WeBS Alerts methods - Data Analysis
Full details pertaining to the use Generalized Additive Models (GAMs) for the calculation of annual waterbird indices and the fitting of smoothed trend curves by the WeBS Alert system are available in Atkinson et al. (2006). An overview is provided below.
The index value for a particular winter is the number of birds present in that winter (summed monthly counts) expressed relative to the number of birds present in the base winter, which is arbitrarily set at 100. The WeBS Alert System assigns the base winter to be the most recent winter in the data being analysed.
Missing values, inevitable with count data, are accounted for by using the Underhill indexing method (Underhill & Pr?s-Jones 1994), as used by WeBS for generating annual indices. The Underhill indexing method fits a model with site, year and month factors to the incomplete data matrix and imputes values for missing observations using an iterative approach. Where all observations are considered to be of equal status the Underhill method produces the equivalent index to a GAM model when fitted specifying (n-1) degrees of freedom (where the number of years = n). However, the Underhill method includes an assessment of counts flagged as incomplete which is not available in GAM analyses. Where these flagged counts are higher than expected from the impution then they used in the subsequent indexing analysis but where they are lower than expected they are treated as missing observations. This ensures that incomplete counts are not allowed to depress index values and this is standard practise in WeBS reporting. Thus, in effect, the Underhill method is used to reassess the data matrix with respect to flagging of incomplete counts before the data are processed using GAM analyses.
Smoothed GAM trends
Use of raw index values to assess Alerts status, or in fact any other comparison between two or more winters, would be undesireable. Natural temporary fluctuations in numbers, for example those caused by variation in the severity of conditions over the winter period, can differ in size and / or direction from longer-term trends, hindering their interpretation. Extreme values may trigger false Alerts due to misinterpretation of temporary, short-term declines as longer-term trends. Alternatively, long-term trends that may have led to Alerts being flagged could be obscured by short-term fluctuations.
In order to avoid such misinterpretations and misidentifications when calculating Alerts, the Alerts System uses GAMs to fit a smoothed trend curve to the annual indices. This it does by a reduction in the number of degrees of freedom available to the GAMs. As the number of degrees of freedom is decreased from (n-1) the trend become increasingly smooth until ultimately with one degree of freedom the smoothed curve becomes a linear fit. The WeBS Alert System adopts a standard (n/3) degrees of freedom to produce a level of smoothing that, while removing temporary fluctuations not likely to be representative of long term trends, capture those aspects of the trends that may be considered to be important.
Changes in numbers calculated using values from a smoothed GAM trend are less likely to be due to the effects of temporary fluctuations in numbers, or to errors when sampling, than results produced had annual index values to be used. Thus, using GAMs reduces the probability that a decline from a short-lived unsustainable peak in numbers would be responsible for triggering an Alert. A decline from a period of sustained high numbers, however, would trigger an Alert using GAMs and clearly would be worthy of investigation. It should be noted that, because a standard degree of smoothing has been applied across all species and spatial scales, the arithmetic derivation could trigger alerts for species showing large year-to-year fluctuations in numbers. In these cases, knowledge of their ecology and population dynamics is essential for correct interpretation.
Proportional changes in the smoothed GAM trend in numbers over short-term (5- year), medium-term (10-year) and long-term (25-year) time-frames, are calculated by subtracting the smoothed GAM trend value at the start of the time-frame from the smoothed GAM trend value in the reference winter. The WeBS Alerts system uses the penultimate winter in the dataset as the reference year. Where data are not available for a 25-year period, for example where species or sites were not included in WeBS from the outset, the longest possible period is used instead. Additionally, an Alert period that corresponds to the period since the site in question was first designated is also reported. In due course, once it has become functionally different from the 25- year Alerts an all-time Alert will also be assessed. Coverage in the early days of WeBS was less extensive than it is currently and so assessing Alerts periods beyond 25 years would result in an unacceptably high proportion of missing counts, leading to comparisons being made between the current value and a value more representative of the long-term average than numbers present in the early winters.
Calculated change values are expressed as a percentage of the index at the start of the period. Larger values therefore indicate larger proportional changes in numbers, with positive values equating to relative increases in the numbers and negative values equating to relative decreases over the specified time period. These values are then categorised according to their magnitude and direction. Declines of between 25% and 50% inclusive are flagged as Medium Alerts and declines of greater than 50% as High Alerts. Although they will not promote discussion within this report, increases are also flagged in the appropriate tables. In order to facilitate comparison of decreases and increases in numbers, increases of between 33% and 100% are described as Medium increases, while increases of greater than 100% are described as High increases. This allows for the proportionally greater increase required to return numbers to their former level following a given decrease. For example, following a 25% decline and the triggering of a Medium Alert (e.g. 1000 birds down to 750 birds), number will be returned to their former level by a 33% increase (e.g. 750 birds up to 1000 birds). Similarly, following a 50% decline and the triggering of a High Alert (e.g. 1000 birds down to 500 birds), numbers will be returned to their former level by a 100% increase (e.g. 500 birds up to 1000 birds).
Calculating percentage change
We calculate the percentage change in numbers with reference to the penultimate winter, currently 2009/10. The short-term percentage change is therefore the change between winter 2004/05 and 2009/10 and is calculated as
Percentage change = 100 x ((W09/10 – W04/05) / W04/05 )
Where W09/10 is the mean winter count for winter 2009/10 and W04/05 is the mean winter count for winter 2004/05. Likewise the medium- and long-term percentage changes are calculated with reference to winter 1999/00 and winter 1984/85 respectively. Where data are not available across a sufficient time series, the long-term percentage change is calculated with reference to the earliest but one available winter.
WeBS Alerts citation
This report should be cited as: Cook, A.S.C.P., Barimore, C., Holt, C.A., Read, W.J. & Austin, G.E. (2013). Wetland Bird Survey Alerts 2009/2010: Changes in numbers of wintering waterbirds in the Constituent Countries of the United Kingdom, Special Protection Areas (SPAs) and Sites of Special Scientific Interest (SSSIs). BTO Research Report 641. BTO, Thetford. http://www.bto.org/webs-alerts
WeBS is a partnership between the British Trust for Ornithology, the Royal Society for the Protection of Birds and the Joint Nature Conservation Committee (the last on behalf of the statutory nature conservation bodies: Natural England, Natural Resources Wales and Scottish Natural Heritage and the Department of Agriculture, Environment and Rural Affairs, Northern Ireland) in association with the Wildfowl and Wetlands Trust. Email: webs [at] bto.org.