Package 'cwad'

Neutral integer-feasible control allocation

Description

Balanced allocation summing to B: every genotype gets floor(B/N) plots and the surplus is placed at random. Averaging the criterion over several draws gives the control against which an optimised allocation should be judged when B/N is not an integer; comparing an integer allocation against a fractional "uniform r = B/N" is not a feasible comparison and inflates the apparent gain.

Usage

balanced_control(B, N, reps = 25L, seed = 11L)

Arguments

B	total plot budget.
N	number of genotypes.
reps	number of random draws to return.
seed	RNG seed.

Value

list of reps replication vectors.

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BLUP of genotype effects from the reduced (means) model

Description

BLUP of genotype effects from the reduced (means) model

Usage

blup(ybar, r, Ginv, alpha)

Arguments

ybar	genotype phenotypic means.
r	numeric vector of replications per genotype.
Ginv	inverse relationship matrix (use diag(N) for independence).
alpha	variance ratio $\sigma^2_e/\sigma^2_g$.

Value

numeric vector of predicted genotype effects.

---

Reduced mixed-model coefficient matrix on genotype means

Description

$M = [[\sum r, r'],[r, diag(r) + \alpha G^{-1}]]$ where $\alpha = \sigma^2_e/\sigma^2_g$. The genotype-mean reduction is exact for the model $\bar y_i = \mu + u_i + \bar e_i$, $Var(\bar e_i) = \sigma^2_e / r_i$.

Usage

build_mme(r, Ginv, alpha)

Arguments

r	numeric vector of replications per genotype.
Ginv	inverse relationship matrix (use diag(N) for independence).
alpha	variance ratio $\sigma^2_e/\sigma^2_g$.

Value

the $(N+1)\times(N+1)$ coefficient matrix.

---

Crossed comparison of allocations and analysis models

Description

Replaces the v0.1.0 compare_designs(). Every allocation is evaluated under BOTH analysis models – kinship-free ($G = I$) and kinship ($G$) – so that the allocation contrast and the analysis-model contrast are crossed rather than confounded. In v0.1.0 the caller supplied one analysis matrix per design, which made it easy (and, in the shipped example, actual) to change allocation and analysis model in the same step and then attribute the whole difference to the allocation.

Usage

compare_designs(G, alpha, sig2e, r_list, idx = NULL)

Arguments

G	relationship (kinship) matrix, $N \times N$.
alpha	variance ratio $\sigma^2_e/\sigma^2_g$.
sig2e	residual variance.
r_list	named list of replication vectors, each of length $N$ (or length $N + n_{check}$ when idx restricts evaluation to the first $N$ entries).
idx	optional 1-based indices of the evaluation set.

Value

a data.frame with one row per allocation and columns PEV_noG, rel_noG, PEV_kin, rel_kin, plus gain_analysis_pp and gain_allocation_pp, the decomposition of the naive gain relative to the first allocation in r_list analysed without kinship.

Examples

g <- make_fs_G(c(12, 12, 4, 4, 1, 1))
Ginv <- solve(g$G); N <- nrow(g$G)
r_unif <- rep(2, N)
r_cwad <- greedy_alloc(Ginv, B = 2 * N, alpha = 2)
compare_designs(g$G, alpha = 2, sig2e = 2,
                list(Uniform = r_unif, CWAD = r_cwad))

---

Greedy A-optimal, connectivity-aware plot allocation

Description

Allocates a plot budget one plot at a time to the genotype whose extra replicate most reduces the mean pairwise PEV, using rank-1 Sherman-Morrison updates of the inverse MME (adding a plot to genotype $i$ is the rank-1 update $v v'$, $v = e_\mu + e_i$). When the relationship matrix carries genetic connectivity, the optimiser spontaneously concentrates replication on genetically isolated genotypes.

Usage

greedy_alloc(
  Ginv,
  B,
  alpha,
  sig2e = 1,
  floor = 1L,
  r_start = NULL,
  idx_eval = NULL,
  check = TRUE
)

Arguments

Ginv	inverse relationship matrix.
B	total plot budget (>= floor * N).
alpha	variance ratio.
sig2e	residual variance.
floor	minimum replication per genotype (default 1).
r_start	optional starting allocation (overrides floor).
idx_eval	evaluation set for the criterion (default all).
check	logical; if TRUE, validate the first Sherman-Morrison score against a brute-force re-inversion (correctness self-test).

Value

numeric vector of replications summing to B.

Examples

g <- make_fs_G(c(12, 12, 4, 4, 1, 1)); Ginv <- solve(g$G)
N <- nrow(Ginv)                   # 34 genotypes
r <- greedy_alloc(Ginv, B = 2 * N, alpha = 2)
tapply(r, g$connectivity, mean)   # isolated genotypes get more plots

---

Full-sib additive relationship matrix

Description

Builds a block-diagonal numerator relationship matrix for a set of full-sib families (diagonal 1, within-family off-diagonal within).

Usage

make_fs_G(fam_sizes, within = 0.5)

Arguments

fam_sizes	integer vector of family sizes.
within	within-family additive relationship (default 0.5 for full sibs).

Value

list with G (relationship matrix), fam_id (0-based family index per genotype) and connectivity (row-sum of off-diagonals).

Examples

g <- make_fs_G(c(12, 12, 4, 4, 1, 1))
range(g$connectivity)

---

u-block of the inverse MME (unit-variance scale)

Description

u-block of the inverse MME (unit-variance scale)

Usage

Muu_inv(r, Ginv, alpha)

Arguments

r	numeric vector of replications per genotype.
Ginv	inverse relationship matrix (use diag(N) for independence).
alpha	variance ratio $\sigma^2_e/\sigma^2_g$.

Value

the $N\times N$ genotype block of $M^{-1}$.

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Mean pairwise prediction-error variance (A-optimality criterion)

Description

Mean pairwise prediction-error variance (A-optimality criterion)

Usage

pev_pairwise(r, Ginv, alpha, sig2e, idx = NULL)

Arguments

r	replications.
Ginv	inverse relationship.
alpha	ratio.
sig2e	residual variance.
idx	optional 1-based indices of the evaluation set (default: all genotypes).

Value

mean variance of a difference between two genotype predictions.

---

Mean genotype reliability

Description

Mean genotype reliability

Usage

reliability(r, Ginv, alpha, idx = NULL)

Arguments

r	replications.
Ginv	inverse relationship.
alpha	ratio.
idx	optional 1-based indices of the evaluation set (default: all genotypes).

Value

mean of $1 - \alpha\, (M^{-1})_{ii}$ over the evaluation set.

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Transgressive-segregant shrinkage experiment, with matched controls

Description

Plants one genotype with a genetic value spike genetic standard deviations above its family mean and measures, by Monte Carlo over residual noise, how far each arm's BLUP is pulled toward the family mean.

Usage

sim_transgressive(
  G,
  alpha,
  sig2e,
  sig2g,
  fam_id,
  t,
  r_list,
  spike = 3,
  reps = 3000,
  seed = 7
)

Arguments

G	relationship matrix.
alpha	variance ratio.
sig2e	residual variance.
sig2g	genetic variance.
fam_id	0-based family index per genotype.
t	1-based index of the transgressive genotype.
r_list	named list of replication vectors.
spike	deviation added to genotype t, in genetic sd units.
reps	Monte Carlo replications.
seed	RNG seed.

Details

Unlike v0.1.0, every allocation in r_list is run under BOTH analysis models, so the shrinkage attributable to borrowing from relatives is separated from the shrinkage attributable to reduced replication. In v0.1.0 the uniform arm was analysed without kinship and the CWAD arm with it, and the whole difference was reported as a property of CWAD; on the shipped example 58 percent of it is the analysis model.

Value

list with true_val, fam_mean, the raw estimates matrix and a data.frame summary carrying one row per (allocation, analysis model) cell.

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Wrong-kinship breaking-point experiment, with matched controls

Description

Generates truth under $G_{true}=(1-\delta)G+\delta I$ but analyses with the assumed kinship G, and reports RMSE of the BLUP for every (allocation, analysis model) cell across $\delta$.

Usage

sim_wrongG(
  G,
  alpha,
  sig2e,
  sig2g,
  r_list,
  split_by_r = TRUE,
  deltas = seq(0, 1, by = 0.1),
  reps = 500,
  seed = 7
)

Arguments

G	assumed relationship matrix.
alpha	variance ratio.
sig2e	residual variance.
sig2g	genetic variance.
r_list	named list of replication vectors; the first is the reference.
split_by_r	logical; if TRUE, additionally report each allocation's $r = 1$ and $r \ge 2$ genotypes separately.
deltas	sequence of mis-specification levels.
reps	Monte Carlo replications per delta.
seed	RNG seed.

Details

The matched control is the reference allocation analysed with the SAME wrong kinship. Comparing an aggressive allocation analysed with kinship against a uniform allocation analysed WITHOUT kinship – as v0.1.0 did – measures the cost of using kinship at all, because a kinship-free analysis cannot be harmed by a wrong kinship matrix; its curve is flat by construction and any crossing with it is an artefact of the mismatch, not a breaking point.

Value

long-format data.frame: delta, allocation, analysis, subset, RMSE.

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