sss_cedp {island}

MacKenzie etal (2003) likelihood approach for estimating colonization/extinction parameters (with imperfect detectability)

Description

sss_cedp conducts a maximum likelihood estimation of model parameters (Colonization, Extinction, Detectability, and Phi_Time_0) of MacKenzie et al (2003) colonization-extinction model. This function is an alternative to mss_cedp that takes a different input (a 2D array), and requires the same sampling structure for all input data matrix rows, this is, no missing data defining a heterogeneous sampling structure across rows are allowed. As an advantage, it may run faster than mss_cedp.

Usage

sss_cedp(
  Data,
  Time,
  Transects,
  Colonization = 0.1,
  Extinction = 0.1,
  Detectability = 0.99,
  Phi_Time_0 = 0.5,
  Tol = 1e-06,
  MIT = 100,
  C_MAX = 2,
  C_min = 0,
  E_MAX = 2,
  E_min = 0,
  D_MAX = 0.999,
  D_min = 0.001,
  P_MAX = 0.999,
  P_min = 0.001,
  I_0 = 0,
  I_1 = 1,
  I_2 = 2,
  I_3 = 3,
  z = 4,
  Verbose = 0,
  Minimization = TRUE
)

Arguments

Data

S x N matrix containing presence data per transect (in cols):

Time

an array of length n containing increasing sampling times (without repetitions)

Transects

an integer array of length n containing the number of transects per sampling time

Colonization

guess value to initiate search / parameter value

Extinction

guess value to initiate search / parameter value

Detectability

guess value to initiate search / param eter value

Phi_Time_0

guess value to initiate search / parameter value

Tol

Stopping criteria of the search algorithm

MIT

max number of iterations of the search algorithm

C_MAX

max value of colonization values

C_min

min value of colonization values

E_MAX

max value of extinction values

E_min

min value of extinction values

D_MAX

max value of detectability values

D_min

min value of detectability values

P_MAX

max value for the initial presence probability on the site

P_min

min value for the initial presence probability on the site

I_0

parameter index of 1st parameter

I_1

parameter index of 2nd parameter

I_2

parameter index of 3rd parameter

I_3

parameter index of 4th parameter

z

dimension of the parameter subspace

Verbose

more/less (1/0) output information

Minimization

TRUE/FALSE.

Details

Maximum likelihood parameter estimation is conducted through bounded searches. This is the reason why the minimum and maximum values for each axis should be given as input arguments. The optimization procedure is the simplex method. A bounded parameter space implies that in case a neg loglikelihood (NLL) evaluation is required outside from these boundaries, the returned value for this NLL evaluation is artifically given as the maximum number the machine can hold. The array Parameters (I_0, I_1, I_2, I_3) has to be a permutation of (0, 1, 3, 4). This parameter indeces along with the imput parameter 'z' are used to define a subparameter space where the search will be conducted. If z = 2, then the search will take place on the plane defined by model parameters (I_0, I_1). These indeces are model parameter keys: colonization (0), extinction (1), detectability (2), and Phi_Time_0 (3). For instance, if (I_0, I_1, I_2, I_3) is (2, 3, 1, 0), and z = 2, then the search will take place whithin the subparemeter space defined by the detection probability (Detectability) and the probability of presence at time 0 (Phi_Time_0). If Minimization is TRUE (default value), then the whole mle is conducted. If FALSE, the function only return the NLL value at the input model parameter values. Likelihood evaluations are exact provided the number of 'absences' corresponding to either true absences or undetected presences in the input data matrix is not to high.

Value

A list with five components (Colonization, Extinction, Detectability, P_0, and Negative Log-Likelihood).

Examples

Data1 <- lakshadweep[[1]]
Name_of_Factors <- c("Species","Atoll","Guild")
Factors <- Filter(is.factor, Data1)
No_of_Factors <- length(Factors[1,])
n <- No_of_Factors + 1
D1 <- as.matrix(Data1[1:nrow(Data1),n:ncol(Data1)])
Time <- as.double(D1[1,])
P1 <- as.matrix(D1[2:nrow(D1),1:ncol(D1)])
# Dealing with time.
Time_Vector <- as.numeric(names(table(Time)))
Transects   <- as.numeric((table(Time)))
R1 <- sss_cedp(P1, Time_Vector, Transects,
                       Colonization=0.5, Extinction=0.5, Detectability=0.5,
                       Phi_Time_0=0.5,
                       Tol=1.0e-8, Verbose = 1)