RPI Raptor Population Trends: Interpreting Trend Graphs and Maps

Our goal was to calculate annual indices and population trends for all stations that had at least 10 years of data (through and including 2019) entered into HawkCount.org. Sites with less than 10 years were considered to have insufficient data to estimate a meaningful long-term trend. Species with fewer than 10 individuals per year at a site were also considered to have insufficient data for trend analysis and were thus excluded.

It is important for users to recognize that the RPI partners do not have the resources or staff to do exhaustive checking of raw data and subsequent results. We rely on the sites contributing data to alert us to problems and to provide accurate data in HawkCount. Any questions on datasets or results can be sent to brown@hmana.org. Site descriptions and protocols are posted within the site profiles on hawkcount.org.

Results are presented in two formats: trend graphs containing the long-term linear trend for each species and site (see trend graphs), and trend maps which graphically show the most recent 10-year trends across sites for a given species, in this case for the period 2009 to 2019 (see trend maps).

How to read the population graphs

The following example shows the long-term trend for Northern Harrier at Hawk Mountain Sanctuary in fall. The black dots on the chart are estimated indices of annual population size as calculated by the statistical model, with error bars representing the 95% credible intervals for the annual indices. Annual indices are expressed on a linear scale and represent the average of the predicted number of individual birds detected per day of survey. If present, the blue line is a smoothed (loess) visualization of the change in annual indices over time.

The subtitle of the plot contains the estimated linear trend value for the long-term trend and for a trend based on 10-year intervals (time periods in parentheses). These trends are expressed as annual percent change in counts and assume a linear change in migration counts among years over the time period examined. The lower and upper limits of the 95% credible interval (CI) of the trends are shown in parentheses. In the example shown, the CI do not include zero for 2009-2019, suggesting strong support for the observed decline in migration counts for this species over the past 10 years. It can be seen from the plot that this decline has extended back several decades (see species assessment). An * following the reported trend and CI provides the posterior probability of the trend: a value greater than or equal to 0.95 provides additional and strong support for the observed trend.

Trend maps

Maps display the trends calculated for each RPI stations with sufficient data for a given species. Maps effectively visualize the spatial variation in trends of a species over a large geographic area. Consistent trends across sites within a region gives us confidence that the results we see are representative of trends in the underlying regional population, and not the result of site-specific biases. To ensure that all trends are directly comparable, maps show only the trend based on the most recent 10 years for each station. The example below represents the population trends of Bald Eagle based on fall count data. Upward arrows suggest a positive trend was observed at a site, and downward arrows suggest a negative trend was observed at a site. Green and red arrows suggest the 10-year trend is strongly supported (95% credible intervals exclude zero), while blue dots represent trends with little or no support, i.e., 95% credible intervals included zero, and the posterior probability was < 0.95. Note that the size of the green and red arrows is proportional to the magnitude of the increase or decline, as explained in the map legend. You can click on any of the markers to see more details about the station name, the trend, and the time period covered. You can also zoom in or out to better see the details in areas where there are several nearby stations, such as along the Appalachian Mountains. The example clearly shows that Bald Eagles are doing very well across all the US with some stable counts mixed in.

Data Collection

The raptor migration data analyzed by the RPI project has been collected over many years at many independent raptor migration watch sites, each operating within their established protocols. Much of this data has been recorded on paper forms and more recently in online databases; many efforts are now underway to pull the historical paper forms into online databases such as hawkcount.org.

HMANA has established various data recording standards for use at hawk watch sites. As part of the RPI project, HMANA has generated a first version of a generalized site data collection protocol. This protocol may be used by individual hawk watch sites as a starting point in the generation of their own operating protocols.

Hawkcount.org is an online raptor migration database established by HMANA as a repository for raptor migration count data. It also allows hawk watch sites to distribute their observations during the migration season through email lists and various online social media platforms. The data entry procedure implemented at hawkcount.org follows the HMANA data collection protocols and standards. As a component of the RPI project, hawkcount.org also exports the raptor migration datasets in a format suitable for the project’s statistical analysis procedures.

Raptor count data is stored in hawkcount.org, and data use as part of RPI is governed by HMANA data submission and data use policies.

Analysis methods

Data filtering

Prior to analysis, we filtered data to exclude days of the year and hours of the day that were not typically sampled at a station by including only those days of the year and hours of the day that included the inner 95% of observations at a station. We also excluded species that were not detected during at least 50% of all years surveyed at a station. Hourly data were aggregated to daily totals, following the recommendations in Crewe et al. 2016.

Regression analysis

Trends in raptor migration counts were estimated independently for each species, site and season in a Bayesian framework using Integrated Nested Laplace Approximation (R-INLA, Rue et al. 2014) in R (version R-4.1.1; R Core Team 2021). We estimated trends using log-linear regression, which included a continuous effect for year (i) to estimate log-linear change in population size over time, first and second order effects for day of year (j) to model the seasonal distribution of counts, and with hierarchical terms to account for random variation in counts among years and among days:

where is a first-order autoregressive (AR1) random effect for year, and is a hierarchical term to account for random variation among days of the year. The random day effect was specified as independent and identically distributed (IID). Number of observation hours in day j was included as an offset to account for variable daily effort.

Models were fit with either a negative binomial or Poisson distribution depending on the distribution of counts. For both data distributions, year estimates and 95% credible intervals were back-transformed to annual rates of population change using 100*exp(estimate)-1. Trends were calculated using the full dataset, as well as for all 10-year subsets to estimate 10-, 20-, 30-year (etc.) trends where appropriate, such that if the final year in the dataset was 2019, a 10-year trend would include 2009-2019.

We estimated annual indices of population size for each species on the response scale (mean hawks per day), by calculating the mean and standard deviation of predicted daily count from 1000 samples from the posterior distribution of the above trend model. The trend was calculated as the % rate of change per year = 100*(exp(year coefficient)-1). This converts the year coefficient, which is an estimate of the instantaneous rate of change per year, into an estimate of the discrete rate of change per year between any year and the following year.

Trend Summary Indices (TSI)

We calculate trend summary indices for each species for 10, 20, and 30 year time periods as follows:

TSI = (# of increasing sites – # of decreasing sites) / (Total # of sites w Trends)

A positive TSI indicates overall increasing counts for a species/time period combination, a negative TSI indicates overall declining counts, and a score near zero indicates stable counts.

Crewe, T. L., P. D. Taylor, and D. Lepage. 2016. Temporal aggregation of migration counts can improve accuracy and precision of trends. Avian Conservation and Ecology (accepted for publication)11(2):8. http://dx.doi.org/10.5751/ACE-00907-110208

R Core Team. 2021. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. [online] URL: http://www.r-project.org.

Rue, H., S. Martino, F. Lindgren, D. Simpson, and A. Riebler. 2014. INLA: Functions which allow to perform full Bayesian analysis of latent Gaussian models using Integrated Nested Laplace Approximation. [online] URL: http://www.r-inla.org.

Availability of data

All graphs and maps are available to download from the trend results page of the RPI website and from Birds Canada’s NatureCounts website http://www.naturecounts.ca/rpi/. Count stations can easily copy a small line of script (available at NatureCounts) and embed the population trends into their own website if they wish. To do so, simply define the population trends that you would like to see on NatureCounts website and look for the link that says “To insert the graphs below in your own website using our web service click here.”

Annual indices and trends can also be downloaded from the trend results page in an Excel-compatible format if you wish to create your own graphs for presentation as well. Simply click the chart context menu button on the top right corner of the graph to view your download options.