# Mark Gibbs sampler

### Description

A Bayesian way of fitting a mark-recapture model to capture history data.

### Usage

1 2 |

### Arguments

`ch` |
A matrix or a collapsed, single-columned data.frame of capture histories, one row for each individual. |

`cov` |
A data.frame of covariates (traits) that should be considered |

`n.iter` |
Number iterations the sampler should take. |

`burn.in` |
The number of iterations to discard from each chain. |

`number.of.models` |
The number of models to calculate the posterior probability for. |

`n.chains` |
The number of chains. Each chain will be run on a separate core if possible. |

`add` |
Should all possilbe addative terms be considered. |

`quad` |
Should all possible quadratic terms be considered. |

`corr` |
Should all possible pairwise interaction terms be considered. |

### Details

This function implements a Gibbs sampler to estimate mark-recapture parameters. It is essentially a wrapper for a Jags or WinBugs model. Things it does not do right now: A. does not handle data with significant time or age dependent effects, B. cannot deal with re-capture heterogeniety (i.e. re-capture dependence on a trait), C. cannot fit a specific predefined model, D. cannot use predefined priors (usues diffuse priors instead, see reference). Other R libraries exist with this functionality, namely marked, RMark, mra. What it can do is do automatic model selection on all combinations of models supplied. See examples for usage.

### Value

(mcmc = mcmc, mcmc.list = mcmc.list, pp = pp.results, estimates = estimates, p = p, gelman = gelman) Returns a list:

`$mcmc` |
A single matrix with all the parameter estimates for each chain combined. |

`$mcmc.list` |
An object of class mcmc.list, one element for each chain. |

`$pp` |
A data.frame of posterior probabilities for each model. |

`$estimates` |
A data.frame of parameter estimates for survival probability. |

`$p` |
The estimated recapture probability. |

`$gelman` |
The the output from gelman.diag in the library coda, a convergence diagnostic. |

### Author(s)

John Waller

### References

Gimenez et al. 2009 "Estimagint and visulizing fitness surfaces using mark-recapture data" Evolution

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 | ```
#' Example 1 perfect detection
## Not run:
#' generate some data to input into our simulator
N = 100
#' Two traits
x1 = rnorm(N,0,1)
x2 = rnorm(N,0,1)
#' Use our simulator function
#' with constant and perfect recapture probability, p.constant = 1
#' with positive linear selection on trait x1 and no selection on trait x2
chObj = Simulate.CH(surv.form = 1 + 0.15*x1 + 0*x2, p.constant = 1, N = N)
str(chObj) #' what is contained in our chObj
ch = chObj$ch #' Let's pull out our simulated capture histories
ch #' what it looks like
#' make a data.frame of covariate values
cov = data.frame(x1 = x1, x2 = x2)
#' cov should have the same number of rows as ch
nrow(ch)
nrow(cov)
#' Now let's estimate the parameters of our simulated data.
#' And test which model best fits the data.
#' We use a small number iteration here,
#' n.iter = 1000, so it runs quickly.
#' One should definitely use many more iterations in practice.
#' We we throw away half of our n.iter in the the burn in, burn.in = 500
MCMC = MARK.MCMC(ch = ch, cov = cov, n.iter = 1000, burn.in = 500, number.of.models = 5,
n.chains = 2, add = TRUE, quad = TRUE, corr = TRUE)
#' Let's look at what is inside our MCMC object
attributes(MCMC)
#' Let's look at the posterior probability, pp
#' Since we did not run very many iterations, the correct model (x1),
#' may not have the highest probability
MCMC$pp
#' Let's look at the recapture probability
#' Since we set it at 1, it should be close to 1
MCMC$p
#' Let's look at our estimates of our parameters.
#' Since we set the gradient on trait x1 to 0.15, x1's parameters should be close to 0.15
#' However, our estimates may not be very good, since we used so few iterations
MCMC$estimates
#' Let's look at our convergence diagnostic
#' These values should be close to 1 for all beta variables and p
#' w and sigmaeps can mostly be ignored
#' See gelman.diag in the coda library for more details.
MCMC$gelman
#' Example 2 imperfect detection
#' Same procedure as in Example 1
N = 100
x1 = rnorm(N,0,1)
x2 = rnorm(N,0,1)
#' Only this time we will lower our recapture probability, p.constant, from 1 to 0.5
chObj = Simulate.CH(surv.form = 1 + 0.15*x1 + 0*x2, p.constant = 0.5, N = N)
ch = chObj$ch
cov = data.frame(x1 = x1, x2 = x2)
MCMC = MARK.MCMC(ch = ch, cov = cov, n.iter = 1000, burn.in = 500, number.of.models = 5,
n.chains = 2, add = TRUE, quad = TRUE, corr = TRUE)
#' look at our output
MCMC$pp
#' p should be close to 0.5
MCMC$p
MCMC$estimates
MCMC$gelman
#' Example 3 Test Only Addative Models
#' Same as before...
N = 100
x1 = rnorm(N,0,1)
x2 = rnorm(N,0,1)
#' Only this time we will lower our recapture probability, p.constant, from 1 to 0.5
chObj = Simulate.CH(surv.form = 1 + 0.15*x1 + 0*x2, p.constant = 0.5, N = N)
ch = chObj$ch
cov = data.frame(x1 = x1, x2 = x2)
#' Now we set quad = FALSE, corr = FALSE
MCMC = MARK.MCMC(ch = ch, cov = cov, n.iter = 1000, burn.in = 500, number.of.models = 5,
n.chains = 2, add = TRUE, quad = FALSE, corr = FALSE)
#' Let's look at the posterior probability
#' It should only show the four possible addative models and blank slots for the rest
#' x1 should have the highest pp, since our data was simulated under those conditions
MCMC$pp
#' Example 3 Stabilizing selection
#' We will bump up the sample size to 500,
#' since stabilizing selection is a little bit harder
#' to detect with small sample sizes
N = 500
x1 = rnorm(N,0,1)
#' For stabilizing selection, we will add a term to our simulator: -0.15*x1^2
#' We will keep our recapture probability at an high value
chObj = Simulate.CH(surv.form = 1 + 0*x1 + -0.3*x1^2, p.constant = 0.7, N = N)
ch = chObj$ch
cov = data.frame(x1 = x1)
#' We will set corr = FALSE, since we only have one trait, x1
#' May take a few minutes ~5 minutes to run...
MCMC = MARK.MCMC(ch = ch, cov = cov, n.iter = 1000, burn.in = 500, number.of.models = 5,
n.chains = 2, add = TRUE, quad = TRUE, corr = FALSE)
#' Let's look at the posterior probability
#' x1^2 should be the model with the higher posterior probability
MCMC$pp
#' x1^2 term should have an estimate close to -0.3
MCMC$estimates
## End(Not run)
``` |