dcatState2Alive2Dead: Density and random generation of a categorical distribution...

In nimbleSCR: Spatial Capture-Recapture (SCR) Methods Using 'nimble'

Density and random generation of a categorical distribution describing state transition with two alive and two dead states.

Description

The dcatState2Alive2Dead distribution is a NIMBLE custom distribution which can be used to model and simulate individual state transition. This function can be used to model transitions from two alive and two dead states. If z_i,t = 1, individual i can be recruited (transition to state 2) with probability prob1To2_t, so z_i,t+1 ~ dcat(1- prob1To2_t, prob1To2_t, 0,0 , 0) where prob1To2_t represent the probability of an unborn individual to be recruited. If z_i,t = 2, individual i can die from one cause of mortality (e.g. culling) and transition to z_i,t+1=4 with probability prob2To4, or die from another cause with probability prob2To5 z_i,t+1=5. If the individual does not die (1-(prob2To4+prob2To5)), it can either transition to the second state alive (z_i,t+1=3) with probability prob2To3 or remain in the first state alive (z_i,t+1=2) with probability (1-prob2To3). If z_i,t = 3, individual i can die from one cause of mortality (e.g. culling) and transition to z_i,t+1=4 with probability prob3To4, or die from another cause with probability prob3To5 z_i,t+1=5. if the individual does not die (1-(prob3To4+prob3To5)), the individual remain in state 3. Individuals in dead states (z_i,t = 4 or 5) transition to z_i,t+1 = 5, the absorbing state, with probability 1. If transition probabilities are spatially variable, a probability vector containing the transition probability value in each habitat window can be provided using the "Hab" arguments (e.g. prob1To2Hab,prob2To3Hab).

Usage

dcatState2Alive2Dead(
  x,
  z,
  prob1To2 = -999,
  prob1To2Hab,
  prob2To3 = -999,
  prob2To3Hab,
  prob2To4 = -999,
  prob2To4Hab,
  prob3To4 = -999,
  prob3To4Hab,
  prob2To5 = -999,
  prob2To5Hab,
  prob3To5 = -999,
  prob3To5Hab,
  s,
  habitatGrid,
  log = 0
)

rcatState2Alive2Dead(
  n,
  z,
  prob1To2 = -999,
  prob1To2Hab,
  prob2To3 = -999,
  prob2To3Hab,
  prob2To4 = -999,
  prob2To4Hab,
  prob3To4 = -999,
  prob3To4Hab,
  prob2To5 = -999,
  prob2To5Hab,
  prob3To5 = -999,
  prob3To5Hab,
  s,
  habitatGrid
)

Arguments

x	Scalar, individual state z_i,t+1.
z	Scalar, initial individual state z_i,t.
prob1To2	scalar, probability to transition from state 1 to 2.
prob1To2Hab	vector, Spatially-explicit probability to transition from state 2 to 3. The length of the vector should be equal the number of habitat windows in habitatGrid.
prob2To3	scalar, probability to transition from state 2 to 3.
prob2To3Hab	vector, Spatially-explicit probability to transition from state 2 to 3. The length of the vector should be equal the number of habitat windows in habitatGrid.
prob2To4	scalar, probability to transition from state 2 to 4.
prob2To4Hab	vector, Spatially-explicit probability to transition from state 2 to 4. The length of the vector should be equal the number of habitat windows in habitatGrid.
prob3To4	scalar, probability to transition from state 3 to 4.
prob3To4Hab	vector, Spatially-explicit probability to transition from state 3 to 4. The length of the vector should be equal the number of habitat windows in habitatGrid.
prob2To5	scalar, probability to transition from state 2 to 5.
prob2To5Hab	vector, Spatially-explicit probability to transition from state 2 to 5. The length of the vector should be equal the number of habitat windows in habitatGrid.
prob3To5	scalar, probability to transition from state 3 to 5.
prob3To5Hab	vector, Spatially-explicit probability to transition from state 3 to 5. The length of the vector should be equal the number of habitat windows in habitatGrid.
s	Vector of x- and y-coordinates corresponding to the AC location of the individual. Used to extract transition spatially-explicit probabilities when they are provided.
habitatGrid	Matrix of habitat window indices. Cell values should correspond to the order of habitat windows in prob1To2Hab, prob2To3Hab and in lowerCoords and upperCoords as used in the dbernppAC function.
log	Logical argument, specifying whether to return the log-probability of the distribution.
n	Integer specifying the number of realizations to generate. Only n = 1 is supported.

Value

dcatState2Alive2Dead gives the (log) probability density of x. dcatState2Alive2Dead gives a randomly generated individual states conditional on the initial state z.

Author(s)

Cyril Milleret

Examples

# Use the distribution in R

z <- 3
prob1To2 <- 0.2
prob2To3 <- 0.4
prob2To4 <- 0.1
prob2To5 <- 0.1

prob3To4 <- 0.2
prob3To5 <- 0.1


lowerCoords <- matrix(c(0, 0, 1, 0, 0, 1, 1, 1), nrow = 4, byrow = TRUE)
upperCoords <- matrix(c(1, 1, 2, 1, 1, 2, 2, 2), nrow = 4, byrow = TRUE)  
logIntensities <- log(rep(1,4))
logSumIntensity <- log(sum(c(1:4))) 
habitatGrid <- matrix(c(1:4), nrow = 2, byrow = TRUE)
numGridRows <- nrow(habitatGrid)
numGridCols <- ncol(habitatGrid)
s <- rbernppAC(n=1, lowerCoords, upperCoords, logIntensities, logSumIntensity, 
              habitatGrid, numGridRows, numGridCols)

## No spatial mortality 
zPlusOne <- rcatState2Alive2Dead( z = z
                                 , prob1To2 = prob1To2
                                 , prob2To3 = prob2To3
                                 , prob2To4 = prob2To4
                                 , prob2To5 = prob2To5
                                 , prob3To4 = prob3To4
                                 , prob3To5 = prob3To5
                                 , s = s
                                 , habitatGrid = habitatGrid)

dcatState2Alive2Dead(  x = zPlusOne
                      , z = z
                      , prob1To2 = prob1To2
                      , prob2To3 = prob2To3
                      , prob2To4 = prob2To4
                      , prob2To5 = prob2To5
                      , prob3To4 = prob3To4
                      , prob3To5 = prob3To5
                      , s = s
                      , habitatGrid = habitatGrid)

##  With spatial mortality
prob2To3Hab <- runif(length(habitatGrid),0,0.1)
prob2To4Hab <- runif(length(habitatGrid),0,0.1)
prob2To5Hab <- runif(length(habitatGrid),0,0.1)
prob3To4Hab <- runif(length(habitatGrid),0,0.1)
prob3To5Hab <- runif(length(habitatGrid),0,0.1)



zPlusOne <- rcatState2Alive2Dead( z = z
                                 , prob1To2 = prob1To2
                                 , prob2To3Hab = prob2To3Hab
                                 , prob2To4Hab = prob2To4Hab
                                 , prob2To5Hab = prob2To5Hab
                                 , prob3To4Hab = prob3To4Hab
                                 , prob3To5Hab = prob3To5Hab
                                 , s = s
                                 , habitatGrid = habitatGrid)

dcatState2Alive2Dead(  x = zPlusOne
                      , z = z
                      , prob1To2 = prob1To2
                      , prob2To3Hab = prob2To3Hab
                      , prob2To4Hab = prob2To4Hab
                      , prob2To5Hab = prob2To5Hab
                      , prob3To4Hab = prob3To4Hab
                      , prob3To5Hab = prob3To5Hab
                      , s = s
                      , habitatGrid = habitatGrid)

nimbleSCR documentation built on Dec. 1, 2022, 1:17 a.m.