In addition to calculating the original AMBI index, and the multivariate M-AMBI, the package allows you to calculate several other benthic fauna indices.
Danish indices
Development of the ambiR package was motivated by a need
to integrate calculation of the AMBI index as well as the
derived DKI index in analyses using R. These analyses
contributed to a study investigating trends in eutrophication status in
Danish coastal waters (Jørgensen et al. 2026) and
necessitated calculation of the Danish quality index DKI (Danish:
Dansk Kvalitetsindeks) based on observations recorded in the
Danish national monitoring program
DKI
DKI is essentially an adaptation of AMBI to Danish
conditions, to account for the lower diversity which can be expected in
the more brackish waters of the Inner Danish waters. It can only be
calculated after first calculating AMBI, the AZTI Marine Biotic
Index, and H’, the Shannon diversity index. Both of these
required index values are included in output generated by the
AMBI() function.
\[ DKI_{v1} = \left( \frac{ \left( 1-
\frac{AMBI}{7}\right) + \left( \frac{H'}{H'_{max}} \right)}{2}
\right) * \left( \frac{\left(1- \frac{1}{N} \right) + \left(1-
\frac{1}{S} \right)}{2} \right) \] The DKI()
function uses a maximum limit value of H’ H_max in
Danish waters as a reference value to normalise DKI. If this
value is not specified as an argument, then the default value is used
(5.0), as described by Borja et al.
(2007):
However, in the present exercise, the Danish method used H’max (~5) as a kind of reference
DKI v2
The DKI2() function calculates an updated version of the
DKI index which uses empirical relationships between salinity
and expected AMBI index and H’ values to adjust the
AMBI result. (Carstensen et al. 2014).
\[ DKI_{v2} = \frac{1}{2} \left( \left( 1- \frac{AMBI-AMBI_{min}}{7} \right) + \left(\frac{H'}{H'_{max}}\right) \right) * \left(1- \frac{1}{N} \right) \] where Hmax and AMBImin are functions of salinity (psu):
\[ H'_{max} = 2.117 + 0.086 * salinity, \frac{H'}{H'_{max}} \le 1.0 \]
and
\[ AMBI_{min} = 3.083 – 0.111 * salinity, AMBI_{min} \ge 0 \]
and N is the number of species.
Norwegian indices
Similarly to the Danish indices, The Norwegian Quality Index (NQI1) is based on modifying the AMBI index to local conditions (Borja et al. (2007), Rygg and Norling (2013)). NQI1 is intercalibrated with other countries in the North East Atlantic Geographical Intercalibration Group (NEAGIG) (Borgersen et al. (2019)).
The other Norwegian indices NSI and ISI are not based on modifying the AMBI index. They do employ a similar approach where each species or taxa is assigned an individual index score which reflects the relative sensitivity of the species to disturbance. Then the combined average score of the index values for a sample show the level of disturbance indicated by the species composition.
The species-specific sensitivity values for NSI and ISI are derived from analyses of large datasets from Norwegian monitoring data, calculating Hurlbert diversity index (ES) values for many samples. The weighted averages of ES values were then calculated for each species across the samples where they occurred. So, species occurring more often in samples having lower diversity will have a lower index value.
NQI1
The NQI1() function is calculated according to this
formula:
\[ NQI_1 = \begin{bmatrix} 0.5* \left( 1- \frac{AMBI}{7} \right) + 0.5 * \left(\frac{\begin{bmatrix} \frac{ln(S)}{ln(ln(N))} \end{bmatrix} }{2.7} \right) * \left( \frac{N}{N+5} \right) \end{bmatrix} \]
where \(S\) is the number of species and \(N\) is the number of individuals.
Rygg and Norling (2013) also developed an alternative index NQI2 which is not yet included in the package.
NSI
The NSI index was developed as an alternative to AMBI for application in Norwegian coastal areas (Rygg and Norling (2013))
The NSI() calculation method:
\[ NSI = \sum_i^S {\begin{bmatrix} \frac{N_i * NSI_i}{N_{NSI}} \end{bmatrix} } \]
ISI
The oldest Norweigan index, the Indicator Species Index (ISI) does not use counts of individuals of each species but is based purely on presence for different species, combined with a species-specific index reflecting sensitivity to disturbance (Rygg (2002)).
\[ ISI = \sum_i^S {\begin{bmatrix} \frac{ISI_i}{S_{ISI}} \end{bmatrix} } \]
Others
So far, the only other index included here is the Hurlbert
diversity index (ES()).
ES
The Hurlbert diversity index estimates the expected species diversity for a given subsample size from a larger population (Hurlbert 1971). ES100 is the expected species diversity where a subsample of 100 individuals is taken from a larger sample population. Obviously, if the sample contains fewer than 100 individuals, then it is not possible to take a subsample of 100 individuals. See Hurlbert (1971) for more information.
Analysis of ES100 across large Norwegian monitoring datasets forms the basis for the species-specific index values used by the ISI and NSI indices.
Missing indices?
Is there an index which is missing? Do you have suggestions for other
index calculations which could be included in a future version of the
ambiR package? Then you are very welcome to contribute
directly or to make a new feature
request.