eco.malecot: Global and local kinship analysis

In EcoGenetics: Management and Exploratory Analysis of Spatial Data in Landscape Genetics

Description

The program computes, for a kinship matrix, a global multilocus correlogram, or a local analysis. When a kinship matrix is not given as input, the program computes the Loiselle's Fij (Kalisz et al., 2001; Loiselle et al., 1995). The program can compute a bearing correlogram (Rosenberg 2000, Born et al. 2012) for the obtention of a directional approach in the global test.

Usage

eco.malecot(
  eco,
  method = c("global", "local"),
  kinmatrix = NULL,
  int = NULL,
  smin = 0,
  smax = NULL,
  nclass = NULL,
  kmax = NULL,
  seqvec = NULL,
  size = NULL,
  type = c("knearest", "radialdist"),
  cubic = TRUE,
  testclass.b = TRUE,
  testmantel.b = TRUE,
  jackknife = TRUE,
  cummulative = FALSE,
  normLocal = TRUE,
  nsim = 99,
  test = c("permutation", "bootstrap"),
  alternative = c("auto", "two.sided", "greater", "less"),
  sequential = TRUE,
  conditional = c("AUTO", "TRUE", "FALSE"),
  bin = c("sturges", "FD"),
  row.sd = FALSE,
  adjust = "holm",
  latlon = FALSE,
  angle = NULL
)

Arguments

eco	Object of class ecogen.
method	Analysis method: "global" or "local".
kinmatrix	Alternative kinship matrix. The program computes the Loiselle's kinship matrix (codominant data) with the genetic information of the ecogen object if kinmatrix = NULL (Defaul option).
int	Distance interval in the units of XY.
smin	Minimum class distance in the units of XY.
smax	Maximum class distance in the units of XY.
nclass	Number of classes.
kmax	Number of nearest-neighbors for local analysis.
seqvec	Vector with breaks in the units of XY.
size	Number of individuals per class.
type	Weighting mode for local analysis: "knearest" for nearest neigbors, "radialdist" for radial distances. Default is knearest.
cubic	Should a cubic interpolation (res~ ln(dij)) be performed, for the regression residuals (res) of (kinship)ij ~ ln(dij) ? Default TRUE.
testclass.b	Carry a permutation test within each individual class? Default TRUE.
testmantel.b	Should a Mantel test for testing the slope (b) be performed? Default TRUE.
jackknife	Compute jackknife within each individual class for obtention of the standard deviation (SD) of the coancestry (class) values. Default TRUE.
cummulative	Should a cummulative correlogram be construced?.
normLocal	Normalize the local kinship values ([local_kinship-mean]/sd)? Default TRUE
nsim	Number of Monte-Carlo simulations.
test	If test = "bootstrap", the program generates a bootstrap resampling and the associated confidence intervals of the null hypothesis. If test = "permutation" (default) a permutation test is made and the P-values are computed.
alternative	The alternative hypothesis. If "auto" is selected (default) the program determines the alternative hypothesis. Other options are: "two.sided", "greater" and "less".
sequential	Use the Holm-Bonberroni sequential method for adjustment of P-values (Legendre and Legendre, 2012) in global analysis? Default TRUE.
conditional	Logical. Use a conditional randomization? (Anselin 1998, Sokal and Thomson 2006). The option "auto" sets conditional = TRUE for LISA methods and G, as suggested by Sokal (2008).
bin	Rule for constructing intervals when a partition parameter (int, nclass or size) is not given. Default is Sturge's rule (Sturges, 1926). Other option is Freedman-Diaconis method (Freedman and Diaconis, 1981).
row.sd	Logical. Should be row standardized the matrix? Default FALSE (binary weights).
adjust	P-values correction method for multiple tests passed to p.adjust. Default is "holm".
latlon	Are the coordinates in decimal degrees format? Default FALSE. If TRUE, the coordinates must be in a matrix/data frame with the longitude in the first column and latitude in the second. The position is projected onto a plane in meters with the function geoXY.
angle	direction for computation of a bearing correlogram (angle in degrees between 0 and 180). Default NULL (omnidirectional).

Details

The GLOBAL ANALYSIS mode, computes a multilocus correlogram, with a detailed summary (see the content of the slot OUT in the "return" section). It also computes (see details about the slot SP in the "return" section): - the slope of the kinship individual values vs the logarithm of the distance, (kinship)ij ~ ln(dij), with a jackknife confidence interval - a Mantel test for testing the association between (kinship)ij and ln(dij) - The Sp statistic (Vekemans and Hardy, 2004) with confidence intervals - A cubic interpolation of (kinship)ij ~ ln(dij) residuals vs ln(dij)

A directional approach is based on the bearing analysis method, and consists in the obtention of a directional correlogram using the method of Rosenberg (2000). A slope is computed for the logarithm of D' (Born et al 2012), where D' is the distance matrix between individuals weighted by cos(alpha - B)^2, being alpha the angle between individuals and B the desired direction angle. With B = 0 the direcction analyzed follows the positive x axis, with B = 0 the positive y axis, and with B = 180 the negative x axis, respectively.

The LOCAL ANALYSIS mode, computes a local kinship estimate, based in a weighted mean (for each individual). The significance of each local statistic is computed using a permutation test, as in eco.lsa (see ?"eco.lsa"). Default option do not adjust the individual P values for multiple comparisons.

Value

For the global analysis, the program returns an object of class "eco.IBD" with the following slots:

> OUT analysis output.

In the permutation test case contains: - d.mean: mean class distance; - d.log: mean logarithm of the class distance; - obs, exp, alter, p.val: observed, and expected value of the statistic under randomization, alternative, P value; - mean.jack, sd.jack, Jack.CI.inf, Jack.CI.sup: jackknifed mean and SD, and confidence intervals for the statistic; - null.lwr, nul.uppr: lower and upper bound of the jackknife confidence interval for the statistic; - cardinal: number of individuals in each class;

In the bootstrap test case contains: - d.mean: mean class distance; - d.log: mean logarithm of the class distance; - obs: observed value of the statistic; - mean.jack, sd.jack, Jack.CI.inf, Jack.CI.sup: jackknifed mean and SD, and confidence intervals for the statistic; - null.lwr, nul.uppr: lower and upper bound of the jackknife confidence interval for the statistic; - cardinal: number of individuals in each class;

> GLOBALTEST Oden's (1984) global test of significance for the correlogram. The test consists in checking if the most significant kinship coefficent is significant at a Bonferroni- corrected significance level of alpha' = alpha/k, where k is the number of distance classes of the correlogram; alpha is set to 0.05. The program return the values: "SIGNIFICANT" or "NOT-SIGNIFICANT"

> IN analysis input data

> SP Sp statistic results

It contains:

- the regression model; - information about the distance interval used for the regression (restricted); - slope (bhat) information (bhat = estimate, SD= bhat jacknife SD, theta = bhat jackknife mean, CI 5% and 95% = 95% confidence interval for bhat); - X-intercept = dij intercept (in the original units) for the line with slope "bhat", F1 = first class statistic value, and F1 5% and 95% = confidence interval for the first class statistic; - mantel.obs.b = observed value of the Mantel test between kinship(Fij) and ln(dij); mantel.pval.b = Mantel test P value; - sp = Sp statistics (sp = Sp observed value, CI 5% and 95% = 95% confidence interval for Sp); - cubic_model = cubic model for (kinship)ij ~ ln(dij) r esiduals vs ln(dij);

> BEAKS breaks

> CARDINAL number of elements in each class

> NAMES variables names

> METHOD analysis method

> DISTMETHOD method used in the construction of breaks

> TEST test method used (bootstrap, permutation)

> NSIM number of simulations

> PADJUST P-values adjust method for permutation tests

——

For the local analysis, the program returns an object of class "eco.lsa" with the following slots:

> OUT results

> In the permutation test case it contains:

- d.mean: mean class distance - obs, exp, alter, p.val: observed, and expected value of the statistic under randomization, alternative, P value; - null.lwr, nul.uppr: lower and upper bound of the jackknife confidence interval for the statistic; - cardinal: number of individuals in each class;

> In the bootstrap test case it contains: - d.mean: mean class distance; - obs: observed value of the statistic; - null.lwr, nul.uppr: lower and upper bound of the jackknife; confidence interval for the statistic; - cardinal: number of individuals in each class;

> METHOD method (coefficent) used in the analysis

> TEST test method used (bootstrap, permutation)

> NSIM number of simulations

> PADJUST P-values adjust method for permutation tests

> COND conditional randomization (logical)

> XY input coordinates

ACCESS TO THE SLOTS The content of the slots can be accessed with the corresponding accessors, using the generic notation of EcoGenetics (<ecoslot.> + <name of the slot> + <name of the object>). See help("EcoGenetics accessors") and the Examples section below.

Author(s)

Leandro Roser [e-mail]

References

Born C., P. le Roux, C. Spohr, M. McGeoch, B. Van Vuuren. 2012. Plant dispersal in the sub-Antarctic inferred from anisotropic genetic structure. Molecular Ecology 21: 184-194.

Double M., R. Peakall, N. Beck, and Y. Cockburn. 2005. Dispersal, philopatry, and infidelity: dissecting local genetic structure in superb fairy-wrens (Malurs cyaneus). Evolution 59: 625-635.

Kalisz S., J. Nason, F.M. Handazawa, and S. Tonsor. 2001. Spatial population genetic structure in Trillium grandiflorum: the roles of dispersal, mating, history, and selection. Evolution 55: 1560-1568.

Loiselle B., V. Sork, J. Nason, and C. Graham. 1995. Spatial genetic structure of a tropical understory shrub, Psychotria officinalis (Rubiaceae). American Journal of Botany 1420-1425.

Oden, N., 1984. Assessing the significance of a spatial correlogram. Geographical Analysis, 16: 1-16.

Rosenberg, M. 2000. The bearing correlogram: a new method of analyzing directional spatial autocorrelation. Geographical Analysis, 32: 267-278.

Vekemans, X., and O. Hardy. 2004. New insights from fine-scale spatial genetic structure analyses in plant populations. Molecular Ecology, 13: 921-935.

Examples

## Not run: 

data(eco.test)

# ---global analysis---

globaltest <- eco.malecot(eco=eco, method = "global", smax=10,
                         size=1000)
eco.plotCorrelog(globaltest)    # Significant mean class coancestry classes at   
                    # individual level (alpha = 0.05, 
                    # out of the red area), 
                    # and family-wise P corrected values (red-blue
                    # points, indicated in the legend)

# ecoslot.SP(globaltest) contains:
# - the slope (bhat) and values with confidence intervals
#  of the regression reg = kinship ~ ln(distance_between_individuals)
#- A Mantel test result for assesing the relation between
#  between  kinship and ln(distance_between_individuals)
#- A cubic interpolation between the residuals of reg and 
#  ln(distance_between_individuals)
#- the sp statistic and its confidence interval

# ecoslot.OUT(globaltest) contains:
# - In permutation case, the values of mean and log-mean distance    
#   classes; observed class value; expected + alternative + P value,
#   the bootstrap null confidence intervals and 
#   jackknife statistics (jackknifed mean, jackknifed SD, and
#                         CI for the class statistic)

# - In bootstrap case, the values of mean and log-mean distance
#   classes;the bootstrap null confidence intervals and 
#   jackknife statistics (jackknifed mean, jackknifed SD, and
#                         CI for the class statistic)


# A directional approach based in bearing correlograms, 30 degrees
globaltest_30 <- eco.malecot(eco=eco, method = "global", smax=10,
                         size=1000, angle = 30)
eco.plotCorrelog(globaltest) 

#----------------------------------------------------------#
# ---local analysis---


# (using the spatial weights). 

# ---local analysis with k nearest neighbors---



localktest <- eco.malecot(eco=eco, method = "local",
                         type = "knearest", kmax = 5, 
                         adjust = "none")
eco.plotLocal(localktest)


# ---local analysis with radial distance---

localdtest <- eco.malecot(eco=eco, method = "local",
                        type = "radialdist", smax = 3, 
                        adjust = "none")
                        
eco.plotLocal(localdtest)                    # rankplot graphic (see ?"eco.rankplot")

                                         # Significant values
                                         # in blue-red scale, 
                                         # non significant 
                                         # values in yellow

eco.plotLocal(localktest, significant = FALSE)    # significant and non
                                              # signficant values
                                              # in blue-red scale

# The slot OUT of localktest (ecoslot.OUT(localktest)) and localdtest 
# (ecoslot.OUT(localdtest)) contains:
# - the mean distance per individual, observed value of the
#   statistic, expected + alternative + P value + null hypotesis
#   confidence intervals,  or boostrap confidence intervals in 
#   permutation or bootstrap cases, respectively.

## End(Not run)

EcoGenetics documentation built on July 8, 2020, 5:46 p.m.