The plot shows TFactor - the average of the rescaled frequency of the species, estimated by Frescalo, across the hectads. The vertical error bars indicate the standard deviation of those estimates.
The red line shows a smoothed curve (a smoothing spline) fitted to these points. It is designed to provide a visual indication of the general trend.
To test whether or not a trend is statistically significant, Spearman's rank correlation (rho) was calculated. We have the TFactor values for a series of years from 1980 to present. A conventional correlation (Pearson's product moment correlation) between these values makes certain assumptions - notably that the deviations of points around the estimated trend line are normally distributed. We can't make this assumption here and, indeed, given the way the data is calculated, a normal distribution is unlikely.
Another way of doing this is to rank the TFactors from smallest to largest and also rank the years and correlate these ranks. This is Spearman's rank correlation and makes fewer assumptions. Like the normal correlation coefficient, a positive value of rho indicates an upwards trend and a negative value a downwards trend and statistical tests can be carried out to estimate how likely it is that the particular value is different from zero (p). So, if p<=0.05 and rho is negative we can conclude there is evidence for a significant decline whilst if rho was positive, a significant increase. Otherwise (p>0.05) we conclude there is no evidence of a change.
In this particular example, Anasimyia transfuga, like many specialist wetland species, has shown a sustained downward trend in the frequency with which it has been recorded. Spearman's rank correlation suggests that this is a strong and highly significant downward trend.
Problems
Frescalo assumes that the species discovery curve, the relationship between how frequently species were observed and the amount of recording effort expended in making these observations, is consistent across time and space. If this assumption is not correct then the analysis will be biased. We have reason to believe that the behaviour of recorders has changed over recent years, notably the numbers of records we are getting that are based on people submitting photographs on line.
This sort of recording has increased markedly, especially since the Hoverfly Facebook page was established and in 2018 more than half of the records received by the HRS were from this source. These photographs are heavily dominated by large, obvious and attractive flower visitors. More obscure, small and difficult-to-identify species are poorly represented, especially if they do not tend to visit flowers. This has the effect of increasing the relative frequency of large, obvious flower visitors and decreasing the frequency with which small, cryptic non-flower visitors are observed. This, in turn, will change the form of the species discovery curve and so effect the validity of the analysis.
Consider the following two plots in which the trend calculated for all records from 1980-2018 (blue) is compared to a trend based on a dataset excluding the photographic records (red) for two species: Eristalis tenax and Platycheirus clypeatus.
These plots illustrate the effect of the change in recorder behaviour. Eristalis tenax is a large and very abundant flower visitor that often occurs in gardens and urban areas. It is one of the most frequently photographed species. By contrast, although Platycheirus clypeatus is a widespread and frequent species, it is small, mainly black in colour and rarely visits flowers (although is does visit flowers of wind-pollinated plants such as grasses, sedges and plantains to obtain pollen). It is not often photographed.
The increasing impact of photographic records over the last decade or so in increasing the relative frequency of the big and obvious flower visitor and decreasing the relative frequency of small and cryptic non-flower visitor are clearly shown. This tends to make it more likely that the photogenic flower visitor will be classed as "Significantly increasing" whilst the small and cryptic species will be classed a "Significantly declining".
Bear this in mind when looking at trend plots! We are working with statisticians to try and develop more sophisticated methods which can take these changes in recorder behaviour into account.