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.
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)
| 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 |
| 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 |
| angle | direction for computation of a bearing correlogram (angle in degrees between 0 and 180). Default NULL (omnidirectional). |
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.
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.
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.
# 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. # }