THE GENERAL CONTEXT Of STATISTICS IN ORNITHOLOGY

PHILIP M. NORTH and BYRON J.T. MORGAN

Mathanatiaa~ In8titute Univer8ity of Kent

CanterbW'y Kent

CT2 '1NF

SUMMARY

This paper sets the scene for those that follow. Particular attention is paid to analyses of ring recovery, census and migration data. Ornithological data are being collected on a wide scale, and they are seen to pose challenging problems of inter­pretation and modelling.

K6Yword8: ORNITHOLOGY; RING RECOVERY; CENSUS DATA; MIGRATION DATA; STATISTICAL ANALYSIS; MODELLING

1. INTRODUCTION

The aim of this paper is to provide a general setting for those that follow. It is not possible in this one paper to provide a comprehensive review of Statistics in Ornithology. Studies in ornithology are inherently statistical, ranging from the collection and management of large sets of national census data, to much smaller experimental investigations. Both 1arge- and small-scale studies are represented in the papers of this volume.

In Britain the British Trust for Ornithology (B.T.O.) co-ordinates most of the major studies of British birds. These include the Common Birds Census, discussed later by Mountford (1985), the national ringing scheme (resulting in data of the kind analysed in papers of Section C and in information on bird movements) and the bird observatories network, discussed later by Darby (1985). In Britain, ornithological studies are also carried out by, amongst others, the Institute of Terrestrial Ecology, the Royal Society for the Protection of Birds and the Edward Grey Institute of Field Ornithology, the last being notable espeCially for the long-running study of the Great Tit (Parou8 maJor) population in Wytham Wood, Oxford. Many of the available data sets contain counts, from censuses or surveys, while others, such as ringing data, include much additional biometric information. A study such as the Nest Record Scheme (organised by the B.T.O.) provides detailed information on breeding habits. B. J. T. Morgan et al. (eds.), Statistics in Ornithology© Springer-Verlag Berlin Heidelberg 1985

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P.M. North and B.J.T. Morgan

Similar studies take place throughout the world, as in, for example, the North American Bre'eding Bird Survey and the Christmas Bird Count, which respectively pro'" vide counts of breeding and wintering birds in North America. The practice of hunting birds in North America can result in data of a kind that one does not encoun­ter in the United Kingdom (see the papers by Boyd and Hyslop, 1985, and Conroy, 1985, which follow). In addition to large-scale surveys, attempts have been made to record the observations made by ordinary bird-watchers (see Darby, 19H5, and Reese, 1985, later). While the data resulting from such attempts would inevitably be treated with caution, serious deficiencies may exist in any data set due to observer variability. Kepler and Scott (1981) point out the alarming 'window species' found with even trained observers. These are species which they consistently fail to record even though conspicuously present. Ramsey and Scott (1981) recommend testing observers for hearing ability, but it is clear that such ground rules cannot be generally fol­lowed. In some cases (see Darby, 1985, and North and Morgan, 1979) factors such as weather may be directly included in data analysis, but more typically the influence of weather conditions is ignored, as is also the effect of sampling terrain. Ripley (1985) later develops methodology for dealing with the difficult edge-effects prob­lems which inevitably arise in census studies.

Digests of data can be found in popular books such as Fisher and Flegg (1978) and Perrins (1974), but here too caution is needed in interpretation. For example, in Perrins (1974, p.129), adult mortality rates and 10ngevities of some common birds are presented which mask the uncertainties and statistical problems which accompany the computation of mortality (survival) rates (see Lakhani, 1985, later).

Historically, the first main impact of statistics in ornithology was in the analy­sis of ring recovery data, and it is no coincidence that Section C of this volume is the largest. The background here is provided in the next section. We continue with a discussion of the analysis of census and migration data before concluding with general remarks about the future.

2. ANALYSIS OF RING RECOVERY DATA 2.1 Survival Studies

For many years now birds have been ringed (or banded in American terminology) and recoveries of rings some time later used to provide information on the birds' movements and survival. Indeed, it is through such information that much of what is currently known about birds' journeys on migration was discovered. Such knowledge

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The general context

was perhaps, pri mari ly what was being sought in the early days of ringing, and is still of immense interest today. Of course, ring recoveries also provide information on birds' survival and it is here that the statistical analysis of ring recoveries has been most extensively developed. However, even now there still remain difficul­ties, which can perhaps be overcome only by supplementing the ringing of young with further ringing of other age classes (see, for example, Brownie et at., 1978) or by some further field information (Lakhani and Newton, 1983; Janz, 1985).

The pioneering work in the estimation of bird survival rates from ring recoveries was done by Lack (1951). His approach is only applicable to 'complete' ring recovery data, in the sense that no mere rings are expected to be recovered in the study in question. This work was extended later by Haldane (1955), to be applicable also to 'incomplete' data sets, where some rings, on birds still alive, remain to be recovered at some time in the future. However, both models are only suitable for adult birds and deal only with ring recoveries from dead birds, which are the most common recover­ies. Some biologists still use these methods, despite the fact that there has been considerable development of relevant statistical methodology over the past fifteen years.

Cormack, in the statistical appendix to Fordham and Cormack (1970), concerning a study of the Dominican Gull, allowed in his model for age-specific survival rates, as opposed to the constant annual adult survival assumed by Lack(1~51) and Haldane (1955). Cormack also considered a full maximum likelihood approach incorporating the information on the number of birds ringed, as well as numbers recovered. Seber (1971) developed a computationally attractive approach to the age-specific survival analysis (but see North and Cormack, 1981, for a critical appraisal of the method) and considered a ca1endar-year-specific case elsewhere (Seber, 1970a). Much of the further development of the methodology was carried out in the U.S.A .• and age-specific and year-specific effects for the survival and/or the recovery rates were built into the various models developed by Brownie and Robson (1976) and by Brownie et at. (1978). The paper in this volume by Dobson (1985) considers age-specific survival rates.

We may note again here the point made in the introduction that most of, the work from North America relates to hunted wildfowl, in contrast to studies in Britain, for example, where most ring recovery data arise from birds found dead, rather than shot. Recently, statisticians have expressed concern about the validity of the assumptions underlying the models used to analyse ring recovery data. In particular the assumption of a constant recovery probability has been questioned by Burnham and Anderson (1979) and Anderson et at. (1981) address this problem, while Lakhani (1985)

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P.M. North and B.J.T. Morgan

(see also Lakhani and Newton, 1983) cons i ders the non-i dentifi abil i ty of the s urvi va 1 estimates, even if all the other model assumptions hold, and warns about the possibly misleading effect of the generally used constraint, viz. that the annual survival prob­abilities for the two or more oldest year groups are equal. The problem considered by Lakhani illustrates the benefit of having additional information available, in this case in the form of a likely range of values for the ring recovery probability. Discussion with ornithologists suggests that in practice it might be possible to obtain information about the likely range of values for the ring recovery probability, so that an approach like that described later by Janz (1985) could then be useful. More research is needed into deciding which kind of further information is most profitable and how best to incorporate it to derive reliable estimates.

The ring recovery analyses that have been discussed so far in this section relate to situations where there is at most one recovery for each bird, usually when the bird is dead. However, in the wider area of animal ecology, the need to assess the abun­dance of animal populations has led to the development of capture-recapture methods when multiple recapture data can be collected. This has not in the past often been the case in ornithological applications. However, recently there have been published analyses of multiple recaptures of birds, and this volume contains further examples (See Section C.)

Boyd (1956) applied capture-recapture methods to data on Pink-footed Geese (Ansel'

brachyrhynchus), and Orians and Le~ie (1958) did so in a study of Manx Shearwaters (Ruffinus puffinus) (see also North, 1981, for futher modelling of multiple recapture data for this specie,S). Long (1975) applied a capture-recapture approach to Reed Warbler (AcrocephaZus scirpaceus) data. More recently, Buckland (1982a) described an approach that can combine both multiple recapture and ring recovery data. Its use is illustrated with data on Fulmars (PUZmarus gZaciaZis) and Galahs (Cacatua

roseicapiZZa). In this volume, Seber (1985) and Seber and Manly (1985) provide further useful extensions to the capture-recapture methodology.

'Recaptures' of birds may sometimes only be resightings as, for example, in the study of colour-ringed Fulmars, reported by Dunnett, Anderson and Cormack (1983) and by Cormack (1973). Buckland, Rowley and Williams (1983) discuss the use of resighting data for Ga1ahs, while Brownie and Robson (1983) have generalised the Jolly-Seber (Jolly, 1965; Seber, 1965) model to estimate tin~-specific survival rates from resightings, and illustrate their approach with data on the Semi-pa1mated Sandpiper (CaZidris pusiZZus).

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In this volume Clobert, Lebreton, Clobert-Gillett and Coquillart (1985) also con­sider the use of sightings as well as recaptures. Pollock (1981a) has earlier develop­ed capture-recapture models allowing for age-dependent survival and capture rates, and illustrated them with an application to Giant Canada Geese (Branta aanadensis

maxima). In the present volume Parkin and White-Robinson (1985) report on a study of Canada Geese (Branua aanadensis). Age-dependent survival is also considered here by Rothery (1985) in his study of Hen Harriers (Ciraus a. aayneus).

Other recent work by Pollock (1974,1975) and Buckland (1982a) has concentrated on the problems of unequal survival and catchability. The latter is likely to be a problem in sone ornithological applications. For example, MacArthur and MacArthur (1974) and Manly (1977a) have pointed out that standard capture-recapture methods should not be used with data resulting from birds being trapped in mist nets. This is because birds which have been captured and released tend to avoid mist nets from then on, and because birds caught in the nets may come from a mixed population of resident and migrant birds. For example, Buckland and Hereward (1982) estimated that immature Yellow Wagtails (Motaaitta !lava ftavissima) at a pre-migratory roost, which had not been captured before, were probably six or seven times more likely to be netted than previously captured birds.

Cormack (1985) later describes how GLIM can be used to fit log-linear models to capture-recapture data, and illustrates the approach with a number of ornithological examples, including an application to data described by Cheke (1985) in this volume.

2.2 Movement Studies

Ring recoveries have provided much valuable information on birds' movements but statisticians have not developed methodology here to anything like the extent that they have for survival studies. This is partly because many problems exist with the data. For a start, recovery rates are typically very low, and may vary over a bird!s range. Many of the possible problems involved are met in a study of Razorbills (AZaa torda), reported by North (1980a), following a study of the same species by Lloyd (1974). For a discussion of ring recovery data for various auks see Mead (1974). Other quantitative studies of seabird movements from ring recoveries are by Coulson and Brazenda le (1968) for the Cormorant (PhaZaaroaorcq; aerbo) and by Bi rkhead (1974) for the Guillemot (Uria aaZge). Later North (1985) discusses random-walk models which might be us~d qualitatively to describe bird movements, based on the evidence of ring recoveries.

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P.M. North and B.J.T. Morgan

The problem of the distinction between migration and dispersal is likely to prove difficult to resolve in many cases. However for some species the situation is quite clear-cut, and Kendall (1974) has elegantly shown how simple migration strategies can result in successful migration passage~.

3. ANALYSIS OF CENSUS DATA

Ornitholo,gical censuses provide another rich area for the involvement of stati­sticians, as can be seen from the Symposium on Estimating numbers of Terrestrial Birds, held at Asilomar, California in 1980. (See Ralph and Scott, 1981.)

The British Common Birds Census has attracted the attention of a number of stati­sticians in recent years. The basis of the census· is a mapping technique which is used to estimate the numbers of territory-holding males of the commoner species on the census plots, using results accumulated over a number of visits to each plot during the breeding season by voluntary observers (one observer per plot). The esti­mation of territory numbers and relative positions can be viewed as a problem in cluster analysis, and is currently carried out by hand. Attempts to produce an automated objective approach to this estimation problem have been reported in a series of recent papers by North (1979,1980b, e.g.). Although it is primarily the numbers of territories that are of interest here, it is also useful to have information on the relative positions of territories. At a simple level these can be shown to correlate well with habitat features, as would be expected - see Morgan and North (1980). However, spatial analysis is also of interest. The paper later by Ripley (1985), giving an analysis of nest spacings, is a current example. Others are by Bartlett (1974), who 'considered Swallows (Hirundo l'ustica), perching on a telegraph wire, and the distribution of nests of two species of gull. Besag and Diggle (1977) present an application of a Monte Carlo test to data relating to Blackbird (Tul'dus

meruZa) migration, and also use Monte Carlo testing to investigate the possible interaction between. nest locations and laying dates in a colony of Kittiwakes (Ris8a

tridactyZa). Ripley (1977) presented an application of his methods to data on nest sites of birds of prey, though Cormack (1977) pointed out the care that needs to be exercised here, since spacing between nests may simply be imposed by the availility of suitable nest sites.

The aim of the Common Birds Census is to monitor the fluctuations in population levels of the commoner species in Britain, and the census is carried out in a number of different types of habitat, but most commonly on farmland or in woodland. Each year, a summary of between-year compari sons for just two consecuti ve years, for each

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of the species monitored, has been presented in Bird Study (this is being continued from 1984 in B.T.O. News). Upton and Lampitt (1981) describe a model for investigating such between-year comparisons, while in the present volume Mountford (1985) discusses an index of population change, illustrated with applications to Common Birds Census data (see also Mountford, 1982). Simple models to describe annual numbers of terri­tories, for single species, over a period of successive years, are discussed by North (1~83). Applications of Taylor's power law (Taylor, 1961) to Common Bird Census data, for individual species, have recently been described by Taylor, Woiwod and Perry

(1978,1980); see also Taylor and Woiwod (1980). Bulmer (1975) provides a test for dens i ty-dependent effects.

Most of the work that has been done in this area to date has concentrated on single species at a time. But the communities being studied on the census plots are made up of many species, and mUlti-species approaches to analysing the data seem desirable and overdue. A simple multi-species comparison between a panr of consecu­tive years is described by North (1982). Later, Buckland and Anderson (1985) present a multivariate analysis of atlas data.

For many years ecologists have been interested in species-area relationships for many-species communities and in the measurements of species diversity. The papers in this volume by Usher (1985) and by Williamson (1985) examine species area rela­tionships, which provide a summary approach to the analysis of data from many-species communities. Related material is to be found in Reese (1985).

Another type of survey much used by ecologists for counting anima·1s, birds or plants is the line transect survey. Although this type of survey is not represented amongst the papers ~n the present volume, it is a topic which has interested stati­sticians considerably in recent years. The monograph by Burnham et aZ. (1980) pro­vides a useful revi'ew of the topic. Recently, the circular plot technique has been increasingly used by ornithologists. Here, the observer remains stationary and counts birds around him/her, for a number of selected positions. Statistical ' development is provided by Buckland (1984).

4. VISIBLE MIGRATION

The discussion on movement in the preceding section covers the evidence provided by ring recoveries. However, information on migration can also be obtained by direct observation. At one extreme, in Europe, this can take the form of the spectacular

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P.M. North and B.J.T. Morgan

visible migration of birds of prey at Fa1sterbo and over the Bosphorus, for example. In the 1960's considerable use was made of radar to study the pattern of bird move­ments, across such passages as the North Sea (see Lack and Eastwood, 1962; Eastwood 1967) .

In Britain data have been collected for many years on visible migration past or through the British bird observatories, all situated on the coast. These data are collected both from sea watches and from observations on the land surrounding the observatories. Darby (1985) describes the use of linear discriminant analysis to investigate the relationship between migration counts and weather conditions.

With the observatory migration work, there is a link with the census work des­cribed earlier. The Common Birds Census aims to produce a population index for each of the species monitored, and one can also consider constructing a population index from migration data. If this can be shown to be useful, it might enable species which are unsuitable for monitoring by the census mapping method to be monitored by the migration index. Recently, similar work has also be done in North America (see H us se 11, 1981).

Part of the data collection procedure at the observatories consists of sea watching. Sometimes it can be difficult to count birds passing by at sea, and it can be especially difficult, in situations where movements are taking place in both direc­tions, to assess the net number of birds involved. Upton (1985) considers this problem later.

5 .. DISCUSSION

The papers by Cheke (1985), Dale (1985) and Greig-Smith (1985) of Section A all deal with particular small-scale investigations, as do those by Lack (1985) in Section B, and by Hensler (1985) in Section C. The data set considered by Dale presents particular problems of analySis on account of the paucity of the available data. Many other studies can also suffer from lack of data, for example due to the small recovery rates of dead ringed birds. To some extent these problems will be alleviated as the studies progress through time.

On a different point, Buckland (1982~ and Burnham (1981) have emphasised the deficiencies that exist in current statistical methods and analysis in ornithology, with new n~thodology quite often taking many years after it is established, before

The general context

it is used in the field. Again, this is a situation which will improve with time, but clearly there needs to be better communication between statisticians and orni­thologists. It is hoped that this volume will help in this respect.

ACKNOWLEDGMENTS

We are grateful to Stephen Buckland and Ken Lakhani for their very helpful com­ments on an earlier draft of this paper.

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