Kendall                package:popbio                R Documentation

_F_i_n_d _t_h_e _b_e_s_t _K_e_n_d_a_l_l'_s _e_s_t_i_m_a_t_e_s _o_f _m_e_a_n _a_n_d _e_n_v_i_r_o_n_m_e_n_t_a_l
_v_a_r_i_a_n_c_e _f_o_r _b_e_t_a-_b_i_n_o_m_i_a_l _v_i_t_a_l _r_a_t_e_s.

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

     This function finds the best estimates of mean and environmental
     variance for beta-binomial vital rates, using a brute force search
     for the best adjusted estimates from a very large number of
     combinations of different possible mean and variance values.

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

     Kendall(rates, grades=1000, maxvar=0.2,minvar=0.00001, maxmean=1, minmean=0.01)

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

   rates: a matrix or dataframe with four columns: Rate identifier,
          Year, Total number of starting individuals, Number growing
          (or surviving).

  grades: number of different levels of means and variances to try,
          default is 1000 

  maxvar: maximum variance to search over, default is 0.20. The maximum
          ever possible is 0.25 and searching a narrower range will
          improve the accuracy of the answer.

  minvar: minimum variance to search, default is 0.00001. 

 maxmean: maximum limit on the mean values to search, default 1

 minmean: minimum limit on the mean values to search, default 0.01 

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

     A list with estimates and confidence intervals 

     est: a matrix with 5 columns: (1) estimated mean, (2) Kendall's
          MLE mean, (3) estimated variance, (4) Kendall's MLE variance,
          (5) Kendall's unbiased MLE variance.

      ci: a matrix with  95% confidence limits for the Kendall's mean
          and unbiased variance estimates with 4 columns: (1) low and
          (3) high mean limits, (3) low and (4) high variance limits.

_N_o_t_e:

     Note that it may deliver warning messages of : 'no finite
     arguments to min; returning Inf', indicating use of very low
     values for variance, but this is not a malfunction.

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

     Adapted to R from Morris & Doak (2002: 267-270) by Patrick Nantel.

_S_o_u_r_c_e:

     converted Matlab code from  Box 8.2 in Morris and Doak (2002)

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

     Kendall, B. E. 1998. Estimating the magnitude of environmental
     stochasticity in survivorship data. Ecological Applications 8(1):
     184-193.

     Morris, W. F., and D. F. Doak. 2002. Quantitative conservation
     biology: Theory and practice of population viability analysis.
     Sinauer, Sunderland, Massachusetts, USA.

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

     'varEst'

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

     ## desert tortoise input from Box 8.2 - compare results to Table 8.3
     tor<-data.frame(rate=rep(c("g4","g5","g6"),each=3),
     year=rep(1:3,3),      ## representing 70s, early 80s, late 80s
     start=c(17,15,7,22,19,4,32,31,10),
     grow=c(8,1,0,5,5,0,2,1,0))
     ## use fewer grades for faster loop
     tor.est<-Kendall(tor, grades=200)
     tor.est

     data(woodpecker) 
     wp.est <- Kendall(woodpecker, grades=200)
     wp.est

