SpaColExt

The goal of SpaColExt R package is to infer spatial colonization and extinction dates of species accounting for the spatial heterogeneity of the data. It uses a Bayesian approach to estimate the probability of species still extant through the time a different spatial level.

We use the Bayesian functions from Solow 1993 and we will also add the Solow & Beet 2014 functions to incorporate the certainty and uncertainty of the data.

In this moment I’m adding a non-homogeneous Poisson processes inspired from Kodikara 2020

Installation

You can install the development version of SpaColExt from GitHub with:

# install.packages("devtools")
devtools::install_github("Clara-Casabona/SpaColExt")

Some notes:

This package is in development. I need to:

• Add spatial prior information

• Add non-homogeneous poisson processes

• Add colonization fonctions

Example 1

This is a basic example which shows you how to estimate the posterior distribution of the extant probability of a extinct species:

library(SpaColExt)

## basic example code
sightings = c(1901,1902,1903,1905,1908,1910)
start_year = 1900
end_year = 1920
dprior_m = function(m) 1 / m
dprior_te = function(te) 1
prior =0.5

compute_posterior_solow1993(sightings = sightings, 
                            start_year = start_year,
                            end_year = end_year, 
                            dprior_m = dprior_m ,
                            dprior_te = dprior_te,
                            prior = prior)
#> [1] 0.1388889

Example 2

This is a basic example which shows you how to estimate the posterior distribution of the extant probability of an extinct species in different sites:

library(SpaColExt)

## Creating data in a matrix 2x2
data = list(c(1880, 1883, 1895, 1897, 1899), NA, NA, c(1882, 1884, 1896, 1898))
dim(data) <- c(2, 2)

## Using Solow 1993 priors
dprior_m = function(m) 1 / m
dprior_te = function(te) 1
prior =0.5

## Study interval
start_year = 1880
stop_year = 1930


# Estimating extant probabilities

extant_probability = spatial_posterior_probability_extinction_varying_end_year(data, 
                                                                               start_year=start_year,
                                                                               stop_year=stop_year)
## Output of one of the sites:

extant_probability[1,1]
#> [[1]]
#>  [1] 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000
#>  [7] 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000
#> [13] 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000
#> [19] 1.00000000 1.00000000 0.94613250 0.89040796 0.83376225 0.77710330
#> [25] 0.72126176 0.66695497 0.61476592 0.56513632 0.51837127 0.47465226
#> [31] 0.43405500 0.39656930 0.36211871 0.33057853 0.30179141 0.27558009
#> [37] 0.25175760 0.23013486 0.21052632 0.19275375 0.17664878 0.16205431
#> [43] 0.14882522 0.13682842 0.12594264 0.11605784 0.10707460 0.09890328
#> [49] 0.09146330 0.08468226 0.07849524

# Ploting the exant probability

plot_posterior_distribution(extant_probability, start_year=start_year, stop_year=stop_year)

With this example we estimate the probability that the species is extant in different sites considering that the observations are independent between the sites.

Example 3 (In development)

This is an example to estimate the posterior distribution of the extant probability of an extinct species in different sites, accounting for the heterogeneity in the observation rate. Using Kodikara 2020 function.

Example 4 (In development)

This example will show you how to estimate the posterior distribution of the extant probability of an extinct species in different sites, assuming that the observations in one site are influenced by the observations in neighbours sites:

library(SpaColExt)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(ggplot2)
#> 
#> Attaching package: 'ggplot2'
#> The following object is masked from 'package:SpaColExt':
#> 
#>     alpha
library(ggpubr)
set.seed(12)

# Create a realistic data set of observations 
n = 40 # number of years with observational data
t_ext = 1940 # True extinction time
t_start = t_ext - n #Year of the possible first observation
t_stop = 2040 # End of the study period
m_rate = 2 # mean time between sighting before extinction

generate_data = function(t_start, t_ext, m_rate) {
  sightings = t_start + unique(floor(cumsum(rexp(2*(t_ext-t_start)/m_rate, 1/m_rate))))
  sightings[sightings<=t_ext]
}

sightings = generate_data(t_start, t_ext, m_rate) # Simulated sighting used to predict extinction in a specific place

sightings2 = generate_data(t_start, t_ext+10, 1)  # Simulated sighting list to estimate the first posterior distribution of extinction date 


posterior = compute_posterior_c2022_extinction(sightings2, t_start, t_stop)

prior_te = approxfun(t_start:t_stop, 1-posterior) # IMPORTANT! The scaling still in progress! This might be modified in the next weeks. 

prior_m = Vectorize(function(m) {
  if(m > 10*m_rate) return(1e-6)
  m_rate**m * exp(-m_rate) / gamma(m+1)
})

vizualize_priors_effects(t_start, t_stop, sightings, prior_te = prior_te, prior_m = prior_m)
#> Joining with `by = join_by(year)`
#> Joining with `by = join_by(year)`
#> Joining with `by = join_by(year)`