Type:	Package
Title:	Tools for Biometry and Applied Statistics in Agricultural Science
Version:	4.3
Date:	2025-04-01
LazyLoad:	yes
LazyData:	yes
Author:	Anderson Rodrigo da Silva [aut, cre]
Maintainer:	Anderson Rodrigo da Silva <anderson.agro@hotmail.com>
Depends:	MASS
Imports:	utils, stats, graphics, boot, grDevices, datasets
Suggests:	soilphysics, tkrplot, tcltk, rpanel, lattice, SpatialEpi, knitr, rmarkdown, testthat (≥ 3.0.0)
Description:	Tools designed to perform and evaluate cluster analysis (including Tocher's algorithm), discriminant analysis and path analysis (standard and under collinearity), as well as some useful miscellaneous tools for dealing with sample size and optimum plot size calculations. A test for seed sample heterogeneity is now available. Mantel's permutation test can be found in this package. A new approach for calculating its power is implemented. biotools also contains tests for genetic covariance components. Heuristic approaches for performing non-parametric spatial predictions of generic response variables and spatial gene diversity are implemented.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
VignetteBuilder:	knitr
URL:	https://arsilva87.github.io/biotools/
BugReports:	https://github.com/arsilva87/biotools/issues
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2025-04-02 13:31:41 UTC; LIVRE
Repository:	CRAN
Date/Publication:	2025-04-02 14:00:02 UTC

Tools for Biometry and Applied Statistics in Agricultural Science

Description

Tools designed to perform and evaluate cluster analysis (including Tocher's algorithm), discriminant analysis and path analysis (standard and under collinearity), as well as some useful miscellaneous tools for dealing with sample size and optimum plot size calculations. A test for seed sample heterogeneity is now available. Mantel's permutation test can be found in this package. A new approach for calculating its power is implemented. biotools also contains tests for genetic covariance components. Heuristic approaches for performing non-parametric spatial predictions of generic response variables and spatial gene diversity are implemented.

Details

Note

biotools is an ongoing project. Any and all criticism, comments and suggestions are welcomed.

Author(s)

Anderson Rodrigo da Silva

Maintainer: Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Rao, R.C. (1952) Advanced statistical methods in biometric research. New York: John Wiley & Sons.

Sharma, J.R. (2006) Statistical and biometrical techniques in plant breeding. Delhi: New Age International.

Da Silva, A.R.; Malafaia, G.; Menezes, I.P.P. (2017) biotools: an R function to predict spatial gene diversity via an individual-based approach. Genetics and Molecular Research, 16: gmr16029655.

Da Silva, A.R., Silva, A.P.A., Tiago-Neto, L.J. (2020) A new local stochastic method for predicting data with spatial heterogeneity. ACTA SCIENTIARUM-AGRONOMY, 43: e49947.

Silva, A.R. & Dias, C.T.S. (2013) A cophenetic correlation coefficient for Tocher's method. Pesquisa Agropecuaria Brasileira, 48: 589-596.

Da Silva, A.R. (2020). On testing for seed sample heterogeneity with the exact probability distribution of the germination count range. Seed Science Research, 30(1): 59-63.

Discriminant Analysis Based on Mahalanobis Distance

Description

A function to perform discriminant analysis based on the squared generalized Mahalanobis distance (D2) of the observations to the center of the groups.

Usage

## Default S3 method:
D2.disc(data, grouping, pooled.cov = NULL)
## S3 method for class 'D2.disc'
print(x, ...)
## S3 method for class 'D2.disc'
predict(object, newdata = NULL, ...)

Arguments

Value

A list of

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Manly, B.F.J. (2004) Multivariate statistical methods: a primer. CRC Press. (p. 105-106).

Mahalanobis, P.C. (1936) On the generalized distance in statistics. Proceedings of The National Institute of Sciences of India, 12:49-55.

See Also

D2.dist, confusionmatrix, lda

Examples

data(iris)
(disc <- D2.disc(iris[, -5], iris[, 5]))
first10 <- iris[1:10, -5]
predict(disc, first10)
predict(disc, iris[, -5])$class

# End (not run)

Pairwise Squared Generalized Mahalanobis Distances

Description

Function to calculate the squared generalized Mahalanobis distance between all pairs of rows in a data frame with respect to a covariance matrix. The element of the i-th row and j-th column of the distance matrix is defined as

D_{ij}^2 = (\bold{x}_i - \bold{x}_j)' \bold{\Sigma}^{-1} (\bold{x}_i - \bold{x}_j)

Usage

D2.dist(data, cov, inverted = FALSE)

Arguments

Value

An object of class "dist".

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Mahalanobis, P. C. (1936) On the generalized distance in statistics. Proceedings of The National Institute of Sciences of India, 12:49-55.

See Also

dist, singh

Examples

# Manly (2004, p.65-66)
x1 <- c(131.37, 132.37, 134.47, 135.50, 136.17)
x2 <- c(133.60, 132.70, 133.80, 132.30, 130.33)
x3 <- c(99.17, 99.07, 96.03, 94.53, 93.50)
x4 <- c(50.53, 50.23, 50.57, 51.97, 51.37)
x <- cbind(x1, x2, x3, x4)
Cov <- matrix(c(21.112,0.038,0.078,2.01, 0.038,23.486,5.2,2.844,
	0.078,5.2,24.18,1.134, 2.01,2.844,1.134,10.154), 4, 4)
D2.dist(x, Cov)

# End (not run)

Apparent Error Rate

Description

A function to calculate the apparent error rate of two classification vectors, i.e., the proportion of observed cases incorrectly predicted. It can be useful for evaluating discriminant analysis or other classification systems.

aer = \frac{1}{n} \sum_{i=1}^{n} I(y_i \neq \hat{y}_i)

Usage

aer(obs, predict)

Arguments

Value

The apparent error rate, a number between 0 (no agreement) and 1 (thorough agreement).

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

See Also

confusionmatrix, lda

Examples

data(iris)
da <- lda(Species ~ ., data = iris)
pred <- predict(da, dimen = 1)
aer(iris$Species, pred$class)

# End (not run)

Box's M-test

Description

It performs the Box's M-test for homogeneity of covariance matrices obtained from multivariate normal data according to one classification factor. The test is based on the chi-square approximation.

Usage

boxM(data, grouping)

Arguments

Value

A list with class "htest" containing the following components:

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Morrison, D.F. (1976) Multivariate Statistical Methods.

Examples

data(iris)
boxM(iris[, -5], iris[, 5])

# End (not run)

Brazil Grid

Description

Lat/Long coordinates within Brazil's limits.

Usage

data("brazil")

Format

A data frame with 17141 observations on the following 2 variables.

x

a numeric vector (longitude)

y

a numeric vector (latitude)

Examples

data(brazil)
plot(brazil, cex = 0.1, col = "gray")

Confusion Matrix

Description

A function to compute the confusion matrix of two classification vectors. It can be useful for evaluating discriminant analysis or other classification systems.

Usage

confusionmatrix(obs, predict)

Arguments

Value

A square matrix containing the number of objects in each class, observed (rows) and predicted (columns). Diagonal elements refers to agreement of obs and predict.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

See Also

aer, lda

Examples

data(iris)
da <- lda(Species ~ ., data = iris)
pred <- predict(da, dimen = 1)
confusionmatrix(iris$Species, pred$class)

# End (not run)

Partial Covariance Matrix

Description

Compute a matrix of partial (co)variances for a group of variables with respect to another.

Take \Sigma as the covariance matrix of dimension p. Now consider dividing \Sigma into two groups of variables. The partial covariance matrices are calculate by:

\Sigma_{11.2} = \Sigma_{11} - \Sigma_{12} \Sigma_{22}^{-1} \Sigma_{21}

\Sigma_{22.1} = \Sigma_{22} - \Sigma_{21} \Sigma_{11}^{-1} \Sigma_{12}

Usage

cov2pcov(m, vars1, vars2 = seq(1, ncol(m))[-vars1])

Arguments

Value

A square numeric matrix.

Author(s)

Anderson Rodrigo da Silva <anderson.agro at hotmail.com>

See Also

cov

Examples

(Cl <- cov(longley))
cov2pcov(Cl, 1:2)

# End (Not run)

Creating Homogeneous Groups

Description

A function to create homogeneous groups of named objects according to an objective function evaluated at a covariate. It can be useful to design experiments which contain a fixed covariate factor.

Usage

creategroups(x, ngroups, sizes, fun = mean, tol = 0.01, maxit = 200)

Arguments

Details

creategroups uses a tol value to evaluate the following statistic: h = \sum_{j}^{ngroups} abs( t_{j+1} - t_j ) / ngroups, where t_j = fun(group_j). If h \leq tol, the groups are considered homogeneous.

Value

A list of

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

Examples

x <- rnorm(10, 1, 0.5)
names(x) <- letters[1:10]
creategroups(x, ngroups = 2, sizes = c(5, 5))
creategroups(x, ngroups = 3, sizes = c(3, 4, 3), tol = 0.05)

# End (not run)

Cluster Distance Matrix

Description

Function to compute a matrix of average distances within and between clusters.

Usage

distClust(d, nobj.cluster, id.cluster)

Arguments

Value

A squared matrix containing distances within (diagonal) and between (off-diagonal) clusters.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

See Also

tocher, dist

Finding an Optimized Subsample

Description

It allows one to find an optimized (minimized or maximized) numeric subsample according to a statistic of interest. For example, it might be of interest to determine a subsample whose standard deviation is the lowest among all of those obtained from all possible subsamples of the same size.

Usage

findSubsample(x, size, fun = sd, minimize = TRUE, niter = 10000)

Arguments

Value

A list of

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

See Also

sample, creategroups

Examples

# Example 1
y <- rnorm(40, 5, 2)
findSubsample(x = y, size = 6)

# Example 2
f <- function(x) diff(range(x)) # max(x) - min(x)
findSubsample(x = y, size = 6, fun = f, minimize = FALSE, niter = 20000)

# End (not run)

Parameter Estimation of the Plot Size Model

Description

Function to estimate the parameters of the nonlinear Lessman & Atkins (1963) model for determining the optimum plot size as a function of the experimental coefficient of variation (CV) or as a function of the residual standard error.

CV = a * plotsize ^ {-b}.

It creates initial estimates of the parameters a and b by log-linearization and uses them to provide its least-squares estimates via nls.

Usage

fitplotsize(plotsize, CV)

Arguments

Value

A nls output.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Lessman, K. J. & Atkins, R. E. (1963) Optimum plot size and relative efficiency of lattice designs for grain sorghum yield tests. Crop Sci., 3:477-481.

See Also

optimumplotsize

Examples

ps <- c(1, 2, 3, 4, 6, 8, 12)
cv <- c(35.6, 29, 27.1, 25.6, 24.4, 23.3, 21.6)
out <- fitplotsize(plotsize = ps, CV = cv)
predict(out) # fitted.values
plot(cv ~ ps)
curve(coef(out)[1] * x^(-coef(out)[2]), add = TRUE)

# End (not run)

Distances Between Garlic Cultivars

Description

The data give the squared generalized Mahalanobis distances between 17 garlic cultivars. The data are taken from the article published by Silva & Dias (2013).

Usage

data(garlicdist)

Format

An object of class "dist" based on 17 objects.

Source

Silva, A.R. & Dias, C.T.S. (2013) A cophenetic correlation coefficient for Tocher's method. Pesquisa Agropecuaria Brasileira, 48:589-596.

Examples

data(garlicdist)
tocher(garlicdist)

# End (not run)

Testing Genetic Covariance

Description

gencovtest() tests genetic covariance components from a MANOVA model. Two different approaches can be used: (I) a test statistic that takes into account the genetic and environmental effects and (II) a test statistic that only considers the genetic information. The first type refers to tests based on the mean cross-products ratio, whose distribution is obtained via Monte Carlo simulation of Wishart matrices. The second way of testing genetic covariance refers to tests based upon an adaptation of Wilks' and Pillai's statistics for evaluating independence of two sets of variables. All these tests are described by Silva (2015).

Usage

## S3 method for class 'manova'
gencovtest(obj, geneticFactor, gcov = NULL,
	residualFactor = NULL, adjNrep = 1,
	test = c("MCPR", "Wilks", "Pillai"),
	nsim = 9999,
	alternative = c("two.sided", "less", "greater"))
## S3 method for class 'gencovtest'
print(x, digits = 4, ...)
## S3 method for class 'gencovtest'
plot(x, var1, var2, ...)

Arguments

Details

The genetic covariance matrix is currently estimated via method of moments, following the equation:

G = (Mg - Me) / (nrep * adjNrep)

where Mg and Me are the matrices of mean cross-products associated with the genetic factor and the residuals, respectively; nrep is the number of replications, calculated as the ratio between the total number of observations and the number of levels of the genetic factor; adjNrep is supposed to adjust nrep, specially when estimating G from unbalanced data.

Value

An object of class gencovtest, a list of

Warning

When using the MCPR test, be aware that dfg should be equal or greater than the number of variables (p). Otherwise the simulation of Wishart matrices may not be done.

A collinearity diagnosis is carried out using the condition number (CN), for the inferences may be affected by the quality of G. Thus, if CN > 100, a warning message is displayed.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Silva, A.R. (2015) On Testing Genetic Covariance. LAP Lambert Academic Publishing. ISBN 3659716553

See Also

manova

Examples

# MANOVA
data(maize)
M <- manova(cbind(NKPR, ED, CD, PH) ~ family + env, data = maize)
summary(M)

# Example 1 - MCPR
t1 <- gencovtest(obj = M, geneticFactor = "family")
print(t1)
plot(t1, "ED", "PH")

# Example 2 - Pillai
t2 <- gencovtest(obj = M, geneticFactor = "family", test = "Pillai")
print(t2)
plot(t2, "ED", "PH")

# End (not run)

Germination Count Range Test for Seed Sample Heterogeneity

Description

A test based on the exact probability distribution of the germination count range, i.e, the difference between germination count of seed samples.

Usage

germinationcount.test(r, nsamples, n, N, K)

Arguments

Value

A list of

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Da Silva, A.R. (2020). On testing for seed sample heterogeneity with the exact probability distribution of the germination count range. Seed Science Research, 30(1): 59–63. doi:10.1017/S0960258520000112

Examples

germinationcount.test(r = 6, nsamples = 4, n = 50, N = 2000, K = 1700)

# End (Not run)

Maize Data

Description

Data from and experiment with five maize families carried out in randomized block design, with four replications (environments).

Usage

data("maize")

Format

A data frame with 20 observations on the following 6 variables.

NKPR

a numeric vector containing values of Number of Kernels Per cob Row.

ED

a numeric vector containing values of Ear Diameter (in cm).

CD

a numeric vector containing values of Cob Diameter (in cm).

PH

a numeric vector containing values of Plant Heigth (in m).

family

a factor with levels 1 2 3 4 5

env

a factor with levels 1 2 3 4

Examples

data(maize)
str(maize)
summary(maize)

Power of Mantel's Test

Description

Power calculation of Mantel's permutation test.

Usage

mantelPower(obj, effect.size = seq(0, 1, length.out = 50), alpha = 0.05)

Arguments

Value

A data frame containing the effect size and its respective power level.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Silva, A.R.; Dias, C.T.S.; Cecon, P.R.; Rego, E.R. (2015). An alternative procedure for performing a power analysis of Mantel's test. Journal of Applied Statistics, 42(9): 1984-1992.

See Also

mantelTest

Examples

# Mantel test
data(garlicdist)
garlic <- tocher(garlicdist)
coph <- cophenetic(garlic)
mt1 <- mantelTest(garlicdist, coph, xlim = c(-1, 1))

# Power calculation, H1: rho = 0.3
mantelPower(mt1, effect.size = 0.3)

# Power calculation, multiple H1s and different alphas
p01 <- mantelPower(mt1, alpha = 0.01)
p05 <- mantelPower(mt1, alpha = 0.05)
p10 <- mantelPower(mt1, alpha = 0.10)
plot(p01, type = "l", col = 4)
lines(p05, lty = 2, col = 4)
lines(p10, lty = 3, col = 4)
legend("bottomright", c("0.10", "0.05", "0.01"),
	title = expression(alpha), col = 4, lty = 3:1, cex = 0.8)

# End (Not run)

Mantel's Permutation Test

Description

Mantel's permutation test based on Pearson's correlation coefficient to evaluate the association between two distance square matrices.

Usage

mantelTest(m1, m2, nperm = 999, alternative = "greater",
	graph = TRUE, main = "Mantel's test", xlab = "Correlation", ...)

Arguments

Value

A list of

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Mantel, N. (1967). The detection of disease clustering and a generalized regression approach. Cancer Research, 27:209–220.

See Also

mantelPower

Examples

# Distances between garlic cultivars
data(garlicdist)
garlicdist

# Tocher's clustering
garlic <- tocher(garlicdist)
garlic

# Cophenetic distances
coph <- cophenetic(garlic)
coph

# Mantel's test
mantelTest(garlicdist, coph,
	xlim = c(-1, 1))

# End (Not run)

Moco Cotton Data

Description

Data set of...

Usage

data("moco")

Format

A data frame with 206 observations (sampling points) on the following 20 variables (coordinates and markers).

Lon

a numeric vector containing values of longitude

Lat

a numeric vector containing values of latitude

BNL1434.1

a numeric vector (marker)

BNL1434.2

a numeric vector

BNL840.1

a numeric vector

BNL840.2

a numeric vector

BNL2496.1

a numeric vector

BNL2496.2

a numeric vector

BNL1421.1

a numeric vector

BNL1421.2

a numeric vector

BNL1551.1

a numeric vector

BNL1551.2

a numeric vector

CIR249.1

a numeric vector

CIR249.2

a numeric vector

BNL3103.1

a numeric vector

BNL3103.2

a numeric vector

CIR311.1

a numeric vector

CIR311.2

a numeric vector

CIR246.1

a numeric vector

CIR246.2

a numeric vector

Source

...

References

...

Examples

data(moco)
str(moco)

Pairwise Correlation t-Test

Description

It performs multiple correlation t-tests from a correlation matrix based on the statistic:

t = r * \sqrt(df / (1 - r^2))

where, in general, df = n - 2.

Usage

multcor.test(x, n = NULL, Df = NULL,
	alternative = c("two.sided", "less", "greater"), adjust = "none")

Arguments

Value

A list with class "multcor.test" containing the following components:

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

See Also

cor, cor.test, p.adjust

Examples

data(peppercorr)
multcor.test(peppercorr, n = 20)

# End (not run)

Multivariate Pairwise Comparisons

Description

Performs pairwise comparisons of multivariate mean vectors of factor levels, overall or nested. The tests are run in the same spirt of summary.manova(), based on multivariate statistics such as Pillai's trace and Wilks' lambda, which can be applied to test multivariate contrasts.

Usage

mvpaircomp(model, factor1, nesting.factor = NULL,
   test = "Pillai", adjust = "none", SSPerror = NULL, DFerror = NULL)

## S3 method for class 'mvpaircomp'
print(x, ...)

Arguments

Value

An object of class mvpaircomp, a list of

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Krzanowski, W. J. (1988) Principles of Multivariate Analysis. A User's Perspective. Oxford.

See Also

manova

Examples

# Example 1
data(maize)
M <- lm(cbind(NKPR, ED, CD, PH) ~ family + env, data = maize)
anova(M)  # MANOVA table
mvpaircomp(M, factor1 = "family", adjust = "bonferroni")

# Example 2 (with nesting factor)
# Data on producing plastic film from Krzanowski (1998, p. 381)
tear <- c(6.5, 6.2, 5.8, 6.5, 6.5, 6.9, 7.2, 6.9, 6.1, 6.3,
          6.7, 6.6, 7.2, 7.1, 6.8, 7.1, 7.0, 7.2, 7.5, 7.6)
gloss <- c(9.5, 9.9, 9.6, 9.6, 9.2, 9.1, 10.0, 9.9, 9.5, 9.4,
           9.1, 9.3, 8.3, 8.4, 8.5, 9.2, 8.8, 9.7, 10.1, 9.2)
opacity <- c(4.4, 6.4, 3.0, 4.1, 0.8, 5.7, 2.0, 3.9, 1.9, 5.7,
             2.8, 4.1, 3.8, 1.6, 3.4, 8.4, 5.2, 6.9, 2.7, 1.9)
Y <- cbind(tear, gloss, opacity)
rate     <- gl(2, 10, labels = c("Low", "High"))
additive <- gl(2, 5, length = 20, labels = c("Low", "High"))

fit <- manova(Y ~ rate * additive)
summary(fit, test = "Wilks")  # MANOVA table
mvpaircomp(fit, factor1 = "rate", nesting.factor = "additive", test = "Wilks")
mvpaircomp(fit, factor1 = "additive", nesting.factor = "rate", test = "Wilks")

# End (not run)

Maximum Curvature Point for Optimum Plot Size

Description

The Meier & Lessman (1971) method to determine the maximum curvature point for optimum plot size as a function of the experimental coefficient of variation.

Usage

optimumplotsize(a, b)

Arguments

Value

The (approximated) optimum plot size value.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Meier, V. D. & Lessman, K. J. (1971) Estimation of optimum field plot shape and size for testing yield in Crambe abyssinia Hochst. Crop Sci., 11:648-650.

See Also

fitplotsize

Examples

ps <- c(1, 2, 3, 4, 6, 8, 12)
cv <- c(35.6, 29, 27.1, 25.6, 24.4, 23.3, 21.6)
out <- fitplotsize(plotsize = ps, CV = cv)
plot(cv ~ ps)
curve(coef(out)[1] * x^(-coef(out)[2]), add = TRUE)
optimumplotsize(a = coef(out)[1], b = coef(out)[2])

# End (not run)

Path Analysis, Simple and Under Collinearity

Description

Function to perform the simple path analysis and the path analysis under collinearity (sometimes called ridge path analysis). It computes the direct (diagonal) and indirect (off-diagonal) effects of each explanatory variable over a response one.

Usage

pathanalysis(corMatrix, resp.col, collinearity = FALSE)

Arguments

Value

A list of

Side Effects

If collinearity = TRUE, an interactive graphic is displayed for dealing with collinearity.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Carvalho, S.P. (1995) Metodos alternativos de estimacao de coeficientes de trilha e indices de selecao, sob multicolinearidade. Ph.D. Thesis, Federal University of Vicosa (UFV), Vicosa, MG, Brazil.

Examples

data(peppercorr)
pathanalysis(peppercorr, 6, collinearity = FALSE)

# End (not run)

Correlations Between Pepper Variables

Description

The data give the correlations between 6 pepper variables. The data are taken from the article published by Silva et al. (2013).

Usage

data(peppercorr)

Format

An object of class "matrix".

Source

Silva et al. (2013) Path analysis in multicollinearity for fruit traits of pepper. Idesia, 31:55-60.

Examples

data(peppercorr)
print(peppercorr)

# End (not run)

Raising a Square Matrix to a Power

Description

raise.matrix raises a square matrix to a power by using spectral decomposition.

Usage

raise.matrix(x, power = 1)

Arguments

Value

An object of class "matrix".

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

See Also

eigen, svd

Examples

m <- matrix(c(1, -2, -2, 4), 2, 2)
raise.matrix(m)
raise.matrix(m, 2)

# End (not run)

Spatial Analysis of Gene Diversity

Description

Estimate spatial gene diversity (expected heterozygozity - He) through the individual-centred approach by Manel et al. (2007). sHe() calculates the unbiased estimate of He based on the information of allele frequency obtained from codominant or dominant markers in individuals within a circular moving windows of known radius over the sampling area.

Usage

sHe(x, coord.cols = 1:2, marker.cols = 3:4,
	marker.type = c("codominant", "dominant"),
	grid = NULL, latlong2km = TRUE, radius, nmin = NULL)

Arguments

Details

The unbiased estimate of expected heterogygozity (Nei, 1978) is given by:

He = (1 - \sum_{i=1}^{n} p_{i}^{2}) \frac{2n}{2n - 1}

where p_{i} is the frequency of the i-th allele per locus considering the n individuals in a certain location.

Value

A list of

Warning

Depending on the dimension of x and/or grid, sHe() can be time demanding.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

Ivandilson Pessoa Pinto de Menezes <ivan.menezes@ifgoiano.edu.br>

References

da Silva, A.R.; Malafaia, G.; Menezes, I.P.P. (2017) biotools: an R function to predict spatial gene diversity via an individual-based approach. Genetics and Molecular Research, 16: gmr16029655.

Manel, S., Berthoud, F., Bellemain, E., Gaudeul, M., Luikart, G., Swenson, J.E., Waits, L.P., Taberlet, P.; Intrabiodiv Consortium. (2007) A new individual-based spatial approach for identifying genetic discontinuities in natural populations. Molecular Ecology, 16:2031-2043.

Nei, M. (1978) Estimation of average heterozygozity and genetic distance from a small number of individuals. Genetics, 89: 583-590.

See Also

levelplot

Examples

data(moco)
data(brazil)

# check points
plot(brazil, cex = 0.1, col = "gray")
points(Lat ~ Lon, data = moco, col = "blue", pch = 20)

# using a retangular grid (not passed as input!)
# ex <- sHe(x = moco, coord.cols = 1:2,
#	marker.cols = 3:20, marker.type = "codominant",
#	grid = NULL, radius = 150)
#ex
# plot(ex, xlab = "Lon", ylab = "Lat")

# A FANCIER PLOT...
# using Brazil's coordinates as prediction grid
# ex2 <- sHe(x = moco, coord.cols = 1:2,
#	marker.cols = 3:20, marker.type = "codominant",
#	grid = brazil, radius = 150)
# ex2
#
# library(maps)
# borders <- data.frame(x = map("world", "brazil")$x,
#	y = map("world", "brazil")$y)
#
# library(latticeExtra)
# plot(ex2, xlab = "Lon", ylab = "Lat",
#	xlim = c(-75, -30), ylim = c(-35, 10), aspect = "iso") +
#   latticeExtra::as.layer(xyplot(y ~ x, data = borders, type = "l")) +
#   latticeExtra::as.layer(xyplot(Lat ~ Lon, data = moco))

# End (not run)

Minimum Sample Size

Description

Function to determine the minimum sample size for calculating a statistic based on its the confidence interval.

Usage

samplesize(x, fun, sizes = NULL, lcl = NULL, ucl = NULL,
	nboot = 200, conf.level = 0.95, nrep = 500, graph = TRUE, ...)

Arguments

Details

If ucl or lcl is NULL, fun must be defined as in boot, i.e., the first argument passed will always be the original data and the second will be a vector of indices, frequencies or weights which define the bootstrap sample. By now, samplesize considers the second argument only as index.

Value

A list of

Side Effects

If graph = TRUE, a graphic with the dispersion of the estimates for each sample size, as well as the graphic containing the number of points outside the confidence interval for the reference sample.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

Examples

cv <- function(x, i) sd(x[i]) / mean(x[i]) # coefficient of variation
x = rnorm(20, 15, 2)
cv(x)
samplesize(x, cv)

par(mfrow = c(1, 3), cex = 0.7, las = 1)
samplesize(x, cv, lcl = 0.05, ucl = 0.20)
abline(h = 0.05 * 500, col = "blue") # sample sizes with 5% (or less) out CI

# End (not run)

Importance of Variables According to the Singh (1981) Criterion

Description

A function to calculate the Singh (1981) criterion for importance of variables based on the squared generalized Mahalanobis distance.

S_{.j} = \sum_{i=1}^{n-1} \sum_{i'>i}^{n} (x_{ij} - x_{i'j}) * (\bold{x}_i - \bold{x}_{i'})' * \bold{\Sigma}_{j}^{-1}

Usage

## Default S3 method:
singh(data, cov, inverted = FALSE)
## S3 method for class 'singh'
plot(x, ...)

Arguments

Value

singh returns a matrix containing the Singh statistic, the importance proportion and the cummulative proprtion of each variable (column) in data.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Singh, D. (1981) The relative importance of characters affecting genetic divergence. Indian Journal Genetics & Plant Breeding, 41:237-245.

See Also

D2.dist

Examples

# Manly (2004, p.65-66)
x1 <- c(131.37, 132.37, 134.47, 135.50, 136.17)
x2 <- c(133.60, 132.70, 133.80, 132.30, 130.33)
x3 <- c(99.17, 99.07, 96.03, 94.53, 93.50)
x4 <- c(50.53, 50.23, 50.57, 51.97, 51.37)
x <- cbind(x1, x2, x3, x4)
Cov <- matrix(c(21.112,0.038,0.078,2.01, 0.038,23.486,5.2,2.844,
	0.078,5.2,24.18,1.134, 2.01,2.844,1.134,10.154), 4, 4)
(s <- singh(x, Cov))
plot(s)

# End (not run)

Spatial Predictions Based on the Circular Variable-Radius Moving Window Method

Description

A heuristic method to perform spatial predictions. The method consists of a local interpolator with stochastic features. It allows to build effective detailed maps and to estimate the spatial dependence without any assumptions on the spatial process.

Usage

spatialpred(coords, data, grid)

Arguments

Details

If grid receives the same input as coords, spatialpred will calculate the Percenntual Absolute Mean Error (PAME) of predictions.

Value

A data.frame containing spatial predictions, standard errors, the radius and the number of observations used in each prediction over the grid.

Warning

Depending on the dimension of coords and/or grid, spatialpred() can be time demanding.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Da Silva, A.R., Silva, A.P.A., Tiago-Neto, L.J. (2020) A new local stochastic method for predicting data with spatial heterogeneity. ACTA SCIENTIARUM-AGRONOMY, 43:e49947.

See Also

sHe

Examples

# data(moco)
# p <- spatialpred(coords = moco[, 1:2], data = rnorm(206), grid = moco[, 1:2])
# note: using coords as grid to calculate PAME
# head(p)
# lattice::levelplot(pred ~ Lat*Lon, data = p)

# End (not run)

Tocher's Clustering

Description

tocher performs the Tocher (Rao, 1952) optimization clustering from a distance matrix. The cophenetic distance matrix for a Tocher's clustering can also be computed using the methodology proposed by Silva and Dias (2013).

Usage

## S3 method for class 'dist'
tocher(d, algorithm = c("original", "sequential"))
## S3 method for class 'tocher'
print(x, ...)
## S3 method for class 'tocher'
cophenetic(x)

Arguments

Value

An object of class tocher. A list of

Warning

Clustering a large number of objects (say 300 or more) can be time demanding.

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Cruz, C.D.; Ferreira, F.M.; Pessoni, L.A. (2011) Biometria aplicada ao estudo da diversidade genetica. Visconde do Rio Branco: Suprema.

Rao, R.C. (1952) Advanced statistical methods in biometric research. New York: John Wiley and Sons.

Sharma, J.R. (2006) Statistical and biometrical techniques in plant breeding. Delhi: New Age International.

Silva, A.R.; Dias, C.T.S. (2013) A cophenetic correlation coefficient for Tocher's method. Pesquisa Agropecuaria Brasileira, 48:589-596.

Vasconcelos, E.S.; Cruz, C.D.; Bhering, L.L.; Resende Junior, M.F.R. (2007) Alternative methodology for the cluster analysis. Pesquisa Agropecuaria Brasileira, 42:1421-1428.

See Also

dist, D2.dist, cophenetic, distClust, hclust

Examples

# example 1
data(garlicdist)
(garlic <- tocher(garlicdist))
garlic$distClust  # cluster distances

# example 2
data(USArrests)
(usa <- tocher(dist(USArrests)))
usa$distClust

# cophenetic correlation
cophUS <- cophenetic(usa)
cor(cophUS, dist(USArrests))

# using the sequential algorithm
(usa2 <- tocher(dist(USArrests), algorithm = "sequential"))
usa2$criterion

# example 3
data(eurodist)
(euro <- tocher(eurodist))
euro$distClust

# End (not run)