About the Analyses
Annual Indices
Annual estimates of population size were estimated for each species in spring and/or fall by fitting a generalized linear model (GLM) with negative binomial distribution (or, in cases where a negative binomial provided a poor fit, a GLM with poisson distribution). All models were fit using the GLM function in the R statistical language version (R-2.5.1). All analyses were restricted to data within the migratory season of each species (see 'Seasonal Graphs' below).
All models included effect of date (1st to 5th order polynomial terms) to model variation in daily counts through time. To account for variation in daily effort and species abundance (e.g. to model the influx of new migrants) we also included a binomial variable in all models that classified daily totals of all species as above or below the 25th percentile.
Annual indices were calculated for each species by using parameters from the fitted models to predict the number of individuals observed on the middle date of the season, for each year, with a daily total number of birds above the 25th percentile.
Population Trends
Options for LOESS smoothed and Best Polynomial Model trend lines are offered in this application. A trend estimate is not available using the LOESS smoothed option. For the Best Polynomial Model option, trends were calculated in the following way:
Trends in annual abundance indices were calculated by fitting a regression model of the indices by year (described fully in Francis and Hussell 1998).
For stations with fewer than 10 years of data we fit simple linear models regressing the annual index on year.
For stations with more than 10 years of data we included polynomial terms for year, reparamaterized as described in Francis and Hussell (1998) to estimate the change between the average indices of the first three years to the average indices of the last three years (e.g., at LPBO: 1967-1969 to 2004-2006; 1997-1999 to 2004-2006). Basing the trend estimate on the mean of the first and last three years reduced the sensitivity of the model to poor estimates of the shape of the curve at the endpoints of the polynomial-fit curve (Francis and Hussell (1998).
The maximum number of polynomial terms to be included in the model was determined by dividing the number of years available for analysis by five. The most parsimonious model was then chosen by minimizing the Akaike's Information Criterion (AIC). For stations that included 3rd or higher order polynomials, we used a step-wise procedure that began with the linear model and added polynomial terms only if the addition of the next polynomial term resulted in a lower AIC score. If it did not, then higher order polynomial terms were not tested. It should be noted that this approach differs from that of Francis and Hussell (1998), who fit all polynomial terms, and selected the model with the lowest AIC. In these reparameterized models, the slope of the first order term gives an estimate of the annual percent change in population size through time (Francis and Hussell 1998).
In this application, the trend estimate for all potential time intervals is estimated based on the best polynomial model for the full time period at each station.
Annual Indices Tool
Long Point Bird Observatory (fall)
Cape May Warbler
The following are displayed only with the "Best Polynomial Order" option:
Order: Polynomial order of best fit model (model with minimum AIC value)
R2: R square based on best fit model
P: P-value of trend estimate; trends with p-value < 0.05 are considered statistically significant.
Trend Maps
Trend maps show the estimated population trend over a comparable period (eg, the most recent ten-year period
1997-2006) at sites or regions with sufficient data. For details on annual index and trend estimation procedures,
see the Annual Indices section above.
Seasonal Graphs
Seasonal graphs are plots of the daily mean log(count) across years sampled at a location (e.g., Canadian Migration Monitoring Network station).
Options are available to display a LOESS smoothed line of the percent of years the selected species was present each day of year, and the raw percent of years the station was in operation during each day of year (i.e., station coverage).
Migration windows show the boundaries of the spring and fall migration window, and are shown only if the species was analyzed during a particular season. The bounds of spring and fall migration windows were restricted to those days of the year when the station operated during at least 50% of total years in operation.
Delta Marsh Bird Observatory - Northern Waterthrush
˜ daily mean log(species count)
____ Percent of years species present each day
____ Percent of years station in operation each day
| Spring and/or fall migration window boundaries
References
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 4:37-66.
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