specpool                package:vegan                R Documentation

_E_x_t_r_a_p_o_l_a_t_e_d _S_p_e_c_i_e_s _R_i_c_h_n_e_s_s _i_n _a _S_p_e_c_i_e_s _P_o_o_l

_D_e_s_c_r_i_p_t_i_o_n:

     The functions estimate the extrapolated species richness in a
     species pool, or the number of unobserved species. Function
     'specpool' is based on incidences in sample sites, and gives a
     single estimate for a collection of sample sites (matrix). 
     Function 'estimateR' is based on abundances (counts) on single
     sample site.

_U_s_a_g_e:

     specpool(x, pool)
     specpool2vect(X, index = c("Jack.1","Jack.2", "Chao", "Boot","Species"))
     estimateR(x, ...)

_A_r_g_u_m_e_n_t_s:

       x: Data frame or matrix with species data.

    pool: A vector giving a classification for pooling the sites in the
          species data. If missing, all sites are pooled together.

       X: A 'specpool' result object.

   index: The selected index of extrapolated richness.

     ...: Other parameters (not used).

_D_e_t_a_i_l_s:

     Many species will always remain unseen or undetected in a
     collection of sample plots.  The function uses some popular ways
     of estimating the number of these unseen species and adding them
     to the observed species richness (Palmer 1990, Colwell &
     Coddington 1994).

     The incidence-based estimates in 'specpool' use the frequencies of
     species in a collection of sites. In the following, S_P is the
     extrapolated richness in a pool, S_0 is the observed number of
     species in the collection, a1 and a2 are the number of species
     occurring only in one or only in two sites in the collection, p_i
     is the frequency of species i, and N is the number of sites in the
     collection.  The variants of extrapolated richness in 'specpool'
     are:

       Chao                    S_P = S_0 + a1^2/2/(a2+1) + a1*a2/2/(a2+1)^2
       First order jackknife   S_P = S_0 + a1*(N-1)/N
       Second order jackknife  S_P = S_0 + a1*(2*n-3)/n - a2*(n-2)^2/n/(n-1)
       Bootstrap               S_P = S_0 + Sum (1-p_i)^N

     The abundance-based estimates in 'estimateR' use counts
     (frequencies) of species in a single site. If called for a matrix
     or data frame, the function will give separate estimates for each
     site.  The two variants of extrapolated richness in 'estimateR'
     are Chao and ACE.  The Chao estimator is identical to the one
     above, except that a_i refers to number of species with abundance
     i instead of incidence.  The ACE is defined as: 

       ACE    S_P = S_abund + S_rare/C_ace + a1/C_ace * gamma^2
       where  C_{ace} = 1- a1/N_{rare}
              gamma^2 = max( S_rare/C_ace (sum[i=1..10] i*(i-1)*a_i) / N_rare/(N_rare-1) -1 , 0)

     Here a_i refers to number of species with abundance i and  S_rare
     is the number of rare species,  S_abund is the number of abundant
     species, with an arbitrary  threshold of abundance 10 for rare
     species, and N_rare is the number  of individuals in rare species.

     Functions estimate the the standard errors of the estimates. These
     only concern the number of added species, and assume that there is
     no variance in the observed richness. The equations of standard
     errors are too complicated to be reproduced in this help page, but
     they can be studied in the R source code of the function. The
     standard error are based on the following sources: Chao (1987) for
     the Chao estimate and Smith and van Belle (1984) for the
     first-order Jackknife and the bootstrap (second-order jackknife is
     still missing).  The variance estimator of S_ace was developed by
     Bob O'Hara (unpublished).

_V_a_l_u_e:

     Function 'specpool' returns a data frame with entries for observed
     richness and each of the indices for each class in 'pool' vector. 
     The utility function 'specpool2vect' maps the pooled values into a
     vector giving the value of selected 'index' for each original
     site. Function 'estimateR' returns the estimates and their
     standard errors for each site.

_N_o_t_e:

     The functions are based on assumption that there is a species
     pool: The community is closed so that there is a fixed pool size
     S_P. Such cases may exist, although I have not seen them yet.  All
     indices are biased for open communities.

     See <URL: http://viceroy.eeb.uconn.edu/EstimateS> for a more
     complete (and positive) discussion and alternative software for
     some platforms.

_A_u_t_h_o_r(_s):

     Bob O'Hara ('estimateR') and Jari Oksanen ('specpool').

_R_e_f_e_r_e_n_c_e_s:

     Chao, A. (1987). Estimating the population size for
     capture-recapture data with unequal catchability. _Biometrics_ 43,
     783-791.

     Colwell, R.K. & Coddington, J.A. (1994). Estimating terrestrial
     biodiversity through extrapolation. _Phil. Trans. Roy. Soc.
     London_ B 345, 101-118.

     Palmer, M.W. (1990). The estimation of species richness by
     extrapolation. _Ecology_ 71, 1195-1198.

     Smith, E.P & van Belle, G. (1984). Nonparametric estimation of
     species richness. _Biometrics_ 40, 119-129.

_S_e_e _A_l_s_o:

     'veiledspec', 'diversity'.

_E_x_a_m_p_l_e_s:

     data(dune)
     data(dune.env)
     attach(dune.env)
     pool <- specpool(dune, Management)
     pool
     op <- par(mfrow=c(1,2))
     boxplot(specnumber(dune) ~ Management, col="hotpink", border="cyan3",
      notch=TRUE)
     boxplot(specnumber(dune)/specpool2vect(pool) ~ Management, col="hotpink",
      border="cyan3", notch=TRUE)
     par(op)
     data(BCI)
     estimateR(BCI[1:5,])

