p.

• t is the number of traits

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	Calculate the deleterious allele count across all taxa.
dafixed	Determine whether a deleterious allele is fixed across all taxa.
dafreq	Calculate the 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 polymorphic or fixed across all taxa.
facount	Calculate the favorable allele count across all taxa.
fafixed	Determine whether a favorable allele is fixed across all taxa.
fafreq	Calculate the favorable allele frequency across all taxa.
fapoly	Determine whether a favorable allele is polymorphic across all taxa.
fit	Fit the model.
fit_numpy	Fit the model.
from_csv_dict	Read an object from a set of CSV files specified by values in a dict.
from_hdf5	Read an object 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 an object 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.
nexplan_u_a	Number of additive genomic marker explanatory variables required by the model.
nexplan_u_d	Number of dominance genomic marker explanatory variables required by the model.
nexplan_u_misc	Number of miscellaneous 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.
nparam_u_a	Number of additive genomic marker parameters.
nparam_u_d	Number of dominance genomic marker parameters.
nparam_u_misc	Number of miscellaneous 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.
u_a	Additive genomic marker effects.
u_d	Dominance genomic marker effects.
u_misc	Miscellaneous random effects.

abstract property beta: object

Fixed effect regression coefficients.

abstract bulmer(gtobj, ploidy, **kwargs)

Calculate the Bulmer effect.

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 – Array of shape (t,) contianing Bulmer effects for each trait. In the event that additive genic variance is zero, NaN’s are produced.

Return type:

numpy.ndarray

abstract bulmer_numpy(Z, p, ploidy, **kwargs)

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 (int) – Ploidy of the species.

• kwargs (dict) – Additional keyword arguments.

Returns:

out – Array of shape (t,) contianing Bulmer effects for each trait. In the event that additive genic variance is zero, NaN’s are produced.

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

abstract daavail(gmat, dtype=None, **kwargs)

Determine whether a deleterious allele is available in the present 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 boolean type.

• kwargs (dict) – Additional keyword arguments.

Returns:

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

Where:

• p is the number of alleles.

• t is the number of traits.

Return type:

numpy.ndarray

abstract dacount(gmat, dtype, **kwargs)

Calculate the deleterious allele count 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 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,t) containing allele counts of the deleterious allele.

Where:

• p is the number of alleles.

• t is the number of traits.

Return type:

numpy.ndarray

abstract dafixed(gmat, dtype, **kwargs)

Determine whether a deleterious allele is fixed 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 fixed.

Where:

• p is the number of alleles.

• t is the number of traits.

Return type:

numpy.ndarray

abstract dafreq(gmat, dtype, **kwargs)

Calculate the deleterious allele frequency 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 allele frequencies of the deleterious allele.

Where:

• p is the number of alleles.

• t is the number of traits.

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

abstract faavail(gmat, dtype=None, **kwargs)

Determine whether a favorable allele is polymorphic or fixed 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 available.

Where:

• p is the number of alleles.

• t is the number of traits.

Return type:

numpy.ndarray

abstract facount(gmat, dtype, **kwargs)

Calculate the favorable allele count 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 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.

Where:

• p is the number of alleles.

• t is the number of traits.

Return type:

numpy.ndarray

abstract fafixed(gmat, dtype, **kwargs)

Determine whether a favorable allele is fixed 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 fixed.

Where:

• p is the number of alleles.

• t is the number of traits.

Return type:

numpy.ndarray

abstract fafreq(gmat, dtype, **kwargs)

Calculate the favorable allele frequency 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 allele frequencies of the favorable allele.

Where:

• p is the number of alleles.

• t is the number of traits.

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

abstract classmethod fit(ptobj, cvobj, gtobj, **kwargs)

Fit the 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.

• kwargs (dict) – Additional keyword arguments.

Return type:

None

abstract classmethod fit_numpy(Y, X, Z, **kwargs)

Fit the 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).

• 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

abstract classmethod from_hdf5(filename, groupname)

Read an object from an HDF5 file.

Parameters:

• filename (str, Path, h5py.File) – If str, an HDF5 file name from which to read. If Path, an HDF5 file name from which to read. If h5py.File, an opened HDF5 file from which to read.

• groupname (str, None) – If str, an HDF5 group name under which object data is stored. If None, object is read from base HDF5 group.

Returns:

out – An object read from an HDF5 file.

Return type:

HDF5InputOutput

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

abstract gebv(gtobj, **kwargs)

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:

gebvmat_hat – Genomic estimated breeding values.

Return type:

BreedingValueMatrix

abstract gebv_numpy(Z, **kwargs)

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

abstract property hyperparams: dict

Model parameters.

abstract lsl(gtobj, ploidy, unscale, **kwargs)

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.

• unscale (bool) – If True, then apply the mean of the fixed effects to the output.

• kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing lower selection limits for each of t traits.

Return type:

numpy.ndarray

abstract lsl_numpy(p, ploidy, unscale, **kwargs)

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.

• unscale (bool) – If True, then apply the mean of the fixed effects to the output.

• kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing lower selection limits for each of t traits.

Return type:

numpy.ndarray

abstract 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 nexplan_u_a: Integral

Number of additive genomic marker explanatory variables required by the model.

abstract property nexplan_u_d: Integral

Number of dominance genomic marker explanatory variables required by the model.

abstract property nexplan_u_misc: Integral

Number of miscellaneous random effect explanatory variables required by the model.

abstract property nparam: Integral

Number of model parameters.

abstract property nparam_beta: Integral

Number of fixed effect parameters.

abstract property nparam_u: Integral

Number of random effect parameters.

abstract property nparam_u_a: Integral

Number of additive genomic marker parameters.

abstract property nparam_u_d: Integral

Number of dominance genomic marker parameters.

abstract property nparam_u_misc: Integral

Number of miscellaneous random effect parameters.

abstract property ntrait: int

Number of traits predicted by the model.

abstract predict(cvobj, gtobj, **kwargs)

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:

bvmat_hat – Estimated breeding values.

Return type:

BreedingValueMatrix

abstract predict_numpy(X, Z, **kwargs)

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 predicted breeding values.

Return type:

numpy.ndarray

abstract score(ptobj, cvobj, gtobj, **kwargs)

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

Parameters:

• ptobj (BreedingValueMatrix or pandas.DataFrame) – An object containing phenotype data. Must be a matrix of breeding values or a phenotype data frame.

• cvobj (object) – 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:

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

Where:

• t is the number of traits.

Return type:

numpy.ndarray

abstract score_numpy(Y, X, Z, **kwargs)

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

abstract to_hdf5(filename, groupname, overwrite)

Write an object to an HDF5 file.

Parameters:

• filename (str, Path, h5py.File) – If str, an HDF5 file name to which to write. If Path, an HDF5 file path to which to write. If h5py.File, an opened HDF5 file to which to write.

• groupname (str, None) – If str, an HDF5 group name under which object data is stored. If None, object is written to the base HDF5 group.

• overwrite (bool) – Whether to overwrite values in an HDF5 file if a field already exists.

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

abstract property trait: ndarray

Names of the traits predicted by the model.

abstract property u: object

Random effect regression coefficients.

abstract property u_a: object

Additive genomic marker effects.

abstract property u_d: object

Dominance genomic marker effects.

abstract property u_misc: object

Miscellaneous random effects.

abstract usl(gtobj, ploidy, unscale, **kwargs)

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.

• unscale (bool) – If True, then apply the mean of the fixed effects to the output.

• kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing upper selection limits for each of t traits.

Return type:

numpy.ndarray

abstract usl_numpy(p, ploidy, unscale, **kwargs)

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.

• unscale (bool) – If True, then apply the mean of the fixed effects to the output.

• kwargs (dict) – Additional keyword arguments.

Returns:

out – An array of shape (t,) containing upper selection limits for each of t traits.

Return type:

numpy.ndarray

abstract var_A(gtobj, **kwargs)

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 – Array of shape (t,) contianing additive genetic variances for each trait.

Return type:

numpy.ndarray

abstract var_A_numpy(Z, **kwargs)

Calculate the population additive genetic variance

Parameters:

• Z (numpy.ndarray) – A matrix of genotypes.

• kwargs (dict) – Additional keyword arguments.

Returns:

out – Array of shape (t,) contianing additive genetic variances for each trait.

Return type:

numpy.ndarray

abstract var_G(gtobj, **kwargs)

Calculate the population genetic variance.

Parameters:

• gtobj (GenotypeMatrix) – An object containing genotype data. Must be a matrix of genotype values.

• kwargs (dict) – Additional keyword arguments.

Returns:

out – Array of shape (t,) contianing genetic variances for each trait.

Return type:

numpy.ndarray

abstract var_G_numpy(Z, **kwargs)

Calculate the population genetic variance.

Parameters:

• Z (numpy.ndarray) – A matrix of genotypes.

• kwargs (dict) – Additional keyword arguments.

Returns:

out – Array of shape (t,) contianing genetic variances for each trait.

Return type:

numpy.ndarray

abstract var_a(gtobj, ploidy, **kwargs)

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.

• kwargs (dict) – Additional keyword arguments.

Returns:

out – Array of shape (t,) contianing additive genic variances for each trait.

Return type:

numpy.ndarray

abstract var_a_numpy(p, ploidy, **kwargs)

Calculate the population additive genic variance

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 – Array of shape (t,) contianing additive genic variances for each trait.

Return type:

numpy.ndarray