# Get started

The goal of the R package `popbayes` is to fit population trajectories over time from counts of individuals collected at various dates and with a variety of methods. It does so under a Bayesian framework where the primary quantity being modeled is the rate of increase between successive years (or any other time units for that matter, the one used for date). The package can deal with multiple species and multiple locations presented in a single data set, but each count series made of the counts relative to one species at one location will be processed independently.

The strength of `popbayes` is to handle, in a single series, counts collected under different types of surveys (aerial vs ground surveys), and estimated by different census methods (total counts, sampling counts, and even guesstimates [i.e. expert estimates]).

Before using this package, users need to install the freeware JAGS.

The workflow of `popbayes` consists in three main steps:

1. Formatting data (`format_data()`)
2. Fitting trends (`fit_trend()`)
3. Visualizing results (`plot_trend()`)

The package also provides a lot of functions to handle individual count series and model outputs. The following figure shows a more complete usage of the package.

Framework of `popbayes`

## The Garamba dataset

The package `popbayes` comes with an example dataset: `garamba`. It contains counts of individuals from 10 African mammal species surveyed in the Garamba National Park (Democratic Republic of the Congo) from 1976 to 2017.

    ## Define filename path ----
    file_path <- system.file("extdata", "garamba_survey.csv", package = "popbayes")

    ## Read CSV file ----
    garamba <- read.csv(file = file_path)

The Garamba dataset (first 20 rows)
location | species | date | stat_method | field_method | count | lower_ci | upper_ci | pref_field_method | conversion_A2G | rmax
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Garamba | Alcelaphus buselaphus | 1976 | S | A | 7750 | 6280 | 9220 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 1983 | S | A | 1932 | 1120 | 2744 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 1984 | S | A | 1224 | 782 | 1666 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 1986 | S | A | 1705 | 1116 | 2294 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 1991 | S | A | 987 | 663 | 1311 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 1993 | S | A | 3444 | 1290 | 5598 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 1995 | S | A | 2819 | 1620 | 4018 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 1998 | S | A | 1685 | 1287 | 2083 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 2000 | S | A | 1169 | 945 | 1393 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 2002 | S | A | 1139 | 907 | 1371 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 2003 | S | A | 1595 | 1142 | 2048 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 2004 | S | A | 1204 | 811 | 1597 | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 2012 | T | A | 552 | NA | NA | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 2014 | T | A | 698 | NA | NA | G | 2.302 | 0.2748
Garamba | Alcelaphus buselaphus | 2017 | T | A | 1051 | NA | NA | G | 2.302 | 0.2748
Garamba | Giraffa camelopardalis | 1976 | S | A | 350 | 100 | 600 | A | 3.011 | 0.1750
Garamba | Giraffa camelopardalis | 1983 | S | A | 175 | 12 | 338 | A | 3.011 | 0.1750
Garamba | Giraffa camelopardalis | 1984 | S | A | 237 | 93 | 381 | A | 3.011 | 0.1750
Garamba | Giraffa camelopardalis | 1986 | S | A | 153 | 13 | 293 | A | 3.011 | 0.1750
Garamba | Giraffa camelopardalis | 1991 | S | A | 346 | 143 | 549 | A | 3.011 | 0.1750

This dataset has a typical structure with a location field (`location`), a species name field (`species`), a date field (`date`), and a count field (`count`).

### Statistical method

In addition to the fields `location`, `species`, `date`, and `count`, a fourth field is mandatory: `stat_method`. This field specifies the census method that produced the count. It can be `T` for a total count, `X` for a guesstimate (i.e. expert estimate), or `S` for a sampling count.

To be usable by the Bayesian model, individual counts are to be accompanied by information on precision in the form of a 95% confidence interval. If counts are :

- `T` or `X`, a confidence interval will be computed automatically by the function `format_data()` according respectively to the following formulas:

\[ CI_{(T)} = [\ 0.95 \times count\ ; 1.20 \times count\ ] \] \[ CI_{(X)} = [\ 0.80 \times count\ ; 1.20 \times count\ ] \]

- `S`, users need to supply a measure of precision. Precision is preferably provided in the form of a 95% CI by means of two fields: `lower_ci` and `upper_ci` (as in the `garamba` dataset). Alternatively, it may also be given in the form of a standard deviation (`sd`), a variance (`var`), or a coefficient of variation (`cv`). Note that precision metrics can be different between counts. For instance, some `S` counts may have an `sd` value and others `lower_ci` and `upper_ci`. In that case, three precision columns would be required (`lower_ci`, `upper_ci`, and `sd`). An `S` count with no measure of precision will be detected as an anomaly by `format_data()` by default. The option `na.rm = TRUE` may be used to automatically remove such counts from the series. If it is desirable to maintain such counts in the count series, we suggest to enter a value for the coefficient of variation, e.g. the average coefficient of variation of the other counts in the series.

### Field method

Another optional column, `field_method`, may be provided. It refers to the type of survey used to collect data. This can be `A` for aerial survey or `G` for ground survey. This column becomes mandatory as soon as both field methods are present in a series.

The detectability of a species is indeed strongly dependent on the survey method and each species has its own preferred field method, the one that is assumed to provide estimates closer to the truth. So, even if a series is homogeneous relative to the `field method`, it is recommended to provide the column `field_method` if counts have been collected under the not preferred field method. That will force conversion towards the preferred field method.

### Count conversion

The function `format_data()` will convert counts (and 95% CI bounds) into their equivalent in the preferred field method for the species. To this aim, two pieces of information are required :

- `pref_field_method`: the preferred field method for the species (`A` or `G`);
- `conversion_A2G`: the multiplicative factor used to convert an aerial count into an equivalent ground count.

The package `popbayes` provides the `species_info` dataset, which contains these two pieces of information for 15 African mammal species.

    data("species_info")

Species with count conversion information in popbayes
species | category | pref_field_method | conversion_A2G | rmax
--- | --- | --- | --- | ---
Aepyceros melampus | MLB | G | 6.747 | 0.4010
Alcelaphus buselaphus | LLB | G | 2.302 | 0.2748
Connochaetes taurinus | LLB | G | 2.302 | 0.2679
Damaliscus lunatus | MLB | G | 6.747 | 0.2990
Eudorcas rufifrons | MLB | G | 6.747 | 0.5270
Giraffa camelopardalis | Giraffe | A | 3.011 | 0.1750
Hippotragus equinus | LLB | G | 2.302 | 0.2420
Kobus ellipsiprymnus | MLB | G | 6.747 | 0.2702
Kobus kob | MLB | G | 6.747 | 0.3802
Loxodonta africana | Elephant | A | 0.659 | 0.1120
Ourebia ourebi | MLB | G | 6.747 | 0.5988
Redunca redunca | MLB | G | 6.747 | 0.4010
Syncerus caffer | LD | A | 0.561 | 0.2080
Tragelaphus derbianus | LLB | G | 2.302 | 0.1500
Tragelaphus scriptus | MLB | G | 6.747 | 0.4487

If users work only with species in this table, the package `popbayes` can automatically retrieve the values of `pref_field_method` and `conversion_A2G` from the `species_info` data set. But for other species, users need to supply the information themselves when running `format_data()`. These values may be provided as additional fields in the count data set. Care must then be taken that the same value is consistently repeated for each count of the same species. For users with sufficient command of R, we recommend rather to create an independent additional table similar to `species_info` and to pass it to the function `format_data()` as the data frame argument `info`.

Note: Currently `format_data()` takes its information for count conversion from one source only with priority given to `info`, then to additional fields in data (if `info` is not provided), and eventually to the `species_info` table of the package (when the other two sources are lacking). That means that the source with the highest priority must be complete with respect to the species present in data, as it will be used exclusively to any other source. If, say, you use `info`, you cannot expect `format_data()` to retrieve conversion information for a species undocumented in `info` from the `species_info` table of the package. However, you can easily construct `info` from a copy of `species_info`, which additionally provides a ready template. It suffices to add any species not already in `species_info` as shown below.

Let’s assume that, in addition to other species present in the package `species_info` table, we have counts of Taurotragus oryx and Taurotragus derbianus. We can construct `info` as follows.

    ## Extract the relevant columns of the package table "species_info" ----
    info_from_package <- species_info[ , c("species", "pref_field_method", "conversion_A2G", "rmax")]

    ## Add the new species ----
    new_conversion_info <- data.frame("species"           = c("Taurotragus oryx","Taurotragus derbianus"),
                                      "pref_field_method" = "G",
                                      "conversion_A2G"    = 2.302,
                                      "rmax"              = 0.1500)

    ## Append the new species ----
    info <- rbind(info_from_package, new_conversion_info)
    info
    #>                   species pref_field_method conversion_A2G   rmax
    #> 1      Aepyceros melampus                 G          6.747 0.4010
    #> 2   Alcelaphus buselaphus                 G          2.302 0.2748
    #> 3   Connochaetes taurinus                 G          2.302 0.2679
    #> 4      Damaliscus lunatus                 G          6.747 0.2990
    #> 5      Eudorcas rufifrons                 G          6.747 0.5270
    #> 6  Giraffa camelopardalis                 A          3.011 0.1750
    #> 7     Hippotragus equinus                 G          2.302 0.2420
    #> 8    Kobus ellipsiprymnus                 G          6.747 0.2702
    #> 9               Kobus kob                 G          6.747 0.3802
    #> 10     Loxodonta africana                 A          0.659 0.1120
    #> 11         Ourebia ourebi                 G          6.747 0.5988
    #> 12        Redunca redunca                 G          6.747 0.4010
    #> 13        Syncerus caffer                 A          0.561 0.2080
    #> 14  Tragelaphus derbianus                 G          2.302 0.1500
    #> 15   Tragelaphus scriptus                 G          6.747 0.4487
    #> 16       Taurotragus oryx                 G          2.302 0.1500
    #> 17  Taurotragus derbianus                 G          2.302 0.1500

If you do not have conversion information of your own for a new species, you can rely on the conversion information of species with similar characteristics (for example the two Taurotragus species belong to the category LLB). The package `popbayes` distinguishes five categories of species:

- MLB: Medium-sized Light and Brown species (20-150kg)
- LLB: Large Light and Brown species (>150kg)
- LD: Large Dark (>150kg)
- Elephant
- Giraffe

The field `category` of the `species_info` table indicates which species belong to each.

### Relative rate of increase

The demographic potential of a species is limited. The intrinsic rate of increase (called `rmax`) is the maximum increase in log population size that a species can attain in a year.

We strongly recommend using the `rmax` values while estimating population trend to limit yearly population growth estimated by the model (the default).

As for `pref_field_method` and `conversion_A2G`, `rmax` values (specific to a species) can be provided in an additional field of the count dataset (`garamba`), as additional field of the `info` data frame, or internally can be retrieved from the internal dataset of `popbayes`.

How to find the species `rmax` value?

According to Sinclair (2003), `rmax` is related to the body mass of adult females `W` by the formula:

\[ rmax = 1.375 \times W^{-0.315} \]

Body masses are found in the literature in publications such as Kingdon & Hoffman (2013), Cornelis et al. (2014), Illius & Gordon (1992), Sinclair (1996), Suraud et al. (2012), or Foley & Faust (2010).

If you know the body mass of adult females of the species, you can compute the `rmax` value with the function `w_to_rmax()`.

Alternatively, `rmax` can be obtained from previous demographic analyses.

Important note: The intrinsic rate of increase refers to a change over one year. If a different time unit is used for the dates (say a month), the rmax to provide must be adapted (here divided by 12). The rmax values in popbayes cannot be used for time units other than one year.

## Checking data

The first thing that the function `format_data()` does is to check the validity of the content of the different fields of the count data set. Here we will explore our data to avoid errors when using the function `format_data()`.

In particular, we need to check `location` and `species` spelling, `date` and `count` field format, and the `stat_method` and `field_method` categories.

Check `location` field

    unique(garamba$"location")
    #> [1] "Garamba"

    sum(is.na(garamba$"location"))   # Are there any missing values?
    #> [1] 0

Field `location` can be either a `character` or a `factor`. It cannot contain any `NA` values.

Check `species` field

    unique(garamba$"species")
    #>  [1] "Alcelaphus buselaphus"  "Giraffa camelopardalis" "Hippotragus equinus"
    #>  [4] "Kobus ellipsiprymnus"   "Kobus kob"              "Loxodonta africana"
    #>  [7] "Ourebia ourebi"         "Redunca redunca"        "Syncerus caffer"
    #> [10] "Tragelaphus scriptus"

    sum(is.na(garamba$"species"))   # Are there any missing values?
    #> [1] 0

    ## Are there species absent from the 'species_info' popbayes dataset?
    garamba_species <- unique(garamba$"species")
    garamba_species[which(!(garamba_species %in% species_info$"species"))]
    #> character(0)

Field `species` can be either a `character` or a `factor`. It cannot contain any `NA` values.

Check `date` field

    is.numeric(garamba$"date")     # Are dates in a numerical format?
    #> [1] TRUE

    sum(is.na(garamba$"date"))     # Are there any missing values?
    #> [1] 0

    range(garamba$"date")          # What is the temporal extent?
    #> [1] 1976 2017

Field `date` must be a `numeric`. It cannot contain any `NA` values. This said, the time unit is arbitrary, and fractional values of years (or another unit) are allowed. As long as numeric values are entered, the package will work.

On the other hand, if you have a date format (e.g. ‘2021/05/19’), you need to convert it to a numeric format. For instance:

    ## Convert a character to a date object ----
    x <- as.Date("2021/05/19")
    x
    #> [1] "2021-05-19"

    ## Convert a date to a numeric (number of days since 1970/01/01) ----
    x <- as.numeric(x)
    x
    #> [1] 18766

    ## Check ----
    as.Date(x, origin = as.Date("1970/01/01"))
    #> [1] "2021-05-19"

Other methods exist to convert a `date` to a `numeric` format. You may prefer computing the number of days since the first date of your survey. It’s up to you.

Check `count` field

    is.numeric(garamba$"count")   # Are counts in a numerical format?
    #> [1] TRUE

    range(garamba$"count")        # What is the range of values?
    #> [1]     0 53312

    sum(is.na(garamba$"count"))   # Are there any missing values?
    #> [1] 0

Field `count` must be a positive `numeric` (zero counts are allowed). `NA` counts cannot be used for fitting trends. The `format_data()` function (see below) has an option for dropping them.

Check `stat_method` field

    unique(garamba$"stat_method")
    #> [1] "S" "T"

    sum(is.na(garamba$"stat_method"))   # Are there any missing values?
    #> [1] 0

Field `stat_method` can be either a `character` or a `factor`. It must contain only `T`, `X`, or `S` categories and cannot contain any `NA` values.

Check `field_method` field

    unique(garamba$"field_method")
    #> [1] "A"

    sum(is.na(garamba$"field_method"))   # Are there any missing values?
    #> [1] 0

Field `field_method` can be either a `character` or a `factor`. It must contain only `A`, or `G` categories and cannot contain any `NA` values.

## Formatting data

This first `popbayes` function to use is `format_data()`. This function provides an easy way to get individual count series ready to be analyzed by the package. It must be used prior to all other functions.

First let’s define the path (relative or absolute) to save objects/results, namely the formatted count series that can be extracted from the data set.

    path <- "the_folder_to_store_outputs"

The function `format_data()` has many arguments to provide the names of the columns in the user’s dataset that contain `location`, `species`, `lower_ci`, etc. By default column names are the same as in the Garamba dataset. If your location field, say, is “site”, you’ll need to use the argument `location` as follows: `location = "site"`.

    garamba_formatted <- popbayes::format_data(data              = garamba,
                                               path              = path,
                                               field_method      = "field_method",
                                               pref_field_method = "pref_field_method",
                                               conversion_A2G    = "conversion_A2G",
                                               rmax              = "rmax")
    #> ✔ Detecting 10 count series.

As said above, if you have to add your own count conversion data, you need specify the names of columns for the preferred field method, the conversion factor, and rmax as this: `pref_field_method = "column_with_preferred_field_method"`, `conversion_A2G = "column_with_conversion_A2Gor"`, `rmax = "column_with_conversion_rmax"`, or alternatively use the argument `info`: `info = "dataframe_with_conversion_info"`.

Let’s explore the output.

    ## Class of the object ----
    class(garamba_formatted)
    #> [1] "list"

    ## Number of elements (i.e. number of count series) ----
    length(garamba_formatted)
    #> [1] 10

    ## Get series names ----
    popbayes::list_series(path)
    #>  [1] "garamba__alcelaphus_buselaphus"  "garamba__giraffa_camelopardalis"
    #>  [3] "garamba__hippotragus_equinus"    "garamba__kobus_ellipsiprymnus"
    #>  [5] "garamba__kobus_kob"              "garamba__loxodonta_africana"
    #>  [7] "garamba__ourebia_ourebi"         "garamba__redunca_redunca"
    #>  [9] "garamba__syncerus_caffer"        "garamba__tragelaphus_scriptus"

Let’s work with the count series `"garamba__alcelaphus_buselaphus"`. We can use the function `filter_series()`.

    ## Retrieve series by species and location ----
    a_buselaphus <- popbayes::filter_series(data     = garamba_formatted,
                                            species  = "Alcelaphus buselaphus",
                                            location = "Garamba")
    #> ✔ Found 1 series with "Alcelaphus buselaphus" and "Garamba".

Let’s display the series content.

    print(a_buselaphus)
    #> $garamba__alcelaphus_buselaphus
    #> $garamba__alcelaphus_buselaphus$location
    #> [1] "Garamba"
    #>
    #> $garamba__alcelaphus_buselaphus$species
    #> [1] "Alcelaphus buselaphus"
    #>
    #> $garamba__alcelaphus_buselaphus$dates
    #>  [1] 1976 1983 1984 1986 1991 1993 1995 1998 2000 2002 2003 2004 2012 2014 2017
    #>
    #> $garamba__alcelaphus_buselaphus$n_dates
    #> [1] 15
    #>
    #> $garamba__alcelaphus_buselaphus$stat_methods
    #> [1] "S" "T"
    #>
    #> $garamba__alcelaphus_buselaphus$field_methods
    #> [1] "A"
    #>
    #> $garamba__alcelaphus_buselaphus$pref_field_method
    #> [1] "G"
    #>
    #> $garamba__alcelaphus_buselaphus$conversion_A2G
    #> [1] 2.302
    #>
    #> $garamba__alcelaphus_buselaphus$rmax
    #> [1] 0.2748
    #>
    #> $garamba__alcelaphus_buselaphus$data_original
    #>    location               species date stat_method field_method
    #> 1   Garamba Alcelaphus buselaphus 1976           S            A
    #> 2   Garamba Alcelaphus buselaphus 1983           S            A
    #> 3   Garamba Alcelaphus buselaphus 1984           S            A
    #> 4   Garamba Alcelaphus buselaphus 1986           S            A
    #> 5   Garamba Alcelaphus buselaphus 1991           S            A
    #> 6   Garamba Alcelaphus buselaphus 1993           S            A
    #> 7   Garamba Alcelaphus buselaphus 1995           S            A
    #> 8   Garamba Alcelaphus buselaphus 1998           S            A
    #> 9   Garamba Alcelaphus buselaphus 2000           S            A
    #> 10  Garamba Alcelaphus buselaphus 2002           S            A
    #> 11  Garamba Alcelaphus buselaphus 2003           S            A
    #> 12  Garamba Alcelaphus buselaphus 2004           S            A
    #> 13  Garamba Alcelaphus buselaphus 2012           T            A
    #> 14  Garamba Alcelaphus buselaphus 2014           T            A
    #> 15  Garamba Alcelaphus buselaphus 2017           T            A
    #>    pref_field_method conversion_A2G   rmax count_orig lower_ci_orig
    #> 1                  G          2.302 0.2748       7750          6280
    #> 2                  G          2.302 0.2748       1932          1120
    #> 3                  G          2.302 0.2748       1224           782
    #> 4                  G          2.302 0.2748       1705          1116
    #> 5                  G          2.302 0.2748        987           663
    #> 6                  G          2.302 0.2748       3444          1290
    #> 7                  G          2.302 0.2748       2819          1620
    #> 8                  G          2.302 0.2748       1685          1287
    #> 9                  G          2.302 0.2748       1169           945
    #> 10                 G          2.302 0.2748       1139           907
    #> 11                 G          2.302 0.2748       1595          1142
    #> 12                 G          2.302 0.2748       1204           811
    #> 13                 G          2.302 0.2748        552            NA
    #> 14                 G          2.302 0.2748        698            NA
    #> 15                 G          2.302 0.2748       1051            NA
    #>    upper_ci_orig
    #> 1           9220
    #> 2           2744
    #> 3           1666
    #> 4           2294
    #> 5           1311
    #> 6           5598
    #> 7           4018
    #> 8           2083
    #> 9           1393
    #> 10          1371
    #> 11          2048
    #> 12          1597
    #> 13            NA
    #> 14            NA
    #> 15            NA
    #>
    #> $garamba__alcelaphus_buselaphus$data_converted
    #>    location               species date stat_method field_method
    #> 1   Garamba Alcelaphus buselaphus 1976           S            A
    #> 2   Garamba Alcelaphus buselaphus 1983           S            A
    #> 3   Garamba Alcelaphus buselaphus 1984           S            A
    #> 4   Garamba Alcelaphus buselaphus 1986           S            A
    #> 5   Garamba Alcelaphus buselaphus 1991           S            A
    #> 6   Garamba Alcelaphus buselaphus 1993           S            A
    #> 7   Garamba Alcelaphus buselaphus 1995           S            A
    #> 8   Garamba Alcelaphus buselaphus 1998           S            A
    #> 9   Garamba Alcelaphus buselaphus 2000           S            A
    #> 10  Garamba Alcelaphus buselaphus 2002           S            A
    #> 11  Garamba Alcelaphus buselaphus 2003           S            A
    #> 12  Garamba Alcelaphus buselaphus 2004           S            A
    #> 13  Garamba Alcelaphus buselaphus 2012           T            A
    #> 14  Garamba Alcelaphus buselaphus 2014           T            A
    #> 15  Garamba Alcelaphus buselaphus 2017           T            A
    #>    pref_field_method conversion_A2G   rmax count_conv lower_ci_conv
    #> 1                  G          2.302 0.2748  17840.500     14456.560
    #> 2                  G          2.302 0.2748   4447.464      2578.240
    #> 3                  G          2.302 0.2748   2817.648      1800.164
    #> 4                  G          2.302 0.2748   3924.910      2569.032
    #> 5                  G          2.302 0.2748   2272.074      1526.226
    #> 6                  G          2.302 0.2748   7928.088      2969.580
    #> 7                  G          2.302 0.2748   6489.338      3729.240
    #> 8                  G          2.302 0.2748   3878.870      2962.674
    #> 9                  G          2.302 0.2748   2691.038      2175.390
    #> 10                 G          2.302 0.2748   2621.978      2087.914
    #> 11                 G          2.302 0.2748   3671.690      2628.884
    #> 12                 G          2.302 0.2748   2771.608      1866.922
    #> 13                 G          2.302 0.2748   1270.704      1207.169
    #> 14                 G          2.302 0.2748   1606.796      1526.456
    #> 15                 G          2.302 0.2748   2419.402      2298.432
    #>    upper_ci_conv field_method_conv
    #> 1      21224.440                 G
    #> 2       6316.688                 G
    #> 3       3835.132                 G
    #> 4       5280.788                 G
    #> 5       3017.922                 G
    #> 6      12886.596                 G
    #> 7       9249.436                 G
    #> 8       4795.066                 G
    #> 9       3206.686                 G
    #> 10      3156.042                 G
    #> 11      4714.496                 G
    #> 12      3676.294                 G
    #> 13      1524.845                 G
    #> 14      1928.155                 G
    #> 15      2903.282                 G

The first elements of the list provide a summary of the count series.

If we compare the two last data frames (`data_original` and `data_converted`), they are not identical. The function `format_data()` has 1) computed 95% CI boundaries for total counts (coded `T` in the column `stat_method`), and 2) converted all counts (and CI boundaries) to their equivalent in the preferred field method (from `A` to `G`) by applying the conversion factor of `2.302`.

The Bayesian model will use counts and precision measures from the `data_converted` data frame.

Before fitting the population size trend we can visualize the count series with `plot_series()`.

    popbayes::plot_series("garamba__alcelaphus_buselaphus", path = path)

The function `format_data()` has also exported the count series as `.RData` files in the `path` folder where they have been dispatched into sub-folders, one per series.

    list.files(path, recursive = TRUE)

    #>  [1] "garamba__alcelaphus_buselaphus/garamba__alcelaphus_buselaphus_data.RData"
    #>  [2] "garamba__giraffa_camelopardalis/garamba__giraffa_camelopardalis_data.RData"
    #>  [3] "garamba__hippotragus_equinus/garamba__hippotragus_equinus_data.RData"
    #>  [4] "garamba__kobus_ellipsiprymnus/garamba__kobus_ellipsiprymnus_data.RData"
    #>  [5] "garamba__kobus_kob/garamba__kobus_kob_data.RData"
    #>  [6] "garamba__loxodonta_africana/garamba__loxodonta_africana_data.RData"
    #>  [7] "garamba__ourebia_ourebi/garamba__ourebia_ourebi_data.RData"
    #>  [8] "garamba__redunca_redunca/garamba__redunca_redunca_data.RData"
    #>  [9] "garamba__syncerus_caffer/garamba__syncerus_caffer_data.RData"
    #> [10] "garamba__tragelaphus_scriptus/garamba__tragelaphus_scriptus_data.RData"

These `*_data.RData` files (count series) can be imported later by running the function `read_series()`.

    a_buselaphus <- popbayes::read_series("garamba__alcelaphus_buselaphus", path = path)

## Fitting trend

The function `fit_trend()` fits population trajectories over time from counts of individuals formatted by `format_data()`. It does so under a Bayesian framework where the primary quantity being modeled is the annual rate of increase (more generally, the rate of increase per the time unit used for dates).

This function only works on the output of `format_data()` (or `filter_series()`).

Here is the default usage of the function `fit_trend()`:

    a_buselaphus_bugs <- popbayes::fit_trend(a_buselaphus, path = path)

The function returns an n-element list (where n is the number of count series). Each element of the list is a BUGS output as provided by JAGS. It has also exported these BUGS outputs as `.RData` files in the `path` folder where they have been dispatched into sub-folders, one per series.

These `*_bugs.RData` files (BUGS outputs) can be imported later by running the function `read_bugs()`.

    a_buselaphus_bugs <- popbayes::read_bugs("garamba__alcelaphus_buselaphus", path = path)

The function `diagnostic()` allows to check if estimation of all parameters of the model has converged. This diagnostic is performed by comparing the `Rhat` value of each parameter to a `threshold` (default is `1.1`).

    popbayes::diagnostic(a_buselaphus_bugs)
    #> All models have converged.

In case convergence was not reached for some series, we suggest rerunning `fit_trend()` on these series after increasing the number of iterations (ni) and possibly the number of initial iterations discarded (nb) from their respective defaults of 50,000 and 10,000. For example:

    a_buselaphus_bugs <- popbayes::fit_trend(a_buselaphus, path = path, ni = 100000, nb = 20000)

This process may be repeated with increasing values of ni and nb until convergence is eventually reached.

Finally we can use the function `plot_trend()` to visualize model predictions and estimated yearly relative growth rates.

    popbayes::plot_trend("garamba__alcelaphus_buselaphus", path = path)

## References

- Cornelis D et al. (2014) Species account: African buffalo (Syncerus caffer). In: Ecology, Evolution and Behaviour of Wild Cattle: Implications for Conservation (Eds M Melletti & J Burton). Cambridge University Press, Cambridge. DOI: 10.1017/CBO9781139568098.

- Foley CAH & Faust LJ (2010) Rapid population growth in an elephant Loxodonta africana population recovering from poaching in Tarangire National Park, Tanzania. Oryx, 44, 205-212. DOI: 10.1017/S0030605309990706.

- Illius AW & Gordon IJ (1992) Modelling the nutritional ecology of ungulate herbivores: evolution of body size and competitive interactions. Oecologia, 89, 428-434. DOI: 10.1017/S0030605309990706.

- Kingdon J & Hoffman M (2013) Mammals of Africa. Volume VI: Pigs, Hippopotamuses, Chevrotain, Giraffes, Deer and Bovids. Bloomsbury Publishing, London, United Kingdom, 680 pp.

- Sinclair ARE (1996) Mammal populations: fluctuation, regulation, life history theory, and their implications for conservation. In: Frontiers of population ecology (Eds RB Floyd & AW Sheppard), pp. 127-154. CSIRO: Melbourne, Australia.

- Sinclair ARE (2003) Mammal population regulation, keystone processes and ecosystem dynamics. Philosophical Transactions: Biological Sciences, 358, 1729-1740. DOI: 10.1098/rstb.2003.1359.

- Suraud JP et al. (2012) Higher than expected growth rate of the endangered West African giraffe Giraffa camelopardalis peralta: a successful human-wildlife cohabitation. Oryx, 46, 577-583. DOI: 10.1017/S0030605311000639.