20 Expected Number of Species
Description: Time Series of Expected Number of Species per Tow in NEFSC BTS
Found in: State of the Ecosystem - Gulf of Maine & Georges Bank (2021+), State of the Ecosystem - Mid-Atlantic (2021+)
Indicator category: Database pull with analysis; Published methods
Contributor(s): Sean Lucey
Data steward: Sean Lucey, sean.lucey@noaa.gov
Point of contact: Sean Lucey, sean.lucey@noaa.gov
Public availability statement:
20.1 Methods
Diversity estimates have been developed to understand whether the overall structure of the ecosystem has remained stable or is changing. There are a large number of diversity indices that can be used to measure diversity; for the purposes of the State of the Ecosystem report we report on the expected number of species in a sample size (\(E(S_n)\)). This index was originally developed by Sanders (1968) and later refined by Hurlbert (1971) using a hypergeometric probability distribution. These “rarefied” samples allow for comparisons between sample sites with varying number of species present. The estimate of \(E(S_n)\) is less biased than other diversity indices which usually increase with sample size. It also has a more meaningful biological interpretation than other indices. For example, if a predator eats 10 random individuals, \(E(S_n)\) will predict the number of species consumed.
20.1.1 Data sources
Data used for the calculation of the expected number of species come from the Northeast Fisheries Science Center’s survey database (SVDBS) as pulled in the Survdat data set. These data are available to qualified researchers upon request. More information on the data request process is available under the “Access Information” field here.
20.1.2 Data analysis
The expected number of species (\(E(S_n)\)) was calculated for each survey tow as:
\[\begin{equation} E(S_n) = \sum_{i=1}^S{ \Bigg( 1 - \frac{\binom{N-N_i}{n}}{\binom{N}{n}} \Bigg) } \end{equation}\]
where \(S\) is the total number of species present, \(N\) the total number of individuals, and \(N_i\) the number of individuals of ith species. The result represents a sample of n individuals randomly selected from the tow without replacement. The calculation is made using the rarefy function of the vegan package (R-vegan?) using an n of 1000.
The number of species represented in these samples of 1000 fishes are then averaged over the survey for each Ecological Production Unit. Due to the lack of survey calibration factor to account for differences in the number of species caught between the NOAA Ship Albatross IV and NOAA Ship Henry B. Bigelow, the time series are kept separate.
20.1.3 Data processing
Data were formatted for inclusion in the ecodata R package using the R code found here.
catalog page https://noaa-edab.github.io/catalog/exp_n.html