diff --git a/NAMESPACE b/NAMESPACE
index b7c922be..2ded31bd 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -232,7 +232,7 @@ export("originality")
 export("haar2level", "mld", "orthobasis.circ", "orthobasis.haar", "orthobasis.line", "orthobasis.mat", "orthobasis.neig", "is.orthobasis")
 
 ## ******* spatial *******
-export("area2link", "area2poly", "area.plot", "dist.neig", "gridrowcol", "multispati.randtest", "mstree", "multispati.rtest", "nb2neig", "neig", "neig2mat", "neig2nb", "poly2area", "scores.neig")
+export("area2link", "area2poly", "area.plot", "dist.neig", "gridrowcol", "mstree", "nb2neig", "neig", "neig2mat", "neig2nb", "poly2area", "scores.neig")
 
 ## ******* misc *********
 export("bwca.dpcoa")
@@ -276,6 +276,8 @@ export("testertracenubisCpp")
 ## "plot.multispati"
 ## "print.multispati"
 ## "plot.multispati"
+## "multispati.randtest"
+## "multispati.rtest"
 
 ## ******* internal utilities *******
 
diff --git a/R/ade4-deprecated.R b/R/ade4-deprecated.R
index c44a6ec3..16aff3f2 100644
--- a/R/ade4-deprecated.R
+++ b/R/ade4-deprecated.R
@@ -1199,3 +1199,81 @@
     s.match(x$li, x$ls, xax = xax, yax = yax, sub = "Scores and lag scores", csub = 2, clabel = 0.75) 
     
 }
+
+"multispati.randtest" <- function (dudi, listw, nrepet = 999, ...) {
+    
+    .Deprecated(new="multispati.randtest", package="ade4", 
+                msg="The 'multispati.randtest' function is now deprecated in 'ade4' and will soon be available in the 'adespatial' package.")
+    
+    if(!inherits(dudi,"dudi")) stop ("object of class 'dudi' expected") 
+    if(!inherits(listw,"listw")) stop ("object of class 'listw' expected") 
+    if(listw$style!="W") stop ("object of class 'listw' with style 'W' expected") 
+    
+    "testmultispati"<- function(nrepet, nr, nc, tab, mat, lw, cw) {
+        .C("testmultispati", 
+           as.integer(nrepet),
+           as.integer(nr),
+           as.integer(nc),
+           as.double(as.matrix(tab)),
+           as.double(mat),
+           as.double(lw),
+           as.double(cw),
+           inersim=double(nrepet+1),
+           PACKAGE="ade4")$inersim
+    }
+    
+    tab<- dudi$tab
+    nr<-nrow(tab)
+    nc<-ncol(tab)
+    mat<-spdep::listw2mat(listw)
+    lw<- dudi$lw
+    cw<- dudi$cw
+    if (!(identical(all.equal(lw,rep(1/nrow(tab), nrow(tab))),TRUE))) {
+        stop ("Not implemented for non-uniform weights")
+    }
+    inersim<- testmultispati(nrepet, nr, nc, tab, mat, lw, cw)
+    inertot<- sum(dudi$eig)
+    inersim<- inersim/inertot
+    obs <- inersim[1]
+    w <- as.randtest(sim = inersim[-1], obs = obs, call = match.call(), ...)
+    return(w)
+}
+
+"multispati.rtest" <- function (dudi, listw, nrepet = 99, ...) {
+    
+    .Deprecated(new="multispati.rtest", package="ade4", 
+                msg="The 'multispati.rtest' function is now deprecated in 'ade4' and will soon be available in the 'adespatial' package.")
+    
+    if(!inherits(listw,"listw")) stop ("object of class 'listw' expected") 
+    if(listw$style!="W") stop ("object of class 'listw' with style 'W' expected") 
+    if (!(identical(all.equal(dudi$lw,rep(1/nrow(dudi$tab), nrow(dudi$tab))),TRUE))) {
+        stop ("Not implemented for non-uniform weights")
+    }
+    
+    n <- length(listw$weights)
+    fun.lag <- function (x) spdep::lag.listw(listw,x,TRUE)
+    fun <- function (permuter = TRUE) {
+        if (permuter) {
+            permutation <- sample(n)
+            y <- dudi$tab[permutation,]
+            yw <- dudi$lw[permutation]
+        } else {
+            y <-dudi$tab
+            yw <- dudi$lw
+        }
+        y <- as.matrix(y)
+        ymoy <- apply(y, 2, fun.lag)
+        ymoy <- ymoy*yw
+        y <- y*ymoy
+        indexmoran <- sum(apply(y,2,sum)*dudi$cw)
+        return(indexmoran)
+    }
+    inertot <- sum(dudi$eig)
+    obs <- fun (permuter = FALSE)/inertot
+    if (nrepet == 0) return(obs)
+    perm <- unlist(lapply(1:nrepet, fun))/inertot
+    w <- as.randtest(obs = obs, sim = perm, call = match.call(), ...)
+    return(w)
+}
+
+
diff --git a/R/multispati.randtest.R b/R/multispati.randtest.R
deleted file mode 100644
index be4ff2ec..00000000
--- a/R/multispati.randtest.R
+++ /dev/null
@@ -1,39 +0,0 @@
-"multispati.randtest" <- function (dudi, listw, nrepet = 999, ...) {
-    
-    .Deprecated(new="multispati.randtest", package="ade4", 
-                msg="The 'multispati.randtest' function is now deprecated in 'ade4' and will soon be available in the 'adespatial' package.")
-    
-    if(!inherits(dudi,"dudi")) stop ("object of class 'dudi' expected") 
-    if(!inherits(listw,"listw")) stop ("object of class 'listw' expected") 
-    if(listw$style!="W") stop ("object of class 'listw' with style 'W' expected") 
-    
-    "testmultispati"<- function(nrepet, nr, nc, tab, mat, lw, cw) {
-        .C("testmultispati", 
-            as.integer(nrepet),
-            as.integer(nr),
-            as.integer(nc),
-            as.double(as.matrix(tab)),
-            as.double(mat),
-            as.double(lw),
-            as.double(cw),
-            inersim=double(nrepet+1),
-            PACKAGE="ade4")$inersim
-    }
- 
-    tab<- dudi$tab
-    nr<-nrow(tab)
-    nc<-ncol(tab)
-    mat<-spdep::listw2mat(listw)
-    lw<- dudi$lw
-    cw<- dudi$cw
-    if (!(identical(all.equal(lw,rep(1/nrow(tab), nrow(tab))),TRUE))) {
-    	stop ("Not implemented for non-uniform weights")
-    }
-    inersim<- testmultispati(nrepet, nr, nc, tab, mat, lw, cw)
-    inertot<- sum(dudi$eig)
-    inersim<- inersim/inertot
-    obs <- inersim[1]
-    w <- as.randtest(sim = inersim[-1], obs = obs, call = match.call(), ...)
-    return(w)
-}
-
diff --git a/R/multispati.rtest.R b/R/multispati.rtest.R
deleted file mode 100644
index bb55288b..00000000
--- a/R/multispati.rtest.R
+++ /dev/null
@@ -1,38 +0,0 @@
-"multispati.rtest" <- function (dudi, listw, nrepet = 99, ...) {
-    
-    .Deprecated(new="multispati.rtest", package="ade4", 
-                msg="The 'multispati.rtest' function is now deprecated in 'ade4' and will soon be available in the 'adespatial' package.")
-    
-    if(!inherits(listw,"listw")) stop ("object of class 'listw' expected") 
-    if(listw$style!="W") stop ("object of class 'listw' with style 'W' expected") 
-    if (!(identical(all.equal(dudi$lw,rep(1/nrow(dudi$tab), nrow(dudi$tab))),TRUE))) {
-    	stop ("Not implemented for non-uniform weights")
-    }
-    
-    n <- length(listw$weights)
-    fun.lag <- function (x) spdep::lag.listw(listw,x,TRUE)
-    fun <- function (permuter = TRUE) {
-        if (permuter) {
-            permutation <- sample(n)
-            y <- dudi$tab[permutation,]
-            yw <- dudi$lw[permutation]
-        } else {
-            y <-dudi$tab
-            yw <- dudi$lw
-        }
-        y <- as.matrix(y)
-        ymoy <- apply(y, 2, fun.lag)
-        ymoy <- ymoy*yw
-        y <- y*ymoy
-        indexmoran <- sum(apply(y,2,sum)*dudi$cw)
-        return(indexmoran)
-    }
-    inertot <- sum(dudi$eig)
-    obs <- fun (permuter = FALSE)/inertot
-    if (nrepet == 0) return(obs)
-    perm <- unlist(lapply(1:nrepet, fun))/inertot
-    w <- as.randtest(obs = obs, sim = perm, call = match.call(), ...)
-    return(w)
-}
-
-
diff --git a/_pkgdown.yml b/_pkgdown.yml
index c0e2470c..6a339811 100644
--- a/_pkgdown.yml
+++ b/_pkgdown.yml
@@ -334,8 +334,6 @@ reference:
   - orthobasis.line
   - orthobasis.mat
   - orthobasis.neig
-  - multispati.randtest
-  - multispati.rtest
   - nb2neig
   - neig
   - neig2mat
diff --git a/man/ade4-deprecated.Rd b/man/ade4-deprecated.Rd
index 4c42b99d..13ad920f 100644
--- a/man/ade4-deprecated.Rd
+++ b/man/ade4-deprecated.Rd
@@ -15,6 +15,8 @@
   - \code{freq2genet}: replaced by \code{df2genind} and \code{genind2genpop} in the \code{adegenet} package \cr
   - \code{fuzzygenet}: replaced by \code{df2genind} in the \code{adegenet} package \cr
   - \code{multispati}: replaced by \code{multispati} in the \code{adespatial} package \cr
+  - \code{multispati.rtest} \cr
+  - \code{multispati.randtest} \cr
   - \code{optimEH}: replaced by \code{optimEH} in the \code{adiv} package \cr
   - \code{orisaved}: replaced by \code{orisaved} in the \code{adiv} package \cr
   - \code{orthogram}: replaced by \code{orthogram} in the \code{adephylo} package \cr
diff --git a/man/multispati.randtest.Rd b/man/multispati.randtest.Rd
deleted file mode 100644
index ded74306..00000000
--- a/man/multispati.randtest.Rd
+++ /dev/null
@@ -1,47 +0,0 @@
-\name{multispati.randtest}
-\alias{multispati.randtest}
-\title{Multivariate spatial autocorrelation test (in C)}
-\description{
-This function is now deprecated in 'ade4' and will soon be available in the 'adespatial' package.
-This function performs a multivariate autocorrelation test.
-}
-\usage{
-multispati.randtest(dudi, listw, nrepet = 999, ...)
-}
-\arguments{
-  \item{dudi}{an object of class \code{dudi} for the duality diagram analysis}
-  \item{listw}{an object of class \code{listw} for the spatial dependence of data observations}
-  \item{nrepet}{the number of permutations}
-  \item{\dots}{further arguments passed to or from other methods}
-}
-\details{
-We note X the data frame with the variables, Q the column weights matrix 
-and D the row weights matrix associated to the duality diagram \emph{dudi}.
-We note L the neighbouring weights matrix associated to  \emph{listw}.
-This function performs a Monte-Carlo Test on the multivariate spatial 
-autocorrelation index : \deqn{r = \frac{trace(X^{t}DLXQ)}{trace(X^{t}DXQ)}}{r = trace(t(X)DLXQ) / trace(t(X)DXQ)}
-}
-\value{
-Returns an object of class \code{randtest} (randomization tests).
-}
-\references{
-Smouse, P. E. and Peakall, R. (1999) Spatial autocorrelation analysis of individual multiallele and multilocus genetic structure. 
-\emph{Heredity}, \bold{82}, 561--573.
-}
-\author{Daniel Chessel  \cr
-Sébastien Ollier \email{sebastien.ollier@u-psud.fr}
-}
-\seealso{\code{\link{dudi}},\code{\link[spdep]{mat2listw}}}
-\examples{
-if (requireNamespace("spdep", quietly = TRUE) & requireNamespace("adespatial", quietly = TRUE)) {
-    data(mafragh)
-    maf.listw <- spdep::nb2listw(mafragh$nb)
-    maf.pca <- dudi.pca(mafragh$env, scannf = FALSE)
-    multispati.randtest(maf.pca, maf.listw)
-    maf.pca.ms <- adespatial::multispati(maf.pca, maf.listw, scannf = FALSE)
-    plot(maf.pca.ms)
-}
-}
-\keyword{multivariate}
-\keyword{spatial}
-\keyword{nonparametric}
diff --git a/man/multispati.rtest.Rd b/man/multispati.rtest.Rd
deleted file mode 100644
index 26bea56f..00000000
--- a/man/multispati.rtest.Rd
+++ /dev/null
@@ -1,47 +0,0 @@
-\name{multispati.rtest}
-\alias{multispati.rtest}
-\title{Multivariate spatial autocorrelation test}
-\description{
-This function is now deprecated in 'ade4' and will soon be available in the 'adespatial' package.
-This function performs a multivariate autocorrelation test.
-}
-\usage{
-multispati.rtest(dudi, listw, nrepet = 99, ...)
-}
-\arguments{
-  \item{dudi}{an object of class \code{dudi} for the duality diagram analysis}
-  \item{listw}{an object of class \code{listw} for the spatial dependence of data observations}
-  \item{nrepet}{the number of permutations}
-  \item{\dots}{further arguments passed to or from other methods}
-}
-\details{
-We note X the data frame with the variables, Q the column weight matrix 
-and D the row weight matrix associated to the duality diagram \emph{dudi}.
-We note L the neighbouring weights matrix associated to  \emph{listw}.
-This function performs a Monte-Carlo Test on the multivariate spatial 
-autocorrelation index : \deqn{r = \frac{X^{t}DLXQ}{X^{t}DXQ}}{r = t(X)DLXQ / t(X)DXQ}
-}
-\value{
-Returns an object of class \code{randtest} (randomization tests).
-}
-\references{
-Smouse, P. E. and Peakall, R. (1999) Spatial autocorrelation analysis of individual multiallele and multilocus genetic structure. 
-\emph{Heredity}, \bold{82}, 561--573.
-}
-\author{Daniel Chessel  \cr
-Sébastien Ollier \email{sebastien.ollier@u-psud.fr}
-}
-\seealso{\code{\link{dudi}},\code{\link[spdep]{mat2listw}}}
-\examples{
-if (requireNamespace("spdep", quietly = TRUE) & requireNamespace("adespatial", quietly = TRUE)) {
-    data(mafragh)
-    maf.listw <- spdep::nb2listw(mafragh$nb)
-    maf.pca <- dudi.pca(mafragh$env, scannf = FALSE)
-    multispati.rtest(maf.pca, maf.listw)
-    maf.pca.ms <- adespatial::multispati(maf.pca, maf.listw, scannf = FALSE)
-    plot(maf.pca.ms)
-}
-}
-\keyword{multivariate}
-\keyword{spatial}
-\keyword{nonparametric}