Methods

Summary

The annual population indices used to estimate population trends are based on daily "estimated totals" (ETs) which are an estimate of the numbers of migrants present in, or passing through the sampling areas at each of the three stations at Long Point. These are then fed into a multiple regression model that adjusts the counts for variation in daily weather and expected numbers at different times in the season. The annual index for each year is based on the average of these adjusted counts for all 3 stations. To estimate trends, we have used polynomial regression to allow for the fact that many population changes are non-linear.

Further details on the methods are described below, as well as in the papers by Hussell et al. (1992) and Francis and Hussell (1998).

Daily estimated totals

The raw data on which the indices are based are daily "estimated totals" (ETs) which are an estimate of the numbers of migrants present in, or passing through the designated areas at each of the 3 stations at Long Point (Old Cut, Breakwater, and the Tip). Not all stations were run every year, or on the same days each year. These indices represent the observers' best estimates of the numbers of birds in the designated area. Various migration monitoring stations use different variants on these methods depending upon their local circumstances. At Long Point, ETs are based on a combination of a standardized "census" (in which all birds seen or heard on a specific route within the census area are counted over a one-hour period), banding totals (based on non-standardized banding), and general observations. Details of the methods, and justifications for using ETs, are given in McCracken et al. (1993).

Annual abundance indices

The numbers of birds detected passing through the census area on a given day reflect many different factors, including the true population levels (the factor to be indexed), seasonal variation, weather conditions, the phase of the moon and additional (error) variation. Some of these factors, such as time in the season or certain weather variables (e.g., the passage of cold fronts in autumn), are likely to affect the numbers of birds migrating on a given day. Other factors, such as cloud cover, rain, or the phase of the moon, may affect the numbers of birds that stop at the monitoring station, or that can be detected.

By modelling variation in these additional factors, the variation in the counts can be reduced, hopefully resulting in indices that more closely reflect changes in the true populations of each species from which the migration sample is drawn (see Hussell et al. 1992). This may increase the sensitivity of the analyses for detecting changes in the populations. For the present analyses I have used multiple regression to estimate relationships between daily estimated totals and various external factors, such as weather and time of year, and then used these relationships to adjust the counts and produce a population index. Factors included in the equation include date (within a season), cloud cover, wind speed and direction, temperature, and phase of the moon. Some of these variables were adjusted using only linear terms, while for others second or higher order polynomial terms were included as well. All variables were assumed to interact additively on a log scale (multiplicatively on the original scale), but to have independent effects in each of the areas. At Long Point, area effects were modelled using dummy variables, so that data from all three areas could be included together (see Hussell et al. 1992, Francis and Hussell 1998 for further details). Indices were calculated separately for spring and fall data. For each species, analyses were restricted to the period when most of that species usually migrate—the migration windows. These were determined by excluding isolated occurrences of the species (early or late records separated by more than 4 days from the next record), then determining the middle 98% of occurrence days. In addition, for species with small breeding populations at a particular site, the late spring cut-off and the early fall cut-off were selected to exclude periods when more than half of individuals detected were probably resident in the area. This involved a judgement call in many cases, but analyses of the data using a variety of different cut-offs suggest that the results were not strongly affected by the precise cut-off dates.

Weather data

Weather data for the analyses at Long Point were obtained from the U. S. meteorological station for Erie, PA. BSC now has complete hourly data for that station from 1961 to December 31, 1998 for several weather variables, including cloud cover, horizontal visibility, wind speed and direction, temperature, relative humidity, station pressure and ceiling height. Sometime in 1995, the wind measurement changed from a 1-minute mean to a 2-minute mean, but this is unlikely to have any noticeable effect on the measurements. In late 1995, the weather station was converted to an automated weather station. For most measurements this should have had little effect, but for Total Sky Cover (= cloud cover) it has had a substantial effect: opaque sky cover is no longer recorded, and any type of sky cover is only recorded up to a height of 12000' (about 3600 m). This means that total cloud cover above this height will be recorded as clear sky. An analysis of ceiling height and cloud cover from earlier years suggests that total cloud cover over that height was not common, but it did happen sometimes. The potential effects of this change on our analyses have not yet been determined, but are unlikely to be very large, especially on the annual indices.

Population trends

Owing to the fact that most of the population changes evident at Long Point have not been linear, polynomial regression provides a better approximation to the true population trajectory than linear regression. For each season, polynomial models were fitted ranging from 1^st order (linear) to 7^th order on the log-transformed indices. The most parsimonious model (model with the lowest order that adequately fits the data) was then selected using the Akaike Information Criterion (AIC) which has been receiving increasing use for model selection in many biological modelling fields.

Literature Cited

Francis, C. M. and D. J. T. Hussell. 1998. Changes in numbers of land birds counted in migration at Long Point Bird Observatory, 1961-1997. Bird Populations 5-6: 37-66.

Hussell, D. J. T., M. H. Mather, and P.M. Sinclair. 1992. Trends in numbers of tropical- and temperate-wintering migrant landbirds in migration at Long Point, Ontario, 1961-1988. Pp. 101-114 in Hagan, J. M. III, & D. W. Johnston [Eds], Ecology and Conservation of Neotropical Migrant Landbirds. Smithsonian Institution Press, Washington, D. C.

McCracken, J. D., D. J. T. Hussell, and E. H. Dunn. 1993. A manual for monitoring bird migration. Long Point Bird Observatory, Port Rowan, Ontario. 65 pp.

by Charles M. Francis and David J. T. Hussell