simGG: Genetic group pedigree and data simulation

In nadiv: (Non)Additive Genetic Relatedness Matrices

Genetic group pedigree and data simulation

Description

Simulates a pedigree and phenotype for a focal population receiving immigrants. Genetic and environmental differences can be specified between the focal and immigrant populations. Further, these differences can have temporal trends.

Usage

simGG(
  K,
  pairs,
  noff,
  g,
  nimm = 2,
  nimmG = seq(2, g - 1, 1),
  VAf = 1,
  VAi = 1,
  VRf = 1,
  VRi = 1,
  mup = 20,
  muf = 0,
  mui = 0,
  murf = 0,
  muri = 0,
  d_bvf = 0,
  d_bvi = 0,
  d_rf = 0,
  d_ri = 0
)

Arguments

K	Integer number of individuals per generation, or the focal population carrying capacity
pairs	Integer number of mating pairs created by sampling with replacement from adults of a given generation
noff	Integer number of offspring each pair contributes to the next generation
g	Integer number of (non-overlapping) generations to simulate
nimm	Integer number of immigrants added to the population each generation of migration
nimmG	Sequence of integers for the generations in which immigrants arrive in the focal population
VAf	Numeric value for the expected additive genetic variance in the first generation of the focal population - the founders
VAi	Numeric value for the expected additive genetic variance in each generation of immigrants
VRf	Numeric value for the expected residual variance in the focal population
VRi	Numeric value for the expected residual variance in each generation of the immigrants
mup	Numeric value for the expected mean phenotypic value in the first generation of the focal population - the founders
muf	Numeric value for the expected mean breeding value in the first generation of the focal population - the founders
mui	Numeric value for the expected mean breeding value for the immigrants
murf	Numeric value for the expected mean residual (environmental) deviation in the first generation of the focal population - the founders
muri	Numeric value for the expected mean residual (environmental) deviation for the immigrants
d_bvf	Numeric value for the expected change between generations in the mean breeding value of the focal population. Sets the rate of genetic selection occurring across generations
d_bvi	Numeric value for the expected change between generations in the mean breeding value of the immigrant population each generation
d_rf	Numeric value for the expected change between generations in the mean residual (environmental) deviation of the focal population each generation
d_ri	Numeric value for the expected change between generations in the mean residual (environmental) deviation of the immigrant population each generation

Details

Offspring total additive genetic values u are the average of their parents u plus a Mendelian sampling deviation drawn from a normal distribution with mean of 0 and variance equal to 0.5V_{A} (1 - f_{sd}) where V_A is VAf and f_{sd} is the average of the parents' coefficient of inbreeding f (p. 447 Verrier et al. 1993). Each ‘immigrant’ (individual with unknown parents in generations >1) is given a total additive genetic effect that is drawn from a normal distribution with mean of mui and variance equal to VAi. Residual deviations are sampled for ‘focal’ and ‘immigrant’ populations separately, using normal distributions with means of murf and muri, respectively, and variances of VRf and VRi, respectively. Phenotypes are the sum of total additive genetic effects and residual deviations plus an overall mean mup.

Trends in total additive genetic effects and/or residual deviations can be specified for both the focal and immigrant populations. Trends in total additive genetic effects occurring in the immigrants, in the residual deviations occurring in the focal population, and in the residual deviations occurring in the immigrants are produced by altering the mean each generation for the separate distribution from which these effects are each drawn. The change in mean over a generation is specified in units of standard deviations of the respective distributions (e.g., square roots of VAi, VRf, and VRi) and is set with d_bvi, d_rf, or d_ri, respectively.

Trends in total additive genetic effects for the focal population are produced by selecting individuals to be parents of the next generation according to their predicted total additive genetic effects. Individuals are assigned probabilities of being selected as a parent of the next generation depending on how closely their predicted total additive genetic effect matches an optimum value. Probabilities are assigned:

exp((\frac{-1}{2\sigma_{x}}) (x - \theta)^{2})

where x is the vector of predicted total additive genetic effects (u), \sigma_{x} is the standard deviation of x, and \theta is the optimum value. Sampling is conducted with replacement based on these probabilities.

The parameter d_bvf specifies how much the optimal total additive genetic effect changes per generation. The optimal total additive genetic effect in a given generation is calculated as: muf + d_bvf *sqrt(VAf) * (i-2). Individuals with predicted total additive genetic effects closest to this optimum have a higher probability of being randomly sampled to be parents of the next generation. This represents selection directly on predicted total additive genetic effects.

Total additive genetic effects are predicted for the first generation of focal individuals and all immigrants using equation 1.3 in Mrode (2005, p.3): h^{2} * (phenotype_{i} - mean population phenotype). The heritability is either VAf / (VAf + VRf) or VAi / (VAi + VRi). Total additive genetic effects are predicted for all other individuals using equation 1.9 in Mrode (2005, p. 10) - or as the average of each individual's parents' predicted total additive genetic effects.

Value

A data.frame with columns corresponding to:

id

Integer for each individual's unique identifying code

dam

Integer indicating each individual's dam

sire

Integer indicating each individual's sire

parAvgU

Numeric value for the average of each individual's dam and sire additive genetic effects

mendel

Numeric value for each individual's Mendelian sampling deviate from the mid-parental total additive genetic value

u

Numeric value of each individual's total additive genetic effect

r

Numeric value of each individual's residual (environmental) deviation

p

Numeric value of each individual's phenotypic value

pred.u

Numeric value of each individual's predicted total additive genetic effect

is

Integer of either 0 if an individual was born in the focal population or 1 if they were born in an immigrant population

gen

Integer value of the generation in which each individual was born

Author(s)

[e-mail]

References

Verrier, V., J.J. Colleau, and J.L. Foulley. 1993. Long-term effects of selection based on the animal model BLUP in a finite population. Theoretical and Applied Genetics. 87:446-454.

Mrode, R.A. 2005. Linear Models for the Prediction of Animal Breeding Values, 2nd ed. Cambridge, MA: CABI Publishing.

See Also

ggTutorial

Examples

  
  # The dataset 'ggTutorial' was simulated as:
  set.seed(102)      		# seed used to simulate ggTutorial
  ggTutorial <- simGG(K = 400, pairs = 200, noff = 4, g = 15,
	nimm = 40, nimmG = seq(2, 14, 1),
	muf = 0, mui = 3)
  

# Use genetic group methods to approximate the breeding values for ggTutorial
  ## First, construct a pedigree with genetic groups
  ggPed <- ggTutorial[, c("id", "dam", "sire", "is", "gen")]
  naPar <- which(is.na(ggPed[, 2]))
  ggPed$GG <- rep("NA", nrow(ggPed))
    # 'focal' population genetic group = "foc0" and 'immigrant' = "g1"
    # obtained by pasting "foc" & "g" with immigrant status "0" or "1", respectively
    ggPed$GG[naPar] <- as.character(ggPed$is[naPar])
    ggPed$GG[ggPed$GG == "0"] <- paste0("foc", ggPed$GG[ggPed$GG == "0"])
    ggPed$GG[ggPed$GG == "1"] <- paste0("g", ggPed$GG[ggPed$GG == "1"])
  ggPed[naPar, 2:3] <- ggPed[naPar, "GG"]

  ## Now create the Q matrix
  Q <- ggcontrib(ggPed[, 1:3], ggroups = c("foc0", "g1"))

  ## obtain the true values of the genetic group means
  foc0_mean <- mean(ggTutorial$u[which(ggTutorial$gen == 1 & ggTutorial$is == 0)])
  g1_mean <- mean(ggTutorial$u[which(ggTutorial$is == 1)])
  g_exp <- matrix(c(foc0_mean, g1_mean), ncol = 1)

  ## breeding values (a) are:
  ### tot. add. gen. effects (u) minus genetic group effects for each individual (Qg):
  a <- ggTutorial$u - Q %*% g_exp

nadiv documentation built on May 29, 2024, 10:40 a.m.