DeLury                 package:VGAM                 R Documentation

_D_e_L_u_r_y'_s _M_e_t_h_o_d _f_o_r _P_o_p_u_l_a_t_i_o_n _S_i_z_e _E_s_t_i_m_a_t_i_o_n

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

     Computes DeLury's method or Leslie's method for estimating a
     biological population size.

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

     DeLury(catch, effort, type=c("DeLury","Leslie"), ricker=FALSE)
            

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

catch, effort: Catch and effort. These should be numeric vectors of
          equal length.

    type: Character specifying which of the DeLury or Leslie models is
          to be fitted. The default is the first value.

  ricker: Logical. If 'TRUE' then the Ricker (1975) modification is
          computed.

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

     This simple function implements the methods of DeLury (1947).
     These are called the DeLury and Leslie models. Note that there are
     many assumptions. These include: (i) Catch and effort records are
     available for a series of consecutive time intervals. The catch
     for a given time interval, specified by t, is c(t), and the
     corresponding effort by e(t). The _catch per unit effort_ (CPUE)
     for the time interval t is C(t) = c(t)/e(t). Let d(t) represent
     the proportion of the population captured during the time interval
     t. Then d(t) = k(t) e(t) so that k(t) is the  proportion of the
     population captured during interval t by one unit of effort. Then
     k(t) is called the _catchability_, and the _intensity_ of effort
     is e(t). Let E(t) and K(t) be the total effort and total catch up
     to interval t, and N(t) be the number of individuals in the
     population at time t. It is good idea to plot log(C(t)) against
     E(t) for 'type="DeLury"' and C(t) versus K(t) for 'type="Leslie"'.

     The other assumptions are as follows. (ii) The population is
     closed-the population must be closed to sources of animals such as
     recruitment and immigration and losses of animals due to natural
     mortality and emigration. (iii) Catchability is constant over the
     period of removals. (iv) The units of effort are independent,
     i.e., the individual units of the method of capture (i.e., nets,
     traps, etc) do not compete with each other. (v) All fish are
     equally vulnerable to the method of capture-source of error may
     include gear saturation and trap-happy or trap-shy individuals.
     (vi) Enough fish must be removed to substantially reduce the CPUE.
     (vii) The catches may remove less than 2% of the population. Also,
     the usual assumptions of simple regression such as (viii) random
     sampling, (ix) the independent variable(s) are measured without
     error-both catches and effort should be known, not estimated, (x)
     a line describes the data, (xi) the errors are independent and
     normally distributed.

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

     A list with the following components.

catch, effort : Catch and effort. Same as the original vectors. These
          correspond to c(t) and e(t) respectively.

type, ricker: Same as input.

      N0: an estimate of the population size at time 0. Only valid if
          the assumptions are satisfied.

    CPUE: Catch Per Unit Effort =C(t). 

    K, E: K(t), E(t). Only one is computed depending on 'type'. 

   lmfit: the 'lm' object from the fit of 'log(CPUE)' on 'K' (when
          'type="Leslie"'). Note that the 'x' component of the object
          is the model matrix.

_N_o_t_e:

     The data in the example below comes from DeLury (1947), and some
     plots of his are reproduced. Note that he used log to base 10
     whereas natural logs are used here. His plots had some
     observations obscured by the y-axis!

     The DeLury method is not applicable to the data frame 'wffc.nc'
     since the 2008 World Fly Fishing Competition was strictly
     catch-and-release.

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

     T. W. Yee.

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

     DeLury, D. B. (1947) On the estimation of biological populations.
     _Biometrics_, *3*, 145-167.

     Ricker, W. E. (1975) Computation and interpretation of biological
     statistics of fish populations. _Bull. Fish. Res. Bd. Can._,
     *191*, 382-

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

     'wffc.nc'.

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

     pounds = c(  147, 2796, 6888, 7723, 5330, 8839, 6324, 3569, 8120, 8084,
                 8252, 8411, 6757, 1152, 1500, 11945, 6995, 5851, 3221, 6345,
                 3035, 6271, 5567, 3017, 4559, 4721, 3613,  473,  928, 2784,
                 2375, 2640, 3569)
     traps  = c(  200, 3780, 7174, 8850, 5793, 9504, 6655, 3685, 8202, 8585,
                 9105, 9069, 7920, 1215, 1471, 11597, 8470, 7770, 3430, 7970,
                 4740, 8144, 7965, 5198, 7115, 8585, 6935, 1060, 2070, 5725,
                 5235, 5480, 8300)
     table1 = DeLury(pounds/1000, traps/1000)

     ## Not run: 
     with(table1, plot(1+log(CPUE) ~ E, las=1, pch=19, main="DeLury method",
          xlab="E(t)", ylab="1 + log(C(t))", col="blue"))
     ## End(Not run)
     omitIndices = -(1:16)
     table1b = DeLury(pounds[omitIndices]/1000, traps[omitIndices]/1000)
     ## Not run: 
     with(table1b, plot(1+log(CPUE) ~ E, las=1, pch=19, main="DeLury method",
          xlab="E(t)", ylab="1 + log(C(t))", col="blue"))
     mylmfit = with(table1b, lmfit)
     lines(mylmfit$x[,2], 1 + predict.lm(mylmfit), col="red", lty="dashed")
     ## End(Not run)


     omitIndices = -(1:16)
     table2 = DeLury(pounds[omitIndices]/1000, traps[omitIndices]/1000, type="L")
     ## Not run: 
     with(table2, plot(CPUE ~ K, las=1, pch=19,
          main="Leslie method; Fig. III",
          xlab="K(t)", ylab="C(t)", col="blue"))
     mylmfit = with(table2, lmfit)
     abline(a=coef(mylmfit)[1], b=coef(mylmfit)[2], col="red", lty="dashed")
     ## End(Not run)

