The standard census method for burrow-nesting petrels involves using an estimated response rate to correct the number of responses to tape playback obtained across a study site. Response rates can vary significantly between sites and between surveys and are estimated by determining the level of response within a calibration plot for which the number of occupied sites must also be estimated. The field methods used for such surveys are well established. However, a range of analytical methods have been employed to determine the number of occupied sites within the calibration plot and hence the response rate. The choice of method can have a huge effect on the estimated population size. Data from surveys of Leach’s Oceanodroma leucorhoa and European Storm-petrel Hydrobates pelagicus on North Rona in 2001, 2009 and 2015 have been used to compare the three methods commonly employed to estimate the number of occupied burrows within the calibration plot. This number is usually subject to uncertainty and is key to estimating the population size. Our analysis suggests that the widely used ‘reciprocal transformation’ method can give rise to implausibly high population estimates which are up to 70% higher than those provided by other methods. We conclude that whilst potentially useful in some situations, this method should not be used in isolation. No single method appears best in all situations, but for North Rona the alternative ‘curve fitting’ and du Feu methods consistently give more plausible population estimates.

The field methods employed for conducting census counts of burrow-nesting species such as Leach’s Oceanodroma leucorhoa and European Storm-petrel Hydrobates pelagicus are well established and based on Ratcliffe et al. (1998) and Gilbert et al. (1998). Tape-playback is employed to locate ‘apparently occupied sites’ (AOS) across a study site. The number of AOS is then corrected for nonresponse using an estimated response rate. A calibration plot is used to estimate the response rate by undertaking daily repeat visits to all burrows in the plot, in order to ascertain the proportion of visits that elicit a response. For more detail see, for example, Bolton et al. (2010) or Murray et al. (2010).

Whilst there is a standard method for the fieldwork, there is less standardisation in the analytical methods employed to arrive at a population estimate. In particular, the response rate relies on estimating the number of AOS in the calibration plot, some of which may not have responded by the last visit. Study site population estimates are very sensitive to this number and the available methods can give very different results. Ensuring that sufficient visits are made and then selecting the correct analytical method is critical to avoid reporting biased population estimates. Bolton et al. (2010) compare two of the available methods using data for European Storm-petrel from Mousa, Shetland Islands, and they encourage others with similar data to conduct analyses to compare with their own findings. Thus, this short paper uses equivalent data from surveys on North Rona to assess the methods currently employed and aims to arrive at some recommendations for future surveys.

The standard method requires repeat visits over at least seven days and whilst, in theory, more visits could be made to increase the likelihood of finding most AOS, this is usually impractical. Also, the assumption is made that the response rate stays reasonably constant but this may only apply during the incubation period or shortly after hatching. Thus, the total number of occupied burrows has to be estimated and at least three methods are in use for this purpose. Once the total has been estimated, the response rate is usually calculated by simply dividing the mean daily number of responses obtained by the number of AOS, although other methods may be applicable if, for example, a declining response rate over the study period is suspected. This was evident for the European Storm-petrel survey on North Rona in 2001 and there the response rate was estimated by only making use of the first response from each burrow (Murray et al. 2010, 2016).

Two of the methods for estimating the calibration plot population are asymptotic approaches. The first fits an exponential curve to the cumulative number of responding burrows by visit (Mayhew et al. 2000). This is fitted using a non-linear regression method and the result is illustrated in the first graph of Figure 1a, with the population size provided by the curve’s asymptote (46 in this example). The full methodology can be found in Appendix 2 of Mitchell et al. (2004). The second approach fits a straight line to a reciprocal version of the same plot, illustrated in the second graph of Figure 1a, and is based on Fowler (2001). The population size is provided by the value at the intercept with the y-axis (in this example 1/0.0169 = 59). For convenience, these methods will be termed the ‘curve fitting’ and ‘reciprocal transformation’ methods respectively. The third approach is du Feu’s mark-recapture method, which treats second and subsequent responses at each burrow as recaptures (du Feu et al. 1983). Assuming each capture is equally likely, du Feu et al. (1983) provides a formula, which can be solved iteratively to estimate the population size. Although this method does make more complete use of the available data, its assumption of equal capture probability of all individuals on all days will be invalidated when, for example, some nests are no longer attended by adults during daylight on later surveys, as chicks no longer require brooding.

The 2009 and 2015 North Rona expeditions were partnership projects, made possible by funding provided by the Seabird Group, Scottish Natural Heritage, the Scottish Ornithologists’ Club, the Gibson Estate, the Royal Society for the Protection of Birds, the Royal Commission on the Ancient and Historical Monuments of Scotland, Historic Scotland and the British Broadcasting Corporation, for which we are very grateful. The 2001 survey was carried out under contract to the Joint Nature Conservation Committee. Thanks are due to Mark Bolton, Mike Smith and an unnamed referee for extremely valuable comments on the draft manuscript.

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