dcatState1Alive1Dead {nimbleSCR}

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

Description

The dcatState1Alive1Dead 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 one dead state. 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 and transition to z_i,t+1=3 with probability prob2To3, or survive with probability 1-prob2To3 Individuals in dead states (z_i,t = 3 ) remain in that state with probability 1, the absorbing state. 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

dcatState1Alive1Dead(
  x,
  z,
  prob1To2 = -999,
  prob1To2Hab,
  prob2To3 = -999,
  prob2To3Hab,
  s,
  habitatGrid,
  log = 0
)

rcatState1Alive1Dead(
  n,
  z,
  prob1To2 = -999,
  prob1To2Hab,
  prob2To3 = -999,
  prob2To3Hab,
  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.

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. dcatState1Alive1Dead gives the (log) probability density of x. rcatState1Alive2Dead gives a randomly generated individual states conditional on the initial state z.

n

Integer specifying the number of realizations to generate. Only n = 1 is supported.

Author(s)

Cyril Milleret

Examples

# Use the distribution in R
z <- 2
prob1To2 <- 0.2
prob2To3 <- 0.7

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 <- rcatState1Alive1Dead( z = z
                                 , prob1To2 = prob1To2
                                 , prob2To3 = prob2To3
                                 , s = s
                                 , habitatGrid = habitatGrid)
zPlusOne     

dcatState1Alive1Dead(  x = zPlusOne
                     , z = z
                     , prob1To2 = prob1To2
                     , prob2To3 = prob2To3
                     , s = s
                     , habitatGrid = habitatGrid)
    
##  With spatial mortality
prob2To3Hab <- c(0.60, 0.70, 0.74, 0.65)
prob1To2Hab <- c(0.4,0.5,0.1,0.3)
zPlusOne <- rcatState1Alive1Dead( z = z
                                , prob1To2Hab = prob1To2Hab
                                , prob2To3Hab = prob2To3Hab
                                , s = s
                                , habitatGrid = habitatGrid)
zPlusOne    
dcatState1Alive1Dead(  x = zPlusOne
                     , z = z
                     , prob1To2Hab = prob1To2Hab
                     , prob2To3Hab = prob2To3Hab
                     , s = s
                     , habitatGrid = habitatGrid)