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Keywords:

  • bayesian state-space models;
  • habitat loss;
  • hedgerows;
  • land-use change;
  • time series;
  • yellowhammer

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  10. Supporting Information

1. Understanding the mechanisms by which environmental change has impacted natural processes typically requires good time series for the environmental change. Unfortunately, other than for climate, detailed time series of historical environments are scarce. In many instances, researchers can only collate disparate and sometimes fragmented information from the literature or from historical or pre-historical sources.

2. Here, we apply modern statistical methods to reconstruct a recent historical time series of environmental change from sparse data collected from heterogeneous sources. Specifically, we deal with record irregularity and the varying levels of uncertainty associated with each datum using state-space models in a hierarchical Bayesian framework.

3. As an example, we reconstruct a time series of a simple landscape feature (hedgerow length) over a large spatial scale (Britain) over a long-time period (50 years), by combining both stock estimates and rate of change estimates, gathered from different historical sources.

4. We illustrate the utility of the method by relating the population trends of a hedgerow-nesting passerine bird, the yellowhammer Emberiza citrinella to the reconstructed trends in hedgerow length. Population density was closely related to hedgerow availability, suggesting a potential key role for nesting habitat loss in the yellowhammer decline.

5. The modelling framework we used is flexible and general. The method can be adapted to reconstruct time series of any environmental variables from a variety of sparse and heterogeneous historical sources.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  10. Supporting Information

Predicting how organisms may respond to environmental change is often built upon understanding gleaned from observed relationships between the physical and natural environments. For example, the observed or reconstructed record of climate has been instrumental in understanding changes in species’ phenologies, ranges, population sizes, at a range of temporal scales (Parmesan & Yohe 2003; Bush, Silman & Urrego 2004; Mayhew, Jenkins & Benton 2008). However, understanding the impact of environmental change that is not climate-related, such as land use, is often hampered by an absence of good records of the environmental change over time (but see, e.g. Zhang et al. 2009).

Over relatively recent times, standardized, quantitative data may be available describing historical land use through inter alia, agricultural censuses (Haines-Young et al. 2000), aerial photographs (Baessler & Klotz 2006), or since the 1970s from remote-sensing technology. Such data may allow exploration of relationships between land use and biodiversity: Benton et al. (2002) were able to relate bird population census data over a 25-year period in Scotland to time series of insect abundance monitoring, climate indices and official agricultural statistics (see also Wretenberg et al. 2006 for a similar study in Sweden). However, homogeneous series are hard to find. For example, in their attempt to quantify historical changes in agriculture and biodiversity in Britain, Robinson & Sutherland (2002) compiled published estimates of seed banks and hedgerows from a number of different sources, but the variety of information sources and inconsistent methodologies used in the original studies complicated both the analysis and interpretation of results.

Nevertheless, in addition to census and remote-sensing data there are a variety of scattered and sparse historical data sources available – e.g. scattered descriptions from naturalists’ diaries (Lawton 1999), historical maps and documentation (Ramankutty & Foley 1999; Yeloff & van Geel 2007), old photographs (Sparks 2007), or collections (Elith & Leathwick 2007). Such records may hold valuable information for reconstructing past environments, if the methodological problems of using them can be overcome. Sparse or opportunistic data typically are problematic for the following reasons: (i) observations are irregular in frequency (i.e. many missing data); (ii) observations vary in location and/or spatial extent; (iii) observations may arise from different methodologies in sampling, analysing or reporting data, giving rise to variable uncertainty associated with any estimate; (iv) data collection may be prompted, or selectively undertaken, in response to observed changes, leading to varying levels of bias and lack of representativeness; and (v) all or part of the data available may only be surrogate for the variable of interest, for instance, plant growth rate as a proxy of temperature (e.g. Rozema et al. 2009), or hunting bags as a proxy of population size (e.g. Shaw et al. 2004). The statistical analysis of such data thus requires the ability to handle multiple sources of variation, in a way that is flexible enough to cope with missing observations and data of differing nature.

Our aim is to reconstruct a quantitative time series of a simple environmental variable by combining information from sparse data sources, using hierarchical Bayesian models. Hierarchical models are designed to decompose the variance in the data into different levels, representing, for instance, different populations or spatial locations (Clark 2005). Furthermore, the Bayesian framework offers opportunities for combining different types of information in two ways. First, prior information can be used to inform parameters in the model. Prior information can be drawn from independent sources of information such as previous studies (McCarthy & Masters 2005), or from expert knowledge (Low Choy, O’Leary & Mengersen 2009). Second, the estimation of modern Bayesian models uses computational approaches such as Markov chain Monte Carlo methods. This allows inference to be based on the likelihood associated with a rich class of complex models that need not be analytically tractable (Clark 2005). Among hierarchical models, state-space models are particularly useful for distinguishing variation in the process of interest from observation error, and can be used to account for the level of uncertainty associated with each datum. This is achieved by expressing the observed value of the measured quantity (the datum) as a function of its true, unknown value, using a specific observation equation (King et al. 2008). In principle, the observation equation could also easily be used to describe the known or assumed relationship between the true value of the variable of interest and an available surrogate covariate. Surrogate covariates can be used either in addition to, or instead of direct data, when the ideal variable is not available (such as hunting bags as a surrogate for population size). Together, Bayesian inference with state-space models gives the possibility of modelling sparse data by combining likelihood functions tailored to the exact nature of each available data set, for instance combining count data with ring-recovery data (King et al. 2008).

Over the last three decades, there have been widespread declines in the populations of European farmland birds (Wretenberg et al. 2006). Despite a general consensus linking these trends to the post-war intensification of agricultural practices in Western Europe (Chamberlain et al. 2000; Benton et al. 2002; Robinson & Sutherland 2002; Donald et al. 2006), the precise external causes and demographic mechanisms are still incompletely understood at the species level (see Newton 2004 for a review).

For many farmland birds, nesting occurs in the field margins in hedgerows and ditches (Arnold 1983) and this habitat has declined sharply over the last 50 years, due to amalgamation of small fields into larger units more suitable for larger machinery (Barr et al. 2003). However, analysis of the association between indices of farmland birds and the availability of such nesting habitat has not been possible at large spatial scales because data on habitat change have not been available (Robinson & Sutherland 2002). Here, we show how Bayesian state-space models can be used to reconstruct a time series of national hedgerow stock from sparse data, which may then have utility in understanding the population decline of hedgerow-nesting farmland passerines, and we demonstrate this by correlating hedgerow stock with population size estimates of the yellowhammer Emberiza citrinella. The method for reconstructing a time series of environmental change has broad applicability.

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  10. Supporting Information

Hedgerow analysis: trend estimation

To evaluate the effect of loss of hedgerow on British farmland bird populations, we constructed a composite time series of hedgerow length from two main types of data available since the 1950s, namely: (i) point estimates of hedgerow lengths in England or Britain (England and Wales), resulting from field censuses (Robinson & Sutherland 2002); and (ii) estimates of hedgerow rates of changes from repeated aerial photograph surveys or from field based surveys. These hedgerow length or hedgerow change estimates rely on different protocols, refer to different geographical units, and resulting estimates were reported either with or without associated errors. When both length and change in length estimates were produced, as in the Institute of Terrestrial Ecology surveys (Barr et al. 2003; Petit et al. 2003), we chose to use the change in length estimates, because these have a greater precision (see Tables 1 and 2).

Table 1.   British hedgerow length data
YearLength (×1000 km)ErrorTypeseSource
  1. *Estimate not used in the model; used corresponding change of length estimates instead (see Methods).

  2. 1Probably based on estimates from BTO data (no reference provided by Hooper 1970).

  3. 2From http://www.countrysidesurvey.org.uk/data.html. Countryside Survey © Database Right/Copyright NERC - Centre for Ecology & Hydrology. All rights reserved.

1945960NANANA Hooper (1970) 1
194779553se53 Environmental Statistics (1984)
1948805NANANA Joyce, Williams & Woods (1988)
1955815115Range57·5 Robinson & Sutherland (2002)
1956990NANANA Locke (1962)
196970351se51 Environmental Statistics (1984)
1970735NANANA Hooper (1970) 1
197256060Range30 Robinson & Sutherland (2002)
1974580NANANA Joyce, Williams & Woods (1988)
1978512·5NANANAITE survey
198065349se49 Environmental Statistics (1984)
1983500NANANA Carter (1983)
1984537*31se31ITE survey2
198562148se48 Environmental Statistics (1984)
1988492NANANARobinson & Sutherland (2002)
1990450*22se22ITE survey2
1993378*26se26ITE survey2
199844921se21CS 20002
Table 2.   Hedgerow rate of change data
Start yearEnd yearChange (×1000 km)seSourceComments
  1. 2Rescaled to be proportional to −137 (England & Wales figure) from 1946 to 1963.

19901993−54·69·6 Barr, Gillespie & Howard (1994) England & Wales
19841998−12313·4CS2000 website1England & Wales
19901998 04·8CS2000 website1England & Wales
19461963−137NA Pollard, Hooper & Moore (1974, p. 61) England & Wales
19461954−34NA Pollard, Hooper & Moore (1974, p. 64, table 2) Eastern England2
19541962−103NA Pollard, Hooper & Moore (1974, p. 64, table 2) Eastern England2
19621966−150NA Pollard, Hooper & Moore (1974, p. 64, table 2) Eastern England2
19661970−85NA Pollard, Hooper & Moore (1974, p. 64, table 2) Eastern England2

Assuming that temporal changes had been fairly smooth at the national level, we used a Bayesian additive, state-space model to estimate year-specific values of hedgerow availability over the period 1960–2000. This required an observation equation, to relate modelled values or differences in values to the available estimates, and a system equation, which in our case enforced smoothness on the modelled values.

Our model was informed by the likelihood associated with the two types of data (direct hedgerow estimates and rate of change estimates), as follows.

For data on hedge lengths, the observation process was assumed to be:

  • image(eqn 1)

where Oi is the observed hedge length at time i provided in the literature, sampled from a normal distribution with mean Hi (the modelled value, i.e. our attempt to reconstruct the corresponding ‘true’, unknown value) and variance inline image of the hedge length estimate i. To inform the standard deviation of the observation process, inline image, we used the value of the standard error provided in the source publication of every datum, rather than assuming a constant measurement error (see also King et al. 2008). Hedge length estimates from 1955 and 1972 were reported as ranges of values; for simplicity, we have treated these ranges as 95% confidence intervals and converted them into standard errors (Table 1). When the standard error was not estimated or reported in the source publication, we used an informative prior for inline image.

For data on changes in hedge length, we assumed the observation process as:

  • image(eqn 2)

where Cjk is the change in length between years j and k, inline image is the associated variance of the change estimate, either taken from the source publication when provided, or given an informative prior.

For the system process of the state-space model, the modelled value, Hi in year i, was smoothed according to the second order difference, Diff2, of the time series of modelled values, defined as follows:

  • image(eqn 3)

The choice of using the second- over the first-order difference was based on the assumption that not only should hedgerow length change smoothly over time, but the pace and direction of the change should also vary smoothly over time. This is because national trends in hedgerow removal or addition is a slow process that is driven either by the gradual mutation of farming systems and farmers’ culture or by political orientations. We achieved this by the random effect distributional assumption on Diff2:

  • image(eqn 4)

which has been implemented computationally by specifying

  • image(eqn 5)

with

  • image(eqn 6)

The amount of smoothing was controlled by the variance parameter, sdD2, which was largely informed by the data, having been given a vague half-normal prior (Gelman 2006): Half-Normal(0, 502).

Some of the data on hedgerow length or on change in hedgerow length were provided by the source publication without an associated standard error. Rather than considering these data as known without error, we chose to use an informative prior on the standard deviation of the observation process, formed as follows, for data on hedge length (eqn 7) and for changes in hedge length (eqn 8):

  • image(eqn 7)
  • image(eqn 8)

where xi and xjk are drawn from a beta(2, 4) distribution. se_minC and se_minH are the minimum standard error values we are prepared to accept for data on hedgerow change and for data on absolute length, when they are unknown. It is highly unlikely that the precision of the data without reported errors could be greater than any of the data from the Institute for Terrestrial Ecology, the latter being the most rigorous and intensive surveys conducted. The minimum value of the standard error was thus set at 14 and 30 respectively, which in each case is the largest standard error reported from standardized surveys (respectively, aerial photographs analysis and the UK’s Institute of Terrestrial Ecology’s countryside surveys in Pollard, Hooper & Moore 1974). The minimum standard error is then expanded by a factor (1 + 3*x), which varies from 1 to 4, with a mode around 1·75 and a mean around 2, to allow for larger but reasonable uncertainty about the estimates. As no information is available on the shape and upper bound of the standard error distributions, these choices have to be based on what is believed to be sensible, with an infinite number of subtle variations. Alternatively, one could also use the distribution of the stated standard errors to form a prior for the missing standard deviations. However in our case, we think that the latter data may not be representative of the former. To assess the sensitivity of the results to the specification of our informative priors, we carried out a sensitivity analysis on the prior by repeating the analysis with an expansion factor of either (1 + 1*xi) or (1 + 7*xi), equivalent to decreasing (expansion factor between 1 and 2, mean = 1·33) and increasing (expansion factor between 1 and 8, mean = 3·33) the value of the standard deviation of the data in the observation process. The latter case is probably too large, as a survey as imprecise as having a standard error near 100 000 km (30*3·33) would not be very useful to carry out. For comparison, we also ran a model without the data with unknown error.

Given the heterogeneous nature of the data, some approximations were required: (i) data from ‘England and Wales’ and from ‘Mainland Britain’ have been assumed to refer to the same geographical unit, as the remainder, Scotland, holds a very small proportion of mainland Britain’s hedgerows despite accounting for 36% of the landmass (Haines-Young et al. 2000); and (ii) data on changes in length from plots in England were assumed to represent the rates of change elsewhere in mainland Britain, and have been rescaled accordingly (Table 2).

The model was fitted with OpenBUGS 2.2.0 called from R’s BRugs library (Lunn et al. 2009). The code and data are given in Appendix S1 (Supporting Information), using the same variable names as in the methods description (eqns 1–8). We used 1 000 000 updates, of which one in 100 was kept to reduce memory storage needs, after a burn-in set of 6000 updates. Computation time for the hedgerow model alone (without bird data) was 240 s on a 2·4 GHz, P9400 Intel Core Duo CPU.

Yellowhammer data

Once reconstructed, the annual time series of hedgerow lengths was considered in conjunction with annual estimates of yellowhammer population sizes to assess the potential of change in the habitat variable as being a cause of change in the population. The British Trust for Ornithology’s Common Birds Census (CBC) is based on intensive bird territory mapping at 200–300 sites annually across lowland England. A national population index and its standard error are obtained using a Poisson GLM expressing counts as a function of the site and year (both categorical), which gives the trend in relative yellowhammer population size (Siriwardena et al. 1998). We compared the two time series by calculating correlation coefficients with varying time-lags within the model. At each step of the MCMC chain, a correlation coefficient was therefore obtained for every time-lag from 0 to 10 years. This provided us with a posterior distribution of the correlation coefficients that allowed for the uncertainty in the bird census and in the modelled hedgerow lengths generated by our analysis.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  10. Supporting Information

The data set collated for our reconstruction of the national hedgerow length arises from a number of sources and is clearly heterogeneous (Tables 1 and 2, Fig. 1a). It comprises both point estimates and estimated rates of change, both with or without associated ranges. The reconstruction amalgamates the heterogeneous data and fits a smooth line to it (Fig. 1b). This fitted time series suggests five successive periods of hedgerow changes: relative stability until 1955, accelerated decline (1955–1970), stability (1970–1983), sharp decline (1983–1994) and partial recovery since about 1994 (Fig. 1b).

image

Figure 1.  Hedgerows in the UK: available data (a) and trend adjusted to data (b). Black dots are published estimates of hedgerow length in the UK, with known 95% confidence intervals (continuous segments) or with 95% credible intervals estimated by the model (dashed segments). Black lines are published data on the rate of hedgerow removal in England, with known confidence intervals (continuous lines) or with credible intervals estimated by the model (dashed lines). The starting point of segments has arbitrary y-coordinate in panel (a), and has been positioned at the corresponding value of the smoothed estimate in panel (b). The thick grey line is the smoothed estimate of hedgerow stock from our Bayesian additive model, with 95% credible interval (dashed grey lines). Diamonds show the Common Bird Census index value for the yellowhammer.

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Five observations on rates of change in hedge length and seven observations on hedge length were provided without useful information on their precision, which we had to estimate in the model. The posterior distribution of standard deviations for these data (median = 28 000 and 58 000 km for change in length and length, respectively) is very close to the prior distribution we specified (median = 27 000 and 58 000 km), except for one observation on rate of change from 1962 to 1966, with a median standard deviation of 35 000 km (Fig. 2). The sensitivity analysis of the fitted trend to changing the prior distribution of standard deviations (Fig. 3), shows that considerably increasing the standard deviations of these data (i.e. assuming that the data are of extremely low precision) makes rather little difference to the fitted trend. However, even under this assumption, the data continue to influence the estimated trend, as shown by the comparison with the analysis excluding the data points with unknown standard errors (see the thin dotted black line in Fig. 3). On the other hand, assuming that the data were relatively precise, by almost halving the assumed values of the standard deviations, makes the fitted trend wigglier (i.e. fitting every data point more closely). However, the effect on the fitted trend is only marginal after 1960.

image

Figure 2.  Comparison of prior (thick grey line) and posterior (black 4 lines) distributions of the unknown standard deviations in thousands of kilometres. (a) data on changes in hedge length. (b) data on hedge length. Each black line shows the posterior samples’ distribution of the estimated standard deviation for one data point. The outlying posterior distribution corresponds to the observation of the change between 1962 and 1966.

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image

Figure 3.  Prior sensitivity analysis for unknown standard deviations. Fitted hedgerow trends under three different prior specifications of standard deviations: sd between 1 and 2 (mean = 1·33) times the base level (black dotted line); sd between 1 and 4 (mean = 2) times the base level (medium grey plain line, our model); sd between 1 and 8 (mean = 3·33) times the base level (light grey dashed line). Base level is set as the maximum se reported for the best data (see Methods). The thin black dotted line shows the hedgerow trend estimate without using the data with unknown standard error.

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Having reconstructed a time series for the environmental variable, we now indicate its potential utility for an analysis relating the environment point estimates to a relevant biological indicator: the population size of a farmland bird that utilizes hedgerows for nesting. Cross-correlation indicates that there are very strong (and significant) associations between hedgerow length and yellowhammer population size from 1966 to 2000, with a direct correlation of r = 0·86 and the strongest relationship occurring with a 2- to 3-year lag (i.e. changing hedgerow leads to subsequent changes in yellowhammer population size 2–3 years later) (r = 0·90; Fig. 4a,b). Figure 4a indicates that although the maximal lag occurs at 2 years, there is statistically little difference in the cross-correlation coefficients between lags 1–5. Calculating R2 from the correlation coefficients indicates that hedgerow length explains between 74% (without lag) and 81% (with 2- or 3-year lag) of the variation in yellowhammer abundance. This relationship is well described by a linear relationship, and is close to one of direct proportionality (Fig. 4b).

image

Figure 4.  Farmland bird abundance in relation to hedgerow stocks in the UK. (a) Cross-correlation coefficients (with associated 95% credible intervals) between time series of hedgerow length and yellowhammer Common Bird Census index. A lag of N years corresponds to hedgerow length N years before the bird census. (b) Relationship between yellowhammer index and hedgerow length in the same year (open grey symbols), or 2 years before (filled symbols). The reference (dotted) line y = ax shows how a direct proportional relationship would look. Error bars are standard errors on length estimates. Standard errors around the Common Bird Census index are too small to be visible on the plot.

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  10. Supporting Information

By developing a hierarchical modelling approach within a Bayesian framework, we have been able to combine data from different sources to reconstruct a series of environmental change from sparse historical data. We also show the utility of such historical series by demonstrating close to direct proportionality between the population size of a farmland bird in the UK and the reconstructed series of hedgerow length.

Sparse data do not always come with adequate information on measurement or sampling error. Assuming that historical data carry some amount of measurement and/or sampling error is safer than not; but it leaves us with the difficulty of deciding how much uncertainty there is about these items of data. We assigned an informative prior to the standard deviation of the observation process for studies in which the standard error of the estimate was not reported. Our sensitivity analysis indicated that assuming the data were precise (i.e. priors for the standard deviations concentrated towards the minimum value) had an effect at the early part of the time series (when the estimates were very variable) but not thereafter. Such a rapid succession of large increases and decreases in hedgerow length before 1960 in Britain is unlikely to reflect real changes. Hedgerow change on a national scale is likely to be a slow process and thus the trend is more likely to be smoother, particularly in older times before the advent of large scale hedgerow policies. Assuming the data with unknown precision were moderately or very imprecise had little effect on the fitted trend at all. It is probably safe to give less weight to data points whose precision is unknown, by assigning them larger prior standard deviations. On the other hand, the assigned standard deviations should not be too large, since this would tend, in practice, to discard the corresponding observations from the analysis by giving them little weight. Our assumption that missing standard errors should range from 1 to 4 times (mean = 2·3) that of the best data where standard errors had been produced, appears to yield satisfactory results, as smaller values produce less realistic trends, while even extremely high values do not significantly affect the results. Furthermore, our final model estimates are consistent with the claim that some of the points (in 1945 and 1970, and see Table 1) are actually overestimates of hedgerow length (Pollard, Hooper & Moore 1974). It should be noted that the use of informative priors becomes less necessary as the number of observations increases, and in fact the choice of the prior had hardly any influence on the results after 1960, the period of most interest in relation to bird population dynamics.

Although we already knew that the hedgerow stock had approximately halved in Britain since the 1960s (Robinson & Sutherland 2002), the data came from different sources, estimated different parameters (hedgerow length or rate of change), were associated with different regions and spatial scales and had different errors associated. Consequently, there were insufficient matching observations of hedgerow lengths to provide a useful explanatory variable in any model seeking to find associated impacts of changing that environmental variable. By combining heterogeneous historical data, we estimated two major periods of hedgerow decline: about 1955–1970 and about 1983–1994. These periods resulted from two independent mechanisms. The first period is consistent with accounts that 42% of hedgerow removals in Eastern England were conducted within field drainage schemes (Sturrock & Cathie 1980), which were subsidized by UK’s Ministry of Agriculture, Fisheries and Forestry between 1955 and 1973. The second period is well estimated through the successive standardized surveys by the UK’s Institute for Terrestrial Ecology (Barr, Gillespie & Howard 1994), and was primarily the result of amalgamation of fields into larger blocks, which are more efficient for modern intensive agricultural practice, and to conversion of hedges into fences (Petit et al. 2003). Spatial variation has occurred in hedgerow rates of change, such as between arable and pastoral areas (Petit et al. 2003). Our model could easily produce regional trends, provided that more data become available, for instance by revisiting collections of old aerial photographs.

Despite well-known population declines in European farmland birds, there is no consensus as to the detailed underlying mechanisms (other than the multiple effects of the ‘intensification of agriculture’) (Benton et al. 2002; Robinson & Sutherland 2002; Donald et al. 2006; Wretenberg et al. 2006). The difficulty of disentangling the causes of decline partially arises from much of the available data being reproductive-census-based, and thus measuring demographic rates (e.g. brood success, survival) and population size of breeding birds. Habitat loss may reduce the proportion of birds able to breed without affecting the demographic rates of the animals in suitable habitat. This may lead to the paradoxical observation that population sizes of several species have declined whereas demographic rates have not, as is indeed the case in the yellowhammer (Siriwardena et al. 2000; Cornulier et al. 2009). Thus, without adequate information on available habitat, it is impossible to disentangle fully the potential drivers of decline. The estimates of the availability of nesting habitat (i.e. hedgerow length) offer much greater resolution of environmental changes than previous accounts that used simple linear regression of hedge length against time (Robinson & Sutherland 2002; Fig. 4c). This allows us to assess relationships between bird and habitat trends over periods with different rates of change, immediately leading to hypotheses about the impacts. The yellowhammer population density index from the Common Bird Census over the period 1966–2000 was most strongly correlated to our estimates of hedgerow length in Britain with a 2- to 3-year time-lag. This time-lag may be an artefact due to imprecision in the estimates of hedgerow length, which tends to increase the confidence intervals of the correlation coefficients. Alternatively, it may reflect genuine delays in population response to habitat loss that may be explained by the buffering effects of density-dependent habitat selection (O’Connor 1980; Ferrer & Donazar 1996), of breeding philopatry, if individuals persist to breed in territories after the loss of optimal habitats such as hedgerows (Ambrosini et al. 2002). Non-breeding individuals, that is individuals that are present in the population but do not produce recruits, can also buffer population response to habitat loss (Durell & Clarke 2004). In this regard, it may not be coincidental that the lag is approximately a generation time: loss of breeding habitat may not reduce population size, simply converting breeders to non-breeders until natural mortality occurs. Previous analyses of yellowhammer demographic parameters have shown a considerable increase in breeding output per nesting attempt over the course of the population decline (Siriwardena et al. 2000; Cornulier et al. 2009). A production of excess recruits may thus also contribute to delay the population response to habitat loss. Finally, there is some suggestion that the recent recovery of the yellowhammer after 1995 is lagging behind the increase in hedgerow availability. This could be explained either by the time required for newly planted hedgerows to become suitable as a nesting habitat, or by a delay in the ability of yellowhammer to colonize the new habitat patches. There seems to be a slight discrepancy in the early 1970s in that hedgerows seem to be declining fast but yellowhammers not. One explanation is the lack of precision we have in the information about hedgerow trends, which could lead to a wrong estimated timing of hedgerow loss in that period, or indeed lack of precision in the yellowhammer CBC estimates at the start of the time series. Another possibility could involve a threshold effect: the amount of hedgerows left may have been sufficient in the first part of the decline to maintain the number of yellowhammer territories, but the second period of hedge decline certainly seems to have had an impact.

In local studies of yellowhammers, Bradbury et al. (2000) and Whittingham et al. (2005) showed that the presence of hedgerows increased local territory density, while Kyrkos, Wilson & Fuller (1998) found a positive effect of hedgerow length on Common Bird Census plots. Owing to its national scale, our analysis averages over small-scale spatial variation in hedge suitability, allowing us not only to confirm the generality of previous results, but also to show that temporal variation in yellowhammer abundance is almost linearly related to that of hedgerows. This tentatively suggests hedgerow loss is a stronger candidate cause for the yellowhammer decline in the UK than hitherto thought (see e.g. Gillings & Fuller 1998; Newton 2004), and that population decline is at least partially driven by a reduction in available high-quality habitat.

Reconstructed time series of environmental change, such as the hedgerow series in this study, can be used as covariates in subsequent analyses, accounting for the uncertainty in the estimates. In the case of the yellowhammer, a complete population dynamics model could be defined where the proportion of breeding individuals, a key component of productivity, would be a function of nesting habitat availability. This model has not been attempted here as the best way to make the fullest use of these data (an integrated population model with observation errors in both the population size estimates and the hedgerow length estimates) is beyond the scope of this study.

Conclusion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  10. Supporting Information

We show, using a simple model system, that it is possible to use modern statistical approaches to reconstruct past environmental change from a variety of sparse and heterogeneous historical sources. We illustrate the utility of this approach by using our reconstructed environmental variable as an explanatory variable, which indicates that the change in the environment may have played a significant role in driving the decline in the national population of an organism utilizing that environment. The modelling framework we used is completely general and can be adapted for reconstruction of any environmental variables. Other applications of the method may involve for instance the combination of data on abundance, presence–absence, or presence only to reconstruct trends in population size. In addition to the temporal dimension, the smoothing method could also be expanded to produce spatial trends.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  10. Supporting Information

This work is the result of a NERC grant awarded through UKPopNet to W.J.S., T.G.B. and X.L. We thank Steve Palmer and David Howard (CEH) for their help with the hedgerow data.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  10. Supporting Information
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Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  10. Supporting Information

Appendix S1. Bugs code and data for the hedgerowmodel and correlation with the yellowhammer population index

FilenameFormatSizeDescription
MEE3_54_sm_SuppMat.docx24KSupporting info item

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