===== Torus =====

Função torus de K. Harms, com pequenas modificações de Ale dez de 2008

<box blue 100%>>

torusonesp=function(species,habitat,allabund,plotdim=c(320,320),gridsize=20)
 {
  plotdimqx=plotdim[1]/gridsize  # Calculates no. of x-axis quadrats of plot.
  plotdimqy=plotdim[2]/gridsize  # Calculates no. of y-axis quadrats of plot.
  hab=unique(habitat)
  num.habs=length(hab)   # Determines tot. no. of habitat types.
  habmat=matrix(habitat,plotdimqy,plotdimqx,byrow=F)
  GrLsEq=matrix(0,1,num.habs*4)       # Creates empty matrix for output.
  rownames(GrLsEq)=species       # Names single row of output matrix.
  for(i in 1:num.habs)           # Creates names for columns of output matrix.
   {
    if(i==1)
      cols=c(paste("N.Hab.",hab[i],sep=""), paste("Gr.Hab.",hab[i],sep=""), paste("Ls.Hab.",hab[i],sep=""), paste("Eq.Hab.",hab[i],sep=""))
    if(i>1)
      cols=c(cols, paste("N.Hab.",hab[i],sep=""), paste("Gr.Hab.",hab[i],sep=""), paste("Ls.Hab.",hab[i],sep=""), paste("Eq.Hab.",hab[i],sep=""))  
   }
  colnames(GrLsEq)=cols    # Names columns of output matrix.
  ## CALCULATIONS  FOR OBSERVED RELATIVE DENSITIES ON THE TRUE HABITAT MAP
    spmat=matrix(allabund[species,],plotdimqy,plotdimqx,byrow=F)  # Fills a matrix, with no. rows = plotdimqy and no. columns = plotdimqx, with the indiv. counts per quadrat of one species.
    tot=numeric()             # Creates empty vector for tot. no. stems per quadrat.
    len=length(allabund[1,])  # Determines the tot. no. of quadrats.
  ###SERÁ QUE PRECISA TUDO ISSO!! 
  ###for(i in 1:len)           # Determines the tot. no. of stems, of all spp., in each quadrat.
  ##    {
  ###     tot[i]=sum(allabund[,i]) 
  ##    }
	tot=apply(allabund,2,sum)  ## assim fica melhor, sem looping (ale dez 2008)
	totmat=matrix(tot[],plotdimqy,plotdimqx,byrow=F)  # Converts "tot" to a matrix, with no. rows = plotdimqy and no. columns = plotdimqx. 
    spstcnthab=numeric()   # Creates empty vector for stem counts per sp. per habitat.
    totstcnthab=numeric()  # Creates empty vector for tot. stem counts per habitat.
    for(i in 1:num.habs)  
     {
      totstcnthab[i]=sum(totmat[habmat==unique(habitat)[i]])  # Determines tot. no. stems per habitat of the true map.
      spstcnthab[i]=sum(spmat[habmat==unique(habitat)[i]])    # Determines tot. no. stems for focal sp. per habitat of the true map.     
     }
    spprophab=spstcnthab/totstcnthab         # Calculates observed relative stem density of focal sp. per habitat of the true map.
 # CALCULATIONS FOR RELATIVE DENSITIES ON THE TORUS-BASED HABITAT MAPS
     for(x in 0:(plotdimqx-1))    # Opens "for loop" through all 20-m translations along x-axis.
      { 
      for(y in 0:(plotdimqy-1))  # Opens "for loop" through all 20-m translations along y-axis.
       { 
        newhab=matrix(0,plotdimqy,plotdimqx)  # Creates empty matrix of quadrats' habitat designations.
        # The following "if" statements create the x,y torus-translation of the habitat map.
        if(y==0 & x==0)          
           newhab=habmat
        if(y==0 & x>0)
           newhab=habmat[c(1:plotdimqy),c((plotdimqx-x+1):plotdimqx,1:(plotdimqx-x))] 
        if(x==0 & y>0)
           newhab=habmat[c((plotdimqy-y+1):plotdimqy,1:(plotdimqy-y)),c(1:plotdimqx)]
       if(x>0 & y>0)
            newhab=habmat[c((plotdimqy-y+1):plotdimqy,1:(plotdimqy-y)),c((plotdimqx-x+1):plotdimqx,1:(plotdimqx-x))] 
        Torspstcnthab=numeric()   # Creates empty vector for stem counts per sp. per habitat in torus-based maps.
        Tortotstcnthab=numeric()  # Creates empty vector for tot. stem counts per habitat in torus-based maps.
        for(i in 1:num.habs)
         {
          Tortotstcnthab[i]=sum(totmat[newhab==unique(habitat)[i]])  # Determines tot. no. stems per habitat of the focal torus-based map.
          Torspstcnthab[i]=sum(spmat[newhab==unique(habitat)[i]])    # Determines tot. no. stems for focal sp. per habitat of the focal torus-based map.
         }
        Torspprophab=Torspstcnthab/Tortotstcnthab   # Calculates relative stem density of focal sp. per habitat of the focal torus-based map.  
        for(i in 1:num.habs)
         {
          if(spprophab[i]>Torspprophab[i])          # If rel. dens. of focal sp. in focal habitat of true map is greater than rel. dens. of focal sp. in focal habitat of torus-based map, then add one to "greater than" count.        
            GrLsEq[1,(4*i)-2]=GrLsEq[1,(4*i)-2]+1  
          if(spprophab[i]<Torspprophab[i])          # If rel. dens. of focal sp. in focal habitat of true map is less than rel. dens. of focal sp. in focal habitat of torus-based map, then add one to "less than" count. 
            GrLsEq[1,(4*i)-1]=GrLsEq[1,(4*i)-1]+1 
          if(spprophab[i]==Torspprophab[i])         # If rel. dens. of focal sp. in focal habitat of true map is equal to rel. dens. of focal sp. in focal habitat of torus-based map, then add one to "equal to" count.
            GrLsEq[1,4*i]=GrLsEq[1,4*i]+1 
          }
       }    # Closes "for loop" through all 20-m translations along x-axis.
     }      # Closes "for loop" through all 20-m translations along y-axis.
    for(i in 1:num.habs)
     {
      GrLsEq[1,(4*i)-3]=spstcnthab[i]
     } 
   return(GrLsEq)
  }
  

 </box>

 
 ** essa função foi usada em dez de 2008 para os resultados a seguir **
 
> torusonesp("Calobr", solo$soil,allspp)->res
> res

         N.Hab.neo Gr.Hab.neo Ls.Hab.neo Eq.Hab.neo N.Hab.trans Gr.Hab.trans
  Calobr       135        244         11          1          43           22
         Ls.Hab.trans Eq.Hab.trans N.Hab.esp.aren Gr.Hab.esp.aren Ls.Hab.esp.aren
  Calobr          233            1            226              58             197
         Eq.Hab.esp.aren N.Hab.esp.hist Gr.Hab.esp.hist Ls.Hab.esp.hist
  Calobr               1             25             116             139
         Eq.Hab.esp.hist
  Calobr               1

Interpretação: 
  - N.Hab.neo: primeira coluna, no. de Calophyllum no habitat Neossolo = 135 indivíduos
  - Gr.Hab.neo: número de simulações onde a densidade relativa observada de Calophyllum no habitat neossolo foi maior que as simulações (Ls.Hab.neo = menor, Eq.Hab neo= igual)...



 ** Para calcular a significancia deve dividir pelo no. de simulações torus (256), note que o número de indivíduos observados nos habitats ficará sem sentido (N.Hab.*)! **

 
> res/256

 
<box blue 100% >
        N.Hab.neo Gr.Hab.neo Ls.Hab.neo Eq.Hab.neo N.Hab.trans Gr.Hab.trans
  Calobr 0.5273438   0.953125 0.04296875 0.00390625   0.1679688    0.0859375
           Ls.Hab.trans Eq.Hab.trans N.Hab.esp.aren Gr.Hab.esp.aren Ls.Hab.esp.aren
  Calobr    0.9101562   0.00390625      0.8828125       0.2265625       0.7695312
         Eq.Hab.esp.aren N.Hab.esp.hist Gr.Hab.esp.hist Ls.Hab.esp.hist
  Calobr      0.00390625     0.09765625        0.453125       0.5429688
         Eq.Hab.esp.hist
  Calobr      0.00390625
</box>


Interpretação: 

  - Gr.Hab.neo = 0.953, significa que o valor observado de densidade relativa do Calophyllum no habitat neossolo
  é em mais de 95% das vezes maior do que a simulação torus! Ou seja sua associação a esse habitat é significativamente positiva


  
**densidade de Calophyllum observada**

> tapply(calo, habitat,sum)

  esp.aren esp.hist      neo    trans 
       226       25      135       43 

** porcentagem relativa de Calophullum por habitat**

> tapply(calo, habitat,sum)/sum(calo)

    esp.aren   esp.hist        neo      trans 
  0.52680653 0.05827506 0.31468531 0.10023310 

   

**densidade de todas as espécies por tipo de solo**

> apply(allspp,2,sum)->totalparc
> tapply(totalparc, habitat,sum)

  esp.aren esp.hist      neo    trans 
     10409     1128     4608     2345
	 
	 
** densidade relativa de Calophyllum por habitat**


> tapply(calo, habitat,sum)/tapply(totalparc, habitat,sum)

    esp.aren   esp.hist        neo      trans 
  0.02171198 0.02216312 0.02929688 0.01833689 

*** a densidade relativa de Calophyllum  média é de 2,3 % dos indivíduos, mas no Neossolo é quase 3% dos indivíduos**

** ou seja a densidade relativa de Calophyllum é cerca de 30% maior no neossolo em comparacão com a sua média em todos os habitats** 



** Vamos ver com o K. Harms  e Valencia et al. apresentaram os resultados deles, para tirar alguma idéia de como apresentá-los **
 

===== Torus 2 =====

Modifiquei a função para fazer dois ciclos de simulação, o primeiro iniciando com a configuração original do habitat e o segundo com o habitat original transposto (mantem a estrutura espacial, mas invertido)

**Nova Função**

<box blue 100% >

torusonesp=function(species,habitat,allabund,plotdim=c(320,320),gridsize=20)
 {
  contar=0
  plotdimqx=plotdim[1]/gridsize  # Calculates no. of x-axis quadrats of plot.
  plotdimqy=plotdim[2]/gridsize  # Calculates no. of y-axis quadrats of plot.
  hab=unique(habitat)
  num.habs=length(hab)   # Determines tot. no. of habitat types.
  habmat=matrix(habitat,plotdimqy,plotdimqx,byrow=F)
  GrLsEq=matrix(0,1,num.habs*4)       # Creates empty matrix for output.
  rownames(GrLsEq)=species       # Names single row of output matrix.
  for(i in 1:num.habs)           # Creates names for columns of output matrix.
   {
    if(i==1)
      cols=c(paste("N.Hab.",hab[i],sep=""), paste("Gr.Hab.",hab[i],sep=""), paste("Ls.Hab.",hab[i],sep=""), paste("Eq.Hab.",hab[i],sep=""))
    if(i>1)
      cols=c(cols, paste("N.Hab.",hab[i],sep=""), paste("Gr.Hab.",hab[i],sep=""), paste("Ls.Hab.",hab[i],sep=""), paste("Eq.Hab.",hab[i],sep=""))  
   }
  colnames(GrLsEq)=cols    # Names columns of output matrix.
   # CALCULATIONS FOR OBSERVED RELATIVE DENSITIES ON THE TRUE HABITAT MAP
    spmat=matrix(allabund[species,],plotdimqy,plotdimqx,byrow=F)  # Fills a matrix, with no. rows = plotdimqy and no. columns = plotdimqx, with the indiv. counts per quadrat of one species.
    tot=numeric()             # Creates empty vector for tot. no. stems per quadrat.
    len=length(allabund[1,])  # Determines the tot. no. of quadrats.
	###SERÁ QUE PRECISA TUDO ISSO!! 
 ###for(i in 1:len)           # Determines the tot. no. of stems, of all spp., in each quadrat.
 ##    {
 ###     tot[i]=sum(allabund[,i]) 
 ##    }
	tot=apply(allabund,2,sum)  ## assim fica melhor, sem looping (ale dez 2008)
	totmat=matrix(tot[],plotdimqy,plotdimqx,byrow=F)  # Converts "tot" to a matrix, with no. rows = plotdimqy and no. columns = plotdimqx. 
    spstcnthab=numeric()   # Creates empty vector for stem counts per sp. per habitat.
    totstcnthab=numeric()  # Creates empty vector for tot. stem counts per habitat.
    for(i in 1:num.habs)  
     {
      totstcnthab[i]=sum(totmat[habmat==unique(habitat)[i]])  # Determines tot. no. stems per habitat of the true map.
      spstcnthab[i]=sum(spmat[habmat==unique(habitat)[i]])    # Determines tot. no. stems for focal sp. per habitat of the true map.     
     }
    spprophab=spstcnthab/totstcnthab         # Calculates observed relative stem density of focal sp. per habitat of the true map.
   # CALCULATIONS FOR RELATIVE DENSITIES ON THE TORUS-BASED HABITAT MAPS
 for (ciclo in 1:2)
  {
  if(ciclo==1)
  habmat=habmat
  if(ciclo==2)
  habmat=t(habmat)
    for(x in 0:(plotdimqx-1))    # Opens "for loop" through all 20-m translations along x-axis.
      { 
      for(y in 0:(plotdimqy-1))  # Opens "for loop" through all 20-m translations along y-axis.
       {
		contar=contar+1
        newhab=matrix(0,plotdimqy,plotdimqx)  # Creates empty matrix of quadrats' habitat designations.
   # The following "if" statements create the x,y torus-translation of the habitat map.
        if(y==0 & x==0)          
           newhab=habmat
        if(y==0 & x>0)
           newhab=habmat[c(1:plotdimqy),c((plotdimqx-x+1):plotdimqx,1:(plotdimqx-x))] 
        if(x==0 & y>0)
           newhab=habmat[c((plotdimqy-y+1):plotdimqy,1:(plotdimqy-y)),c(1:plotdimqx)]
        if(x>0 & y>0)
            newhab=habmat[c((plotdimqy-y+1):plotdimqy,1:(plotdimqy-y)),c((plotdimqx-x+1):plotdimqx,1:(plotdimqx-x))] 
        Torspstcnthab=numeric()   # Creates empty vector for stem counts per sp. per habitat in torus-based maps.
        Tortotstcnthab=numeric()  # Creates empty vector for tot. stem counts per habitat in torus-based maps.
        for(i in 1:num.habs)
         {
          Tortotstcnthab[i]=sum(totmat[newhab==unique(habitat)[i]])  # Determines tot. no. stems per habitat of the focal torus-based map.
          Torspstcnthab[i]=sum(spmat[newhab==unique(habitat)[i]])    # Determines tot. no. stems for focal sp. per habitat of the focal torus-based map.
         }
        Torspprophab=Torspstcnthab/Tortotstcnthab   # Calculates relative stem density of focal sp. per habitat of the focal torus-based map.  
        for(i in 1:num.habs)
         {
          if(spprophab[i]>Torspprophab[i])          # If rel. dens. of focal sp. in focal habitat of true map is greater than rel. dens. of focal sp. in focal habitat of torus-based map, then add one to "greater than" count.        
            GrLsEq[1,(4*i)-2]=GrLsEq[1,(4*i)-2]+1  

          if(spprophab[i]<Torspprophab[i])          # If rel. dens. of focal sp. in focal habitat of true map is less than rel. dens. of focal sp. in focal habitat of torus-based map, then add one to "less than" count. 
            GrLsEq[1,(4*i)-1]=GrLsEq[1,(4*i)-1]+1 
          if(spprophab[i]==Torspprophab[i])         # If rel. dens. of focal sp. in focal habitat of true map is equal to rel. dens. of focal sp. in focal habitat of torus-based map, then add one to "equal to" count.
            GrLsEq[1,4*i]=GrLsEq[1,4*i]+1 
         }
       }    # Closes "for loop" through all 20-m translations along x-axis.
     }      # Closes "for loop" through all 20-m translations along y-axis.
  cat("\n ciclo no.= ", ciclo, "\t simulações = ", contar, "\n") 
} ## Fechar ciclos de diferentes configurações do habitat original (a principio apenas mais o transposto) Ale 2008 
    for(i in 1:num.habs)
     {
      GrLsEq[1,(4*i)-3]=spstcnthab[i]
     } 
  return(GrLsEq)
 } 
</box>

>torusonesp("Calobr",habitat,allspp)

   ciclo no.=  1   simulações =  256 
   ciclo no.=  2   simulações =  512 
         N.Hab.neo Gr.Hab.neo Ls.Hab.neo Eq.Hab.neo N.Hab.trans Gr.Hab.trans Ls.Hab.trans Eq.Hab.trans N.Hab.esp.aren
  Calobr       135        494         17          1          43           46          465            1            226
         Gr.Hab.esp.aren Ls.Hab.esp.aren Eq.Hab.esp.aren N.Hab.esp.hist Gr.Hab.esp.hist Ls.Hab.esp.hist Eq.Hab.esp.hist
  Calobr              97             414               1             25             236             275               1

  
 **Os resultados permanencem consistentes com a primeira simulação, não houve grande diferença, apenas aumentou um pouco a significancia da associação com o neossolo.**