Assessment methodology for imposex annual indices

Overview

This file describes the assessment methodology when imposex data have been submitted as annual indices, or when there is insufficient variation in stage between individuals to model individual measurements. The time series are assessed in three stages:

  1. Where data have been submitted as individual measurements, the measurements each year are summarised by an annual index.
  2. A generalised linear model is fitted to the annual indices. The type of model depends on the number of years of data:
    • 1-2 years: no model
    • 3 years: mean
    • 4+ years: linear trend
  3. The fitted models are used to assess environmental status against available assessment critreia and evidence of change in imposex levels over time.


Calculating annual indices

Let \(y_{ij}\) be the imposex measurement of the \(j\)th female snail in year \(t_i\), \(j = 1...n_i\), \(i = 1...N\). The annual index in year \(t_i\) is the mean of these measurements:

\[y_i = \frac {1} {n_i} \sum_j y_{ij}\]


Modelling the annual indices

The annual indices are constrained to lie between 0 and 1 by dividing by the largest permissible value (below). For example, the indices for VDS in Nucella lapillus are divided by 6.

Measure Species Largest Value
VDS Buccinum undatum 4
VDS Neptunea antiqua 4
VDS Nucella lapillus 6
VDS Ocenebra erinaceus 6
VDS Tritia nitida / reticulata 4
INTS Littorina littorea 4


The transformed indices are then modelled using a generalised linear model with a logistic link (McCullagh & Nelder, 1989). Usually, the data are assumed to have a quasi-binomial distribution with weights given by the number of female snails \(n_i\). However, the distribution of VDS in dog whelks is specified by a more appropriate mean - variance relationship derived in Fryer & Gubbins (2007). The mean index is given by:

\[\text{logit } \text E (y_i) = f(t_i)\]

where \(f(t)\) is a function of time that depends on the number of years of data:

1-2 years
no model is fitted as there are too few years for formal statistical analysis
3 years
mean model \(f(t) = \mu\)
there are too few years for a formal trend assessment, but the mean level is summarised by and is used to assess status
4+ years
linear trend \(f(t) = \mu + \beta t\)
the indices vary as a linear logistic function of time; the fitted model is used to assess status and evidence of temporal change

Fryer R & Gubbins M, 2007. Modelling VDSI in Nucella lapillus. ICES Working Group on Statistical Aspects of Environmental Monitoring

McCullagh P & Nelder JA, 1989. Generalized Linear Models (second edition). Chapman & Hall, London.


Assessing environmental status and temporal trends

Temporal trends are assessed for time series with at least 4 years of data using the model fitted to the annual indices. There is evidence of a temporal trend if the slope of the linear logistic regression of \(y_i\) on \(t_i\) is significant at the 5% level.

Environmental status is also assessed using the model fitted to the annual indices. The upper one-sided 95% confidence limit on the fitted value in the most recent monitoring year is compared to the available assessment criteria. For example, if the upper confidence limit is below the Background Assessment Concentration (BAC), then the mean index in the most recent monitoring year is significantly below the BAC and imposex levels are said to be ‘at background’.


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