Introduction to the benthos-package
Introduction
The benthos-package provides functions for analysing
benthic data sets. To use the benthos package, some basic
knowledge of programming in R (R Core Team, 2017; www.r-project.org) is
assumed.
The functions in the benthos-package have been designed
to integrate seamlessly with those of the dplyr-package
(Wickham et al., 2017). The dplyr-package
implements a grammar of data manipulation to make data analysis more
efficient and clear.
The benthos-package is designed to use the forward-pipe
operator (%>%) provided by the
magrittr-package (Milton Bache & Wickham, 2014). This
operator can be used for chaining multiple data operations together.
This reduces the need for temporary variables or nested function calls
and leads to cleaner and more readable code. Consult the references
below and the corresponding package vignettes for more information.
The benthos-package follows the same philosophy as the
dplyr package: in stead of providing complicated functions
that can do many tasks (‘Swiss army knife’-functions), we provide a set
of ‘small functions that each do one thing well’ (Wickham &
Francois, 2017; ‘Introduction to dplyr vignette’). As a
consequence, you will not find functions in this package which perform a
complete analysis, rather it provides basic building blocks that you can
use to build your own functions and applications.
Loading the package
The benthos-package can be attached by means of
In this vignette, we also attach the dplyr,
tidyr, readr and ggplot2 packages
for data manipulation and visualization.
Sample data set
In the sections below, we will illustrate the
benthos-package by means of the Oosterschelde marine
benthos data set. This data set ships with the
benthos-package and can be loaded by typing:
The first 10 records of these data set are given below:
oosterschelde
# A tibble: 4,269 × 8
OBJECTID SAMPLEID DATE ID HABITAT AREA TAXON COUNT
<chr> <int> <date> <int> <chr> <dbl> <chr> <int>
1 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Aphelochaeta marioni 1
2 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Crangon crangon 1
3 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Nephtys hombergii 4
4 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Oligochaeta 5
5 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Pygospio elegans 12
6 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Scoloplos armiger 1
7 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Spio martinensis 1
8 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Spiophanes bombyx 8
9 nl89_oostsde 14957 2010-09-06 2 Polyhaline-Subtidal 0.0157 Corophium arenarium 1
10 nl89_oostsde 14957 2010-09-06 2 Polyhaline-Subtidal 0.0157 Nephtys cirrosa 1
# ℹ 4,259 more rowsType
to see the documentation of this data set.
Preprocessing
Data preprocessing is an important first step. In this section we will demonstrate some preprocessing steps.
Selecting variables and observations
As a simple preprocessing step, we will only consider samples (stored in rows) taken in August and September. These can be selected as follows:
Standardization of taxon names
Taxon names need to be standardized to comply with the names in the
WoRMS-database. The as_accepted-function does this
conversion by using the TWN-list (https://taxainfo.nl/). This list is based on the WoRMS
database (World Register of Marine Species, https://www.marinespecies.org/).
We can use the is_accepted-function to check if a taxon
complies with WoRMS:
oosterschelde %>%
mutate(COMPLIANT = is_accepted(taxon = TAXON)) %>%
select(OBJECTID, HABITAT, DATE, TAXON, COUNT, COMPLIANT)
# A tibble: 3,737 × 6
OBJECTID HABITAT DATE TAXON COUNT COMPLIANT
<chr> <chr> <date> <chr> <int> <lgl>
1 nl89_oostsde Polyhaline-Subtidal 2010-09-06 Aphelochaeta marioni 1 TRUE
2 nl89_oostsde Polyhaline-Subtidal 2010-09-06 Crangon crangon 1 TRUE
3 nl89_oostsde Polyhaline-Subtidal 2010-09-06 Nephtys hombergii 4 TRUE
4 nl89_oostsde Polyhaline-Subtidal 2010-09-06 Oligochaeta 5 TRUE
5 nl89_oostsde Polyhaline-Subtidal 2010-09-06 Pygospio elegans 12 TRUE
6 nl89_oostsde Polyhaline-Subtidal 2010-09-06 Scoloplos armiger 1 TRUE
7 nl89_oostsde Polyhaline-Subtidal 2010-09-06 Spio martinensis 1 TRUE
8 nl89_oostsde Polyhaline-Subtidal 2010-09-06 Spiophanes bombyx 8 TRUE
9 nl89_oostsde Polyhaline-Subtidal 2010-09-06 Corophium arenarium 1 TRUE
10 nl89_oostsde Polyhaline-Subtidal 2010-09-06 Nephtys cirrosa 1 TRUE
# ℹ 3,727 more rowsThis returns a logical vector with TRUE if a taxon
complies with WoRMS and FALSE otherwise. The total number
of records, compliant names, and missing names is given below
oosterschelde %>%
mutate(COMPLIANT = is_accepted(taxon = TAXON)) %>%
summarise(
N_RECORDS = n(),
N_COMPLIANT = sum(COMPLIANT),
N_MISSING = N_RECORDS - N_COMPLIANT
)
# A tibble: 1 × 3
N_RECORDS N_COMPLIANT N_MISSING
<int> <int> <int>
1 3737 3718 19Taxa not compliant with WoRMS (if any) are given below and will be removed:
oosterschelde %>%
filter(!is_accepted(taxon = TAXON))
# A tibble: 19 × 8
OBJECTID SAMPLEID DATE ID HABITAT AREA TAXON COUNT
<chr> <int> <date> <int> <chr> <dbl> <chr> <int>
1 nl89_oostsde 14964 2010-09-06 8 Polyhaline-Subtidal 0.0774 Crustacea 1
2 nl89_oostsde 14972 2010-09-06 16 Polyhaline-Subtidal 0.0157 Insecta 1
3 nl89_oostsde 14983 2010-09-07 17 Polyhaline-Subtidal 0.0157 Insecta 1
4 nl89_oostsde 15005 2010-09-07 39 Polyhaline-Subtidal 0.0157 Crustacea 1
5 nl89_oostsde 15025 2010-09-10 59 Polyhaline-Intertidal 0.0157 Insecta 3
6 nl89_oostsde 15075 2010-09-24 73 Polyhaline-Intertidal 0.0157 Insecta 1
7 nl89_oostsde 15468 2011-08-18 134 Polyhaline-Intertidal 0.0157 Animalia 1
8 nl89_oostsde 15260 2011-09-08 199 Polyhaline-Subtidal 0.0157 Animalia 1
9 nl89_oostsde 15507 2011-09-13 205 Polyhaline-Intertidal 0.0157 Animalia 1
10 nl89_oostsde 15241 2011-09-13 206 Polyhaline-Intertidal 0.0157 Animalia 1
11 nl89_oostsde 15509 2011-09-14 215 Polyhaline-Intertidal 0.0157 Animalia 1
12 nl89_oostsde 15631 2012-08-29 295 Polyhaline-Subtidal 0.0774 Animalia 1
13 nl89_oostsde 15633 2012-08-27 297 Polyhaline-Subtidal 0.0157 Crustacea 1
14 nl89_oostsde 15651 2012-08-29 315 Polyhaline-Subtidal 0.0157 Animalia 1
15 nl89_oostsde 15675 2012-08-27 339 Polyhaline-Subtidal 0.0157 Animalia 1
16 nl89_oostsde 15707 2012-09-18 369 Polyhaline-Intertidal 0.0157 Animalia 1
17 nl89_oostsde 15708 2012-09-06 370 Polyhaline-Intertidal 0.0157 Animalia 1
18 nl89_oostsde 15710 2012-08-20 372 Polyhaline-Intertidal 0.0157 Animalia 1
19 nl89_oostsde 15720 2012-08-20 382 Polyhaline-Intertidal 0.0157 Animalia 1
oosterschelde <- oosterschelde %>%
filter(is_accepted(taxon = TAXON))Other examples of the usage of the is_accepted and
as_accepted-functions are:
is_accepted(taxon = "Petricola pholadiformis")
[1] FALSE
as_accepted(taxon = "Petricola pholadiformis")
[1] "Petricolaria pholadiformis"
is_accepted(taxon = "Petricolaria pholadiformis")
[1] TRUEIf we want to make sure that all taxa names comply with WoRMS we simply use:
Taxon names that are not in the WoRMS/TWN-list get name
NA (not available):
In our case all names comply with those in WoRMS.
Genus to species conversion
Genus to species conversion reallocates the counts of taxa that are identified at the genus level to taxa in the same sampling unit and of the same genus but that are identified on the species level. The redistribution of counts is proportional to the number of counts of taxa at the species level (Van Loon et al., 2015).
The Oosterschelde data set only contains individuals at the genus and species level (individuals at higher order taxonomic levels have been removed for didactic purposes only).
It is convenient to split each taxon into its generic and specific name. This can be accomplished as follows:
oosterschelde <- oosterschelde %>%
mutate(
GENERIC = generic_name(TAXON),
SPECIFIC = specific_name(TAXON)
)
oosterschelde
# A tibble: 3,718 × 10
OBJECTID SAMPLEID DATE ID HABITAT AREA TAXON COUNT GENERIC SPECIFIC
<chr> <int> <date> <int> <chr> <dbl> <chr> <int> <chr> <chr>
1 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Apheloc… 1 Aphelo… marioni
2 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Crangon… 1 Crangon crangon
3 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Nephtys… 4 Nephtys homberg…
4 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Oligoch… 5 <NA> <NA>
5 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Pygospi… 12 Pygosp… elegans
6 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Scolopl… 1 Scolop… armiger
7 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Spio ma… 1 Spio martine…
8 nl89_oostsde 14956 2010-09-06 1 Polyhaline-Subtidal 0.0157 Spiopha… 8 Spioph… bombyx
9 nl89_oostsde 14957 2010-09-06 2 Polyhaline-Subtidal 0.0157 Corophi… 1 Coroph… arenari…
10 nl89_oostsde 14957 2010-09-06 2 Polyhaline-Subtidal 0.0157 Nephtys… 1 Nephtys cirrosa
# ℹ 3,708 more rowsBoth functions generic_name and
specific_name return NA if TAXON is not a
valid binomial. That is the case if a taxon has only been identified on
the genus level. For example:
We will create a new column to indicate these cases.
oosterschelde <- oosterschelde %>%
mutate(
IS_GENUS = is.na(GENERIC),
GENERIC = ifelse(IS_GENUS, TAXON, GENERIC)
)The number of taxa that has been identified at the genus level is
Genus to species conversion is performed for each genus in a sample
by means of the genus_to_species function:
oosterschelde <- oosterschelde %>%
group_by(ID, GENERIC) %>%
mutate(NEWCOUNT = genus_to_species(is_genus = IS_GENUS, count = COUNT)) %>%
ungroup
Corophium arenarium (left) and Corophium volutator (right) (source: https://nature22.com/)
To illustrate the algorithm, consider all records with generic name Corophium in sample 130:
oosterschelde %>%
filter(GENERIC == "Corophium", ID == 130) %>%
arrange(TAXON)
# A tibble: 3 × 12
OBJECTID SAMPLEID DATE ID HABITAT AREA TAXON COUNT GENERIC SPECIFIC IS_GENUS NEWCOUNT
<chr> <int> <date> <int> <chr> <dbl> <chr> <int> <chr> <chr> <lgl> <dbl>
1 nl89_oost… 15432 2011-08-18 130 Polyha… 0.0236 Coro… 5 Coroph… <NA> TRUE 0
2 nl89_oost… 15432 2011-08-18 130 Polyha… 0.0236 Coro… 17 Coroph… arenari… FALSE 21.5
3 nl89_oost… 15432 2011-08-18 130 Polyha… 0.0236 Coro… 2 Coroph… volutat… FALSE 2.53In this sample, the genus Corophium is identified 19 times at the species level, i.e., 17 times as Corophium arenarium and twice as Corophium volutator. For five individuals, the analyst was unable to identify the species name, and only reported the genus. The genus to species algorithm now proportionally reallocates the 5 individuals at the genus level to the taxa at the species level. That is, an additional $5 \times \frac{17}{17 + 2} = 4.47$ individuals will be classified as Corophium arenarium and $5 \times \frac{2}{17 + 2} = 0.53$ as Corophium volutator.
Note that the total number of species will not be affected:
oosterschelde %>%
summarise(sum(COUNT), sum(NEWCOUNT))
# A tibble: 1 × 2
`sum(COUNT)` `sum(NEWCOUNT)`
<int> <dbl>
1 33079 33079To finalize our analysis, we will set COUNT to the value of NEWCOUNT, and remove redundant columns and records.
oosterschelde <- oosterschelde %>%
mutate(COUNT = NEWCOUNT) %>%
select(ID, HABITAT, AREA, DATE, TAXON, COUNT) %>%
filter(COUNT > 0)
oosterschelde
# A tibble: 3,562 × 6
ID HABITAT AREA DATE TAXON COUNT
<int> <chr> <dbl> <date> <chr> <dbl>
1 1 Polyhaline-Subtidal 0.0157 2010-09-06 Aphelochaeta marioni 1
2 1 Polyhaline-Subtidal 0.0157 2010-09-06 Crangon crangon 1
3 1 Polyhaline-Subtidal 0.0157 2010-09-06 Nephtys hombergii 4
4 1 Polyhaline-Subtidal 0.0157 2010-09-06 Oligochaeta 5
5 1 Polyhaline-Subtidal 0.0157 2010-09-06 Pygospio elegans 12
6 1 Polyhaline-Subtidal 0.0157 2010-09-06 Scoloplos armiger 1
7 1 Polyhaline-Subtidal 0.0157 2010-09-06 Spio martinensis 1
8 1 Polyhaline-Subtidal 0.0157 2010-09-06 Spiophanes bombyx 8
9 2 Polyhaline-Subtidal 0.0157 2010-09-06 Corophium arenarium 1
10 2 Polyhaline-Subtidal 0.0157 2010-09-06 Nephtys cirrosa 1
# ℹ 3,552 more rowsData pooling
Analysis results make only sense when all sampling units are collected on the same support. That is not the case for the oosterschelde data:
d <- oosterschelde %>%
group_by(AREA) %>%
summarise(n = n())
d
# A tibble: 3 × 2
AREA n
<dbl> <int>
1 0.0157 3229
2 0.0236 81
3 0.0774 252We distinguish three different supports (0.0157, 0.0236, 0.0774 m2). In this section, we will demonstrate how to pool these data to approximately the same support in the range from 0.09 to 0.11 m2. See Van Loon et al. (2015) for more details.
We will only pool samples of the same year, so we’ll start by adding a new column to our table containing the year:
Next, we will randomly pool samples for each HABITAT and YEAR. We
will pool several times (in the example below
n_pool_runs = 10), to reduce the effect of pool composition
and to make sure that each sample will be represented in a pool (no
leftovers on average).
n_pool_runs <- 10
pool_runs <- replicate(
n = n_pool_runs, {
oosterschelde %>%
group_by(HABITAT, YEAR) %>%
mutate(
POOLID = pool(
sample_id = ID,
area = AREA,
target_area = c(0.09, 0.11)
)
) %>%
ungroup %>%
select(POOLID)
}
)This procedure will return al list of pool identifiers (POOLID) for each pool run:
names(pool_runs) <- paste0("POOLRUN", 1:n_pool_runs)
pool_runs <- pool_runs %>% as_tibble
pool_runs
# A tibble: 3,562 × 10
POOLRUN1 POOLRUN2 POOLRUN3 POOLRUN4 POOLRUN5 POOLRUN6 POOLRUN7 POOLRUN8 POOLRUN9 POOLRUN10
<int> <int> <int> <int> <int> <int> <int> <int> <int> <int>
1 7 NA 3 1 2 NA 10 NA NA NA
2 7 NA 3 1 2 NA 10 NA NA NA
3 7 NA 3 1 2 NA 10 NA NA NA
4 7 NA 3 1 2 NA 10 NA NA NA
5 7 NA 3 1 2 NA 10 NA NA NA
6 7 NA 3 1 2 NA 10 NA NA NA
7 7 NA 3 1 2 NA 10 NA NA NA
8 7 NA 3 1 2 NA 10 NA NA NA
9 9 2 6 3 2 4 8 3 8 10
10 9 2 6 3 2 4 8 3 8 10
# ℹ 3,552 more rowsEach row in this table corresponds to the row with the same index in
oosterschelde. Therefore, it is quite easy to combine this
table with the ‘oosterschelde’ data:
oosterschelde_orig <- oosterschelde
oosterschelde <- oosterschelde %>%
bind_cols(pool_runs) %>%
as_tibble
oosterschelde
# A tibble: 3,562 × 17
ID HABITAT AREA DATE TAXON COUNT YEAR POOLRUN1 POOLRUN2 POOLRUN3 POOLRUN4 POOLRUN5
<int> <chr> <dbl> <date> <chr> <dbl> <chr> <int> <int> <int> <int> <int>
1 1 Polyhalin… 0.0157 2010-09-06 Aphe… 1 2010 7 NA 3 1 2
2 1 Polyhalin… 0.0157 2010-09-06 Cran… 1 2010 7 NA 3 1 2
3 1 Polyhalin… 0.0157 2010-09-06 Neph… 4 2010 7 NA 3 1 2
4 1 Polyhalin… 0.0157 2010-09-06 Olig… 5 2010 7 NA 3 1 2
5 1 Polyhalin… 0.0157 2010-09-06 Pygo… 12 2010 7 NA 3 1 2
6 1 Polyhalin… 0.0157 2010-09-06 Scol… 1 2010 7 NA 3 1 2
7 1 Polyhalin… 0.0157 2010-09-06 Spio… 1 2010 7 NA 3 1 2
8 1 Polyhalin… 0.0157 2010-09-06 Spio… 8 2010 7 NA 3 1 2
9 2 Polyhalin… 0.0157 2010-09-06 Coro… 1 2010 9 2 6 3 2
10 2 Polyhalin… 0.0157 2010-09-06 Neph… 1 2010 9 2 6 3 2
# ℹ 3,552 more rows
# ℹ 5 more variables: POOLRUN6 <int>, POOLRUN7 <int>, POOLRUN8 <int>, POOLRUN9 <int>,
# POOLRUN10 <int>It was not always possible to use all samples for pooling. These
‘leftover’ samples have POOLID NA. However, on average each
sample has been pooled between 5 and 10 times.
For further analysis, it is convenient to convert this table from
‘wide’ to ‘long’-format. This can be done efficiently by functions of
the tidyr-package (Wickham, 2017), which provides an
interesting framework to tidy your data (Wickham, 2014).
oosterschelde <- oosterschelde %>%
gather(key = "POOLRUN", value = "POOLID", starts_with("POOLRUN")) %>%
mutate(POOLRUN = parse_number(POOLRUN) %>% as.integer) %>%
filter(!is.na(POOLID)) %>%
select(POOLRUN, POOLID, HABITAT, AREA, YEAR, ID, TAXON, COUNT)
oosterschelde
# A tibble: 33,439 × 8
POOLRUN POOLID HABITAT AREA YEAR ID TAXON COUNT
<int> <int> <chr> <dbl> <chr> <int> <chr> <dbl>
1 1 7 Polyhaline-Subtidal 0.0157 2010 1 Aphelochaeta marioni 1
2 1 7 Polyhaline-Subtidal 0.0157 2010 1 Crangon crangon 1
3 1 7 Polyhaline-Subtidal 0.0157 2010 1 Nephtys hombergii 4
4 1 7 Polyhaline-Subtidal 0.0157 2010 1 Oligochaeta 5
5 1 7 Polyhaline-Subtidal 0.0157 2010 1 Pygospio elegans 12
6 1 7 Polyhaline-Subtidal 0.0157 2010 1 Scoloplos armiger 1
7 1 7 Polyhaline-Subtidal 0.0157 2010 1 Spio martinensis 1
8 1 7 Polyhaline-Subtidal 0.0157 2010 1 Spiophanes bombyx 8
9 1 9 Polyhaline-Subtidal 0.0157 2010 2 Corophium arenarium 1
10 1 9 Polyhaline-Subtidal 0.0157 2010 2 Nephtys cirrosa 1
# ℹ 33,429 more rowsTo check if the pooling algorithm succeeded in its task, we compute the area of each pool. These areas should vary between 0.09 and 0.11 m2, i.e., our target area.
d <- oosterschelde %>%
group_by(HABITAT, YEAR, POOLRUN, POOLID) %>%
select(ID, AREA) %>%
distinct(ID, AREA) %>%
summarise(AREA = sum(AREA))
Adding missing grouping variables: `HABITAT`, `YEAR`, `POOLRUN`, `POOLID`
`summarise()` has grouped output by 'HABITAT', 'YEAR', 'POOLRUN'. You can override using the
`.groups` argument.
d
# A tibble: 569 × 5
# Groups: HABITAT, YEAR, POOLRUN [60]
HABITAT YEAR POOLRUN POOLID AREA
<chr> <chr> <int> <int> <dbl>
1 Polyhaline-Intertidal 2010 1 1 0.0942
2 Polyhaline-Intertidal 2010 1 2 0.0942
3 Polyhaline-Intertidal 2010 1 3 0.0942
4 Polyhaline-Intertidal 2010 1 4 0.0942
5 Polyhaline-Intertidal 2010 1 5 0.0942
6 Polyhaline-Intertidal 2010 1 6 0.0942
7 Polyhaline-Intertidal 2010 1 7 0.0942
8 Polyhaline-Intertidal 2010 2 1 0.0942
9 Polyhaline-Intertidal 2010 2 2 0.0942
10 Polyhaline-Intertidal 2010 2 3 0.0942
# ℹ 559 more rowsThe following code computes the frequencies of the available areas:
d <- d %>%
select(AREA) %>%
group_by(AREA) %>%
summarise(n = n()) %>%
arrange(AREA)
Adding missing grouping variables: `HABITAT`, `YEAR`, `POOLRUN`
d
# A tibble: 6 × 2
AREA n
<dbl> <int>
1 0.0931 65
2 0.0942 421
3 0.0943 10
4 0.102 46
5 0.109 25
6 0.11 2This is also visualized in the bar graph below. All the pooled areas are nicely within the target area demarcated by the red lines.
Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
The pooled samples can be used to estimate biodiversity measures (see the next section for details). For instance, the species richness for each pool is given by:
d <- oosterschelde %>%
group_by(HABITAT, YEAR, POOLRUN, POOLID) %>%
summarise(S = species_richness(taxon = TAXON, count = COUNT))
`summarise()` has grouped output by 'HABITAT', 'YEAR', 'POOLRUN'. You can override using the
`.groups` argument.
d
# A tibble: 569 × 5
# Groups: HABITAT, YEAR, POOLRUN [60]
HABITAT YEAR POOLRUN POOLID S
<chr> <chr> <int> <int> <int>
1 Polyhaline-Intertidal 2010 1 1 24
2 Polyhaline-Intertidal 2010 1 2 41
3 Polyhaline-Intertidal 2010 1 3 21
4 Polyhaline-Intertidal 2010 1 4 27
5 Polyhaline-Intertidal 2010 1 5 31
6 Polyhaline-Intertidal 2010 1 6 28
7 Polyhaline-Intertidal 2010 1 7 28
8 Polyhaline-Intertidal 2010 2 1 25
9 Polyhaline-Intertidal 2010 2 2 25
10 Polyhaline-Intertidal 2010 2 3 29
# ℹ 559 more rowsThe annual mean species richness for each habitat and year is given by:
d <- d %>%
group_by(HABITAT, YEAR) %>%
summarise(S = mean(S))
`summarise()` has grouped output by 'HABITAT'. You can override using the `.groups` argument.
d
# A tibble: 6 × 3
# Groups: HABITAT [2]
HABITAT YEAR S
<chr> <chr> <dbl>
1 Polyhaline-Intertidal 2010 28.6
2 Polyhaline-Intertidal 2011 34.8
3 Polyhaline-Intertidal 2012 32.3
4 Polyhaline-Subtidal 2010 35.6
5 Polyhaline-Subtidal 2011 46.7
6 Polyhaline-Subtidal 2012 46.9
Biodiversity measures
Several biodiversity measures have been implemented in the
benthos-package. In the sections below, we will demonstrate
how to calculate these measures. To simplify things, all analysis will
be performed on a single sampling unit:
d <- oosterschelde %>%
filter(HABITAT == "Polyhaline-Subtidal", YEAR == 2010, POOLRUN == 1, POOLID == 1) %>%
select(TAXON, COUNT) %>%
arrange(TAXON)
d
# A tibble: 41 × 2
TAXON COUNT
<chr> <dbl>
1 Angulus tenuis 1
2 Aphelochaeta marioni 1
3 Aphelochaeta marioni 25
4 Bathyporeia 2
5 Capitella capitata 2
6 Cossura longocirrata 1
7 Echinocardium cordatum 1
8 Ensis 1
9 Lanice conchilega 4
10 Magelona johnstoni 2
# ℹ 31 more rows
Measures of species abundance
Total abundance
The total abundance is the total number of individuals in a sampling unit, and is computed by:
Abundance
The abundance is the total number of individuals per taxon in a
sampling unit. It can be computed by means of the
abundance-function:
d %>% abundance(taxon = TAXON, count = COUNT) %>% as.matrix
[,1]
Angulus tenuis 1
Aphelochaeta marioni 26
Bathyporeia 2
Capitella capitata 2
Cossura longocirrata 1
Echinocardium cordatum 1
Ensis 1
Lanice conchilega 4
Magelona johnstoni 3
Magelona papillicornis 1
Malmgreniella lunulata 1
Mytilus edulis 1
Nemertea 1
Nephtys 8
Nephtys hombergii 1
Oligochaeta 8
Ophiura albida 6
Peringia ulvae 1
Poecilochaetus serpens 1
Pseudopolydora pulchra 1
Retusa obtusa 4
Scoloplos armiger 22
Spio martinensis 1
Spiophanes bombyx 17
Spisula 1
Streblospio benedicti 1
Tellimya ferruginosa 1
Terebellidae 1
Urothoe poseidonis 12Measures of species richness
Species richness
Species richness S is the number of different species in a (pooled) sample. It can be computed by means of
Margalef’s index of diversity
Species richness S is strongly dependent on sampling size. Margalef’s diversity index DM takes sampling size into account. It is given by $$ D_\mathrm{M} = \frac{S-1}{\ln(N)} $$ where N is the total abundance, i.e, the total number of individuals in the sampling unit. In case N = 1, this index will be set to zero.
It can be computed for a specific sampling unit by:
Rygg’s index of diversity
Species richness S is strongly dependent on sampling size. Like Margalef’s diversity index DM, Rygg’s index of diversity takes sampling size into account (Rygg, 2006). It is given by $$ SN = \frac{\ln{S}}{\ln(\ln(N))} $$ where N is the total abundance, i.e, the total number of individuals in the sampling unit.
It can be computed for a specific sampling unit by:
Rygg’s index shows some inconsistencies for small N and S ((S=2, N=2), (S=2, N=3) and (S=3, N=3)). This is illustrated in the third figure below. As a reference, also Margalef’s index is given in the top figure.
The second figure shows a graph based on the adjusted version of Rygg’s index. It is given by:
$$ SNA = \frac{\ln{S}}{\ln(\ln(N+1)+1)} $$
The adjusted version of Rygg’s index can be computed by means of:
Hurlbert’s E(Sn)
Hurlbert (1971) gives the expected number of species in a sample of n individuals selected at random (without replacement) from a collection of N individuals and S species:
$$ \mathrm{E}(S_n) = \sum_{i=1}^S \left[1 - \frac{\binom{N-N_i}{n}}{\binom{N}{n}} \right] $$
Contrary to species richness, this measure is not dependent on the number of individuals. It can be computed for a specific sampling unit by:
E(Sn) can be computed for n ∈ 1, 2, …, N, where N is the total abundance. This has been done in the figure below.
Note that E(Sn) can be computed for n ≤ N. Extrapolation, i.e. n > N, is not possible.
Measures of heterogeneity/evenness
Simpson’s Measure of Concentration
Simpson’s Measure of Concentration gives the probability that two individuals selected at random from a sample will belong to the same species. For an infinite sample Simpson’s Index is given by: $$ \lambda = \sum_{i=1}^S \pi_i^2 $$ where πi the proportion of the individuals in species i. For a finite sample, Simpson’s index is: $$ L = \sum_{i=1}^S \frac{n_i (n_i-1)}{N (N-1)} $$ where ni the number of individuals in species i and N the total number of individuals.
The finite sample case can be computed by:
Hurlbert’s Probability of Interspecific Encounter (PIE)
Related to Simpson’s index is Hurlbert’s probability of inter-specific encounter (PIE). It gives the probability that two individuals selected at random (without replacement) from a sample will belong to different species (Hurlbert, 1971, p.579, Eq. 3): $$ \Delta_1 = \sum_{i=1}^S \left(\frac{N_i}{N}\right)\left(\frac{N-N_i}{N-1}\right) = \left(\frac{N}{N-1}\right)\Delta_2 $$ where Δ2 (Hurlbert, 1971, p.579, Eq. 4) is the probability that two individuals selected at random (with replacement) from a sample will belong to different species: $$ \Delta_2 = 1 - \sum_{i=1}^S \pi_i^2 $$ where Ni is the number of individuals of the ith species in the community, N is the total number of individuals in the community, πi = Ni/N, and S is the number of species in the community.
Hurlbert’s PIE can be computed by means of:
Note that it is the complement of Simpson’s Measure of Concentration (for finite sample sizes):
Shannon’s Index
Shannon’s index (or entropy) is given by:
H′ = −∑ipilog2pi where pi is the proportion of individuals found in taxon i. It can be computed for a specific sampling unit by:
Hill’s Diversity Numbers
According to Hill (1973): ‘a diversity number is figuratively a measure of how many species are present if we examine the sample down to a certain depth among its rarities. If we examine superficially (e.g., by using N2) we shall see only the more abundant species. If we look deeply e.g. by using N0 we shall see all the species present.’. His diversity number is given by: $$ N_a = \left(\sum_{i=1}^S p_i^a\right)^{1/(1-a)} $$
Depending on parameter a, Hill’s numbers gradually give more weight to the rarest species (small a) or most common species (large a).
Special cases are:
- N0: total number of species present
- N1: exp (H′), where H′: Shannon’s index
- N2: reciprocal of Simpson’s index ($\frac{1}{\lambda}$)
d %>% hill(taxon = TAXON, count = COUNT, a = 0)
[1] 29
d %>% hill(taxon = TAXON, count = COUNT, a = 1)
N_a(a=1) is undefined. Therefore N_a(lim a->1) will be returned
[1] 14.11342
d %>% hill(taxon = TAXON, count = COUNT, a = 2)
[1] 9.413604or (efficient) short cuts:
d %>% hill0(taxon = TAXON, count = COUNT)
[1] 29
d %>% hill1(taxon = TAXON, count = COUNT)
[1] 14.11342
d %>% hill2(taxon = TAXON, count = COUNT)
[1] 9.413604The figure below shows Hill’s Diversity Number as function of a. From right to left, the focus is
more and more on rare species.
Measures of species sensitivity
AZTI Marine Biotic Index (AMBI)
Borja et al. (2000) introduced the Biotic Coefficient. The expression in their paper can be rewritten as: $$ c_\mathrm{b} = \frac{3}{2} \sum_{i=2}^5 (i-1) p_i $$ where p is a vector of length 5 containing the proportions of species in the sensitivity classes (I, II, III, IV, V) respectively.
It can be computed for a specific sampling unit by:
d %>%
ambi(taxon = TAXON, count = COUNT)
Warning: `filter_()` was deprecated in dplyr 0.7.0.
ℹ Please use `filter()` instead.
ℹ See vignette('programming') for more help
ℹ The deprecated feature was likely used in the benthos package.
Please report the issue to the authors.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
Warning: `select_()` was deprecated in dplyr 0.7.0.
ℹ Please use `select()` instead.
ℹ The deprecated feature was likely used in the benthos package.
Please report the issue to the authors.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
Warning: `summarise_()` was deprecated in dplyr 0.7.0.
ℹ Please use `summarise()` instead.
ℹ The deprecated feature was likely used in the benthos package.
Please report the issue to the authors.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
Warning: `mutate_()` was deprecated in dplyr 0.7.0.
ℹ Please use `mutate()` instead.
ℹ See vignette('programming') for more help
ℹ The deprecated feature was likely used in the benthos package.
Please report the issue to the authors.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
Warning: `arrange_()` was deprecated in dplyr 0.7.0.
ℹ Please use `arrange()` instead.
ℹ See vignette('programming') for more help
ℹ The deprecated feature was likely used in the benthos package.
Please report the issue to the authors.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
Warning: `group_by_()` was deprecated in dplyr 0.7.0.
ℹ Please use `group_by()` instead.
ℹ See vignette('programming') for more help
ℹ The deprecated feature was likely used in the benthos package.
Please report the issue to the authors.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
[1] 2.734615The accuracy of the AMBI depends (among other things) on the number
of taxa for which a sensitivity group is available. The
has_ambi function indicates if a group has been assigned to
a taxa or not: Taxa with an AMBI sensitivity group are
d %>%
mutate(HAS_GROUP = has_ambi(taxon = TAXON))
# A tibble: 41 × 3
TAXON COUNT HAS_GROUP
<chr> <dbl> <lgl>
1 Angulus tenuis 1 TRUE
2 Aphelochaeta marioni 1 TRUE
3 Aphelochaeta marioni 25 TRUE
4 Bathyporeia 2 TRUE
5 Capitella capitata 2 TRUE
6 Cossura longocirrata 1 TRUE
7 Echinocardium cordatum 1 TRUE
8 Ensis 1 TRUE
9 Lanice conchilega 4 TRUE
10 Magelona johnstoni 2 TRUE
# ℹ 31 more rowsThe percentage of the total abundance without an AMBI group is given below
d %>%
mutate(HAS_GROUP = has_ambi(taxon = TAXON)) %>%
summarise(percentage = 100 * sum(COUNT[!HAS_GROUP]) / sum(COUNT)) %>%
as.numeric
[1] 0.7633588Infaunal Trophic Index (ITI)
The infaunal trophic index (ITI) is calculated as: $$ \mathrm{ITI} = 100 \sum_{i=1}^3 \frac{(4-i)}{3} p_i $$ where pi is the proportion of species in class i, where
- class 1 are suspension feeders (highest quality);
- class 2 are interface feeders;
- class 3 are surface deposit feeders and
- class 4 are subsurface deposit feeders (lowest quality).
See Gittenberger & van Loon (2013) for more information.
We can estimate the ITI by means of:
The accuracy of the ITI depends (among other things) on the number of
taxa for which a sensitivity group is available. The
has_iti function indicates if a group has been assigned to
a taxa or not: Taxa with an ITI sensitivity group are
d %>%
mutate(HAS_GROUP = has_iti(taxon = TAXON))
# A tibble: 41 × 3
TAXON COUNT HAS_GROUP
<chr> <dbl> <lgl>
1 Angulus tenuis 1 TRUE
2 Aphelochaeta marioni 1 TRUE
3 Aphelochaeta marioni 25 TRUE
4 Bathyporeia 2 TRUE
5 Capitella capitata 2 TRUE
6 Cossura longocirrata 1 TRUE
7 Echinocardium cordatum 1 TRUE
8 Ensis 1 TRUE
9 Lanice conchilega 4 TRUE
10 Magelona johnstoni 2 TRUE
# ℹ 31 more rowsThe percentage of the total abundance without an ITI group is given below
d %>%
mutate(HAS_GROUP = has_iti(taxon = TAXON)) %>%
summarise(percentage = 100 * sum(COUNT[!HAS_GROUP]) / sum(COUNT)) %>%
as.numeric
[1] 0.7633588
Calculating multiple biodiversity measures in one go
Multiple measures of biodiversity for a specified grouping of the data can be computed for all sampling units by means of:
oosterschelde %>%
group_by(HABITAT, YEAR, POOLRUN, POOLID) %>%
summarise(
N = total_abundance(count = COUNT),
S = species_richness(taxon = TAXON, count = COUNT),
D = margalef(taxon = TAXON, count = COUNT),
SN = rygg(taxon = TAXON, count = COUNT),
SNa = rygg(taxon = TAXON, count = COUNT, adjusted = TRUE),
H = shannon(taxon = TAXON, count = COUNT)
)
`summarise()` has grouped output by 'HABITAT', 'YEAR', 'POOLRUN'. You can override using the
`.groups` argument.
# A tibble: 569 × 10
# Groups: HABITAT, YEAR, POOLRUN [60]
HABITAT YEAR POOLRUN POOLID N S D SN SNa H
<chr> <chr> <int> <int> <dbl> <int> <dbl> <dbl> <dbl> <dbl>
1 Polyhaline-Intertidal 2010 1 1 519 24 3.68 1.73 1.60 2.41
2 Polyhaline-Intertidal 2010 1 2 616 41 6.23 2.00 1.85 3.64
3 Polyhaline-Intertidal 2010 1 3 370 21 3.38 1.71 1.57 2.67
4 Polyhaline-Intertidal 2010 1 4 283 27 4.61 1.90 1.74 3.58
5 Polyhaline-Intertidal 2010 1 5 515 31 4.80 1.87 1.73 2.79
6 Polyhaline-Intertidal 2010 1 6 368 28 4.57 1.88 1.72 3.45
7 Polyhaline-Intertidal 2010 1 7 595 28 4.23 1.80 1.67 3.16
8 Polyhaline-Intertidal 2010 2 1 500 25 3.86 1.76 1.63 2.66
9 Polyhaline-Intertidal 2010 2 2 413 25 3.98 1.79 1.65 3.33
10 Polyhaline-Intertidal 2010 2 3 394 29 4.69 1.88 1.73 3.83
# ℹ 559 more rowsor more concise:
oosterschelde %>%
group_by(HABITAT, YEAR, POOLRUN, POOLID) %>%
summarise(
N = total_abundance(., COUNT),
S = species_richness(., TAXON, COUNT),
D = margalef(., TAXON, COUNT),
SN = rygg(., TAXON, COUNT),
SNa = rygg(., TAXON, COUNT, adjusted = TRUE),
H = shannon(., TAXON, COUNT)
)
`summarise()` has grouped output by 'HABITAT', 'YEAR', 'POOLRUN'. You can override using the
`.groups` argument.
# A tibble: 569 × 10
# Groups: HABITAT, YEAR, POOLRUN [60]
HABITAT YEAR POOLRUN POOLID N S D SN SNa H
<chr> <chr> <int> <int> <dbl> <int> <dbl> <dbl> <dbl> <dbl>
1 Polyhaline-Intertidal 2010 1 1 519 24 3.68 1.73 1.60 2.41
2 Polyhaline-Intertidal 2010 1 2 616 41 6.23 2.00 1.85 3.64
3 Polyhaline-Intertidal 2010 1 3 370 21 3.38 1.71 1.57 2.67
4 Polyhaline-Intertidal 2010 1 4 283 27 4.61 1.90 1.74 3.58
5 Polyhaline-Intertidal 2010 1 5 515 31 4.80 1.87 1.73 2.79
6 Polyhaline-Intertidal 2010 1 6 368 28 4.57 1.88 1.72 3.45
7 Polyhaline-Intertidal 2010 1 7 595 28 4.23 1.80 1.67 3.16
8 Polyhaline-Intertidal 2010 2 1 500 25 3.86 1.76 1.63 2.66
9 Polyhaline-Intertidal 2010 2 2 413 25 3.98 1.79 1.65 3.33
10 Polyhaline-Intertidal 2010 2 3 394 29 4.69 1.88 1.73 3.83
# ℹ 559 more rows
Advanced topics
Number of pool runs and species richness
In the previous section we used 10 pool runs. But is this sufficient to stabilize the results? In this section we will demonstrate the effect of pooling on the average species richness. We will reuse large sections of the code given earlier in this document:
oosterschelde <- oosterschelde_orig
n_pool_runs <- 100
pool_runs <- replicate(
n = n_pool_runs, {
oosterschelde %>%
group_by(HABITAT, YEAR) %>%
mutate(
POOLID = pool(
sample_id = ID,
area = AREA,
target_area = c(0.09, 0.11)
)
) %>%
ungroup %>%
select(POOLID)
}
)
names(pool_runs) <- paste0("POOLRUN", 1:n_pool_runs)
d <- pool_runs %>%
as_tibble %>%
bind_cols(oosterschelde) %>%
as_tibble %>%
gather(key = "POOLRUN", value = "POOLID", starts_with("POOLRUN")) %>%
mutate(POOLRUN = parse_number(POOLRUN) %>% as.integer) %>%
filter(!is.na(POOLID)) %>%
select(POOLRUN, POOLID, HABITAT, AREA, YEAR, ID, TAXON, COUNT) %>%
group_by(HABITAT, YEAR, POOLRUN, POOLID) %>%
summarise(S = species_richness(taxon = TAXON, count = COUNT)) %>%
group_by(HABITAT, YEAR, POOLRUN) %>%
summarise(S = mean(S)) %>%
mutate(S_rm = cummean(S))
`summarise()` has grouped output by 'HABITAT', 'YEAR', 'POOLRUN'. You can override using the
`.groups` argument.
`summarise()` has grouped output by 'HABITAT', 'YEAR'. You can override using the `.groups`
argument.
d
# A tibble: 600 × 5
# Groups: HABITAT, YEAR [6]
HABITAT YEAR POOLRUN S S_rm
<chr> <chr> <int> <dbl> <dbl>
1 Polyhaline-Intertidal 2010 1 29.4 29.4
2 Polyhaline-Intertidal 2010 2 29.9 29.6
3 Polyhaline-Intertidal 2010 3 27 28.8
4 Polyhaline-Intertidal 2010 4 27.9 28.5
5 Polyhaline-Intertidal 2010 5 28.6 28.5
6 Polyhaline-Intertidal 2010 6 27.6 28.4
7 Polyhaline-Intertidal 2010 7 28.7 28.4
8 Polyhaline-Intertidal 2010 8 27.4 28.3
9 Polyhaline-Intertidal 2010 9 27.7 28.2
10 Polyhaline-Intertidal 2010 10 28.9 28.3
# ℹ 590 more rowsThe results are given in the figure below. The blue dots give the species richness for each pool-run for each year and habitat. The red line is the running mean species richness. In general, it stabilizes quickly.
References
Borja, A., J. Franco and V. Perez (2000). A Marine Biotic Index to Establish the Ecological Quality of Soft-Bottom Benthos Within European Estuarine and Coastal Environments. Marine Pollution Bulletin 40: 1100-1114
Gittenberger A. and W. van Loon, (2013). Sensitivities of marine macrozoobenthos to environmental pressures in the Netherlands. Nederlandse Faunistische Mededelingen 41: 79-112.
Hill, M.O., 1973. Diversity and Evenness: A Unifying Notation and Its Consequences. Ecology 54:427-432
Hurlbert, S.H., 1971. The Nonconcept of Species Diversity: A Critique and Alternative Parameters. Ecology 52:577-586.
Milton Bache, S. and H. Wickham (2014). magrittr: A Forward-Pipe Operator for R. R package version 1.5. https://CRAN.R-project.org/package=magrittr
Peet, R. K. 1974, The Measurement of Species Diversity. Annual Review of Ecology and Systematics 5:285-307.
R Core Team (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
Rygg, B. (2006). Developing indices for quality-status classification of marine soft-bottom fauna in Norway. Norwegian Institute for Water Research, Oslo, Norway. NIVA Report SNO 5208-2006.
Van Loon, W.M.G.M. A.R. Boon, A. Gittenberger, D.J.J. Walvoort, M. Lavaleye, G.C.A. Duineveld, A.J. Verschoor, 2015. Application of the Benthic Ecosystem Quality Index 2 to benthos in Dutch transitional and coastal waters. Journal of Sea Research 103:1-13.
Wickham, H. (2014). Tidy data. The Journal of Statistical Software, vol. 59, 2014.
Wickham, H. (2017). tidyr: Easily Tidy Data with spread() and gather() Functions. R package version 0.7.2. https://CRAN.R-project.org/package=tidyr
Wickham, H. R. Francois, L. Henry and K. Müller (2017). dplyr: A Grammar of Data Manipulation. R package version 0.7.4. https://CRAN.R-project.org/package=dplyr