Avifauna Supplement — Statistical Analysis of Changes in Migrant Arrival Dates

Statistical Analysis of Changes in Migrant Arrival Dates

John Arnfield & John Tucker

Shropshire’s Migrant Arrival Date Database

Shropshire’s Migrant Arrival Database (SMAD, Tucker 2016) holds the first dates for 32 species from 1886 to 2014, plus a single Cuckoo record from 1871 by Rocke, described by Beckwith. Apart from this case, they have all come from the CSVFC’s Record and Transactions and latterly from SBRs, and now number almost 3,000 records. These dates appeared in the published record within individual species accounts or in summary tables. In SMAD, first dates are held for each species as day, month and year, along with the equivalent day-number (count of days into the year) used to calculate, for example, average arrival dates. A few of the early records come from two locations just outside the County boundary, Churchstoke and Knighton. Table 1 shows the 32 species included, ranked by column in order of the number of years (not necessarily continuous) for which first arrival dates are known. Dates after 1974 have been excluded for Chiffchaff and Blackcap, because of the difficulty of separating early arrivals from late over-wintering birds that started to appear around that time.

The Time Series of First Arrival Dates

Graphs of arrival dates versus year for individual species are available by selecting this link. To aid comparison, the axes of all graphs for the same season are identical. The horizontal axis shows years from 1860 to 2020. The vertical axis shows arrival day-number. For spring arrivals, this runs from from 60 (March 1) to 160 (June 9). For autumn arrivals, the equivalent range is from 230 (August 18) to 250 (September 7).

The graphs are shown in five groups, the nature of which will be explained below. The red trend line is included as a generalised measure of the time-dependence of first arrival date over the period of record for each species; it is not intended as a predictive tool. The red line is the least-squares regression line (Fowler & Cohen 1996, p. 90) and is shown whenever the slope of the line is significantly different from zero at the 95% confidence level.

In addition, the same type of graph showing first arrival dates for all species for spring and autumn migrant groups can be seen here.

Several of these graphs suggest a marked shift to earlier arrival dates over time, particularly those in Species Group 1. Others show more complex patterns that will be discussed in a later section.

First Arrival Date Trends in SMAD

To identify potential long-term changes in migrant arrival dates over the period covered by the SMAD, and to identify differences among species, dates were extracted for all years having records for three 29-year sub-periods centred on the years 1900, 1950 and 2000, extending 14 years on each side of the nominal date and averaged for each species. (The term ‘average’ in this account implies arithmetic mean (Fowler & Cohen 1996, p. 29).

Table 2 presents a summary of the average arrival dates obtained in this way (columns 2-4). The differences in arrival dates (in days) over the 1900-1950 and 1950-2000 periods are shown following the average first-arrival dates, in columns 5-6, and the difference over the whole century is shown in column 7. Differences are defined such that positive numbers indicate a change to an earlier date over the period.

These averages include a level of uncertainty since they are derived from 29 apparent first arrival dates that are, in turn, selected from samples of a theoretical population[1] of all bird occurrences in the County (whether observed or not), thus clouding the relationship between the calculated average and the population (‘true’) date. This ‘sample’ is not the well-designed subset characteristic of formal statistical studies but is created by factors such as observer location, effort, perseverance and enthusiasm for reporting observations, as well as environmental factors such as visibility within different habitats, difficulty of accessing certain areas, weather conditions and the like. Even though this process is not random in a statistical sense (i.e. every case of a theoretical ‘true’ earliest arrival date does not possess the same probability of appearing in SMAD), some consideration of the effect of this uncertainty on calculated changes in arrivals would be wise, to avoid drawing unwarranted conclusions. This was assessed (using a t-test; Fowler & Cohen 1996, p.113) by making the working assumption that a date’s inclusion in the 29-year average was random and testing each difference, based on its size, the variability around each average and the number of arrival dates used, to see if it was large enough to be considered significantly different from zero, which would imply no difference and no change in arrival date over the period. The criterion used was that the probability that the difference was due to chance had to be 5% or less; this is equivalent to a confidence level of 95% (as employed by the BTO in assessing the significance of BBS population change data). Differences that fall outside this confidence level are shown in parentheses in Table 2, columns 5-7.

Table 2 is subdivided into five Species Groups with different characteristics. These Groups are also used to classify the graphs of first arrival date against year, referenced above. Table 2 (column 7) shows that, for 21 of the 29 springtime arrivals, there has been an apparent shift in arrival dates to earlier in the year. Species Group 1 contains a single species – Yellow Wagtail – which shows the strongest signal for a dependence of arrival date on year, with statistically significant advances in average arrival date in both sub-periods and over the whole century. Group 2 is similar, to the extent that the change between 1950 and 2000 is meaningful as is the advance over the whole interval, but with small or even reversed arrival data advances (negative differences) between 1900 and 1950, all of which must be considered indistinguishable from no change.

Species Group 3 exhibits more ambiguous results. Whitethroat and Cuckoo exhibit statistically significant advances in arrival date over the 1900-2000 period but not in the sub-periods. Lesser Whitethroat, Grasshopper Warbler, Tree Pipit and Whinchat show minimal (possibly zero) change over the century. The statistics for Reed Warbler and Spotted Flycatcher suggest a shift in arrival date to later in the year. However, in the first of these two species, there were very few records available until regular access to suitable habitat at Allscott Sugar Factory was gained in 1960 and the period after that date shows a well-marked advance in arrival date. Arrival dates for the latter species are particularly unreliable, as it has declined by 86% since 1970, and 44% since 1995, greatly reducing the likelihood of observers encountering the first-arriving individual.

Group 4 represents species for which data deficiencies weaken conclusions that might be drawn from the difference statistics. The first five show large population declines over the period: three are on the Red List of Birds of Conservation Concern (50% decline since 1970), one is on the Amber List (25% decline since 1970) and one is a former breeder, now only an uncommon passage visitor. SMAD data for Nightingale and Wryneck end in 1990 and for Corncrake and Nightjar in 2001. Dates for Turtle Dove exhibit great variability after about 2010. Their arrival dates have apparently not changed, but any change that may have occurred has almost certainly been obscured by the decreasing likelihood of the first recorded date being close to the ‘true’ first date with so few recent observations. Chiffchaff and Blackcap, while not scarce, are subject to erroneous first arrival dates owing to an increasing propensity for overwintering and/or winter in-migration in recent years, which is why results from 1975 onwards have been excluded from this analysis. Little Ringed Plover, in contrast, has only been recorded as a spring migrant in recent years and so lacks data from the early and mid-1900s with which to compare.

Group 5 includes only the autumn migrant species. Redwing shows a strong (and statistically significant) advance in arrival date over the twentieth century. Fieldfare and Brambling, in contrast, show later arrival in the first sub-period and the opposite trend in the second. The ambiguity in these results may perhaps reflect the differences in the driving forces on spring and autumn migrants. The former need to arrive at their breeding sites to claim the best territories (and maybe the fittest mates), as well as to time their breeding cycle to synchronise with the availability of food items for their young, factors that are not relevant to immigrants from Scandinavia and other northern European locations in autumn.

First Arrivals Date Change 1900-2014

SMAD data end in 2014, the cut-off date for observations contributing to the Avifauna. To estimate first arrival dates and the advance of arrival date to that year, the following procedure was adopted. Both the data of Table 2 (columns 5-6) and visual inspection of graphs of arrival dates versus year suggest that, for many species, the pattern of change before and after 1950 was different. Hence, least-squares linear regression parameters (Fowler & Cohen 1996, p. 90) were calculated for the relationship between arrival date and year only for the years 1950-2014 using all annual first arrival dates that occur in SMAD for this period. The formula for the regression line was then used to calculate the estimated 2014 arrival date, except when the regression slope was not statistically significantly different from zero (Fowler & Cohen 1996, p. 96), indicating no meaningful change over the period), when the date for 2000 was used for 2014. Graphs showing the first arrival date – year relationship for 1950-2014 can be seen here. On these figures, the presence of a red trend line implies a slope significantly different from zero at the 95% confidence level. Cases which do not meet this criterion are identified by the symol # against the estimated 2014 date (column 8 in Table 2.) Estimated arrival date changes for both 1900-2014 and 1950-2014 were calculated (where possible) and are shown in columns 9 and 10 in Table 2.

For Species Groups 1 and 2, changes in first arrival dates over both the 1900-2014 and 1950-2014 periods were notable (all but one in excess of one week), with Wheatear showing a remarkable 26-day change between 1950 and 2014. The species in Group 3, which were characterised by less pronounced arrival date change over time, naturally exhibited smaller advances (generally a week or less).

Autumn-arriving migrants (Group 5) exhibited little consistency in arrival date change to 2014 other than the fact that all were advances over both the 64-and 114-year periods.

Overall, there is no obvious correlation between the size of the arrival date change to 2014 and bird taxonomic group, behaviour, habitat needs or over-wintering location.


How credible are these results and do they resemble those from other assessments of first arrival date advance? Cotton (2003) used regression analysis to determine advances for a variety of spring migrants in Oxfordshire that include 17 species from the first three groups in Table 2. For these species, the average advance was 8 days over the period 1971 to 2000. This compares with a figure of 10 days for the same species in Table 2 for the longer 1950-2000 period. The ranking of the 17 species by the size of the advance showed little relationship between the two studies. Sparks et al (2007) found that 50% of the cases they examined for six locations in England showed significantly earlier dates over a 50-year period, with a springtime average advance of 0.25 days/year. The significant data of column 6 in Table 2 for those species in Groups 1-3 show a rather larger proportion of advances and an average rate of change of 0.20 days/year. More recently, Newson et al (2016), using UK data from three citizen science sources (Inland Observation Points, Migration Watch and BirdTrack) reported an earlier arrival of 9 days for 11 of the species in the first three groups in Table 2, from the mid-1960s to 2002–2011 (equivalent to a rate of change of 0.22 days/year). Interestingly, the date shifts recorded by Newson et al were significantly correlated with those found from SMAD (Pearson’s product-moment correlation coefficient r=0.85, significant at the 95% confidence level; see Fowler & Cohen 1996, p.82), with Sand Martin showing the largest and Whinchat the smallest advance.

It seems likely, therefore, that the results shown in Table 2 are consistent with data reported by others (using different analyses), which is both reassuring and lends support to the methodology employed here.

A Note of Caution

As with all generalisations drawn from observed data, our assessment of their reliability should be moderated by an understanding of the uncertainties in the original observations and their subsequent manipulations. Uncertainties in the case of calculating trends from recorded first arrival dates reflect both ornithological judgements (how likely is it that the recorded date is close to the ‘true’ date), and uncertainty inherent in inferences from statistical techniques.

Arrival date observations are straightforward and, short of misidentification or recording error, can only be erroneously late, not early. However, there may be little or no correlation between the date of the first record and the ‘true’ first date, especially for scarce species or in areas with few observers or poor accessibility. Many of the species listed have niche habitats, which are unlikely to have been visited by observers at the right time in every year. The increase in observers over the period since 1870 may have affected the detectability of early arrivals, potentially reducing the internal consistency of the dataset over time. Furthermore, ‘population size may influence the first observation…, particularly pronounced for bird species which are difficult to observe and/or are at low population numbers’ so ‘caution needs to be used in interpreting arrival dates of species whose population is low and changing’ (Sparks et al. 2001). This is an important factor in interpreting the results for many species, particularly those in Group 4.

Naturally, like all statistics, averaged dates of arrival and the arrival date advance have levels of reliability associated with them. Hence, a calculated advance of (say) 10 days in arrival for a species is associated with a given probability (say 95%) that the true advance is between (say) 7 and 13 days. This aspect of the analysis should be explored in more detail in subsequent work with SMAD. The practical implication of this is that we should be careful about attributing biological meaning to arrival date differences that are not large, particularly if statistical analysis suggests that these differences cannot be considered to be meaningfully different from zero.

 Despite these caveats, the results of the SMAD analysis display sufficient internal consistency and adequate correspondence to results from other studies to suggest that they are reflecting real changes in bird behaviour over the past 114 years.


Notwithstanding these reservations, and accepting that causality cannot be inferred from this analysis, the changes observed are consistent with the hypothesis that a warming climate is driving earlier migration into the County. This position is lent further support in that Table 2 suggests greater changes in first arrival dates occurred in the second half of the twentieth century than in the first half, which is consistent with the fact that global and regional temperature series show a much more modest warming prior to 1950 than since (Met Office, 2017). Sparks et al (2001) reviewed numerous studies, and stated that ‘in many incidences [sic] there is sufficient correlative evidence with temperature to suggest that temperature has an influence on bird migration timing’, and called for further discussion and research. Analysis of the extensive SMAD records provides an important contribution to this and further work is encouraged.


[1] The term “population” in this context is used in its statistical sense to mean “any collection of individual items or units which are the subject of investigation” (see Fowler & Cohen 1996, p. 11). It should not be confused with a biological population. The items in this case are all Shropshire bird occurrences. Populations may be “countable” (e.g. the words on this webpage) or “uncountable” (also called “theoretical” or “infinite”), as in the case of “all Shropshire bird occurrences.”


Cotton, P.A. (2003) Avian migration phenology and global climate change. Proceedings of the National Academy of Sciences of the United States of America, 100, 12219-12222.

Fowler, J. & Cohen, L. (1996). Statistics for Ornithologists. BTO Guide 22. (Second Edition). British Trust for Ornithology, Thetford.

Kington, J. (Ed.) (1988). The Weather Journals of a Rutland Squire. Thomas Barker of Lyndon Hall. Rutland County Museum, Oakham.

Met Office. (2017) http://www.metoffice.gov.uk/research/monitoring/climate/surface-temperature (accessed 16/04/2017).

Newson, S.E., Moran, N.J., Musgrove, A.J., Pearce-Higgins, J.W., Gillings, S., Atkinson, P.W., Miller, R., Grantham, M.J. & Baillie, S.R. (2016). Long-term changes in the migration phenology of UK breeding birds detected by large-scale citizen science recording schemes. Ibis, 158, 481-495.

Sparks, T.H., Roberts, D.R. & Crick, H.Q.P. (2001). What is the value of first arrival dates of spring migrants in phenology? Avian Ecology and Behaviour7, 75-85.

Sparks, T.H., Huber, K, Bland, R.L., Crick, H.Q.P., Croxton, P.J., Flood, J., Loxton, R.J., Mason, C.F., Newnham, J.A. & Tryjanowski, P. (2007)  How consistent are trends in arrival (and departure) dates of migrant birds in the UK? Journal of Ornithology, 148, 503-511.

Tucker, J. (2016). Shropshire’s Migrant Arrivals Database, SMAD. http://www.lanius.org.uk/sos/general/Resources/2016b%20Tucker%26R%20SMADss.pdf (accessed 13/07/2017)

Walker, R.H., Robinson, R.A., Leech, D.I., Moss, D., Kew, A.J., Barber, L.J., Barimore, C.J., Blackburn, J.R., De Palacio, D.X., Grantham, M.J., Griffin, B.M., Schäfer, S., Clark, J.A. (2014). Bird ringing and nest recording in Britain and Ireland in 2013. Ringing and Migration 29, 90-150.


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