dcatState1Alive2Dead {nimbleSCR}

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

Description

The dcatState1Alive2Dead 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 one 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=3 with probability prob2To3, or die from another cause with probability prob2To4 z_i,t+1=4. If the individual does not die it can survive and remain in state 2 with probability (1-(prob2To3+prob2To4)). Individuals in dead states (z_i,t = 3 or 4) transition to z_i,t+1 = 4, 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

dcatState1Alive2Dead(
  x,
  z,
  prob1To2 = -999,
  prob1To2Hab,
  prob2To3 = -999,
  prob2To3Hab,
  prob2To4 = -999,
  prob2To4Hab,
  s,
  habitatGrid,
  log = 0
)

rcatState1Alive2Dead(
  n,
  z,
  prob1To2 = -999,
  prob1To2Hab,
  prob2To3 = -999,
  prob2To3Hab,
  prob2To4 = -999,
  prob2To4Hab,
  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.

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

dcatState1Alive2Dead gives the (log) probability density of x. rcatState1Alive2Dead gives a randomly generated individual states conditional on the initial state z.

Author(s)

Cyril Milleret

Examples

# Use the distribution in R

z <- 2
prob1To2 <- 0.2
prob2To3 <- 0.4
prob2To4 <- 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 <- rcatState1Alive2Dead( z = z
                                 , prob1To2 = prob1To2
                                 , prob2To3 = prob2To3
                                 , prob2To4 = prob2To4
                                 , s = s
                                 , habitatGrid = habitatGrid)
   
dcatState1Alive2Dead(  x = zPlusOne
                     , z = z
                     , prob1To2 = prob1To2
                     , prob2To3 = prob2To3
                     , prob2To4 = prob2To4
                     , s = s
                     , habitatGrid = habitatGrid)
     
##  With spatial mortality
prob2To3Hab <- c(0.10, 0.20, 0.15, 0.30)
prob2To4Hab <- c(0.13, 0.21, 0.12, 0.08)
phiSpatial <- 1-(prob2To3Hab+prob2To4Hab)
zPlusOne <- rcatState1Alive2Dead( z = z
                                 , prob1To2Hab = prob1To2Hab
                                 , prob2To3Hab =  prob2To3Hab
                                 , prob2To4Hab = prob2To4Hab
                                 , s = s
                                 , habitatGrid = habitatGrid)

dcatState1Alive2Dead(  x = zPlusOne
                     , z = z
                     , prob1To2Hab = prob1To2Hab
                     , prob2To3Hab =  prob2To3Hab
                     , prob2To4Hab = prob2To4Hab
                     , s = s
                     , habitatGrid = habitatGrid)