RPI Raptor Population Trends: Interpreting Trend Graphs and Maps

We calculated annual indices and population trends for all count sites with at least 10 years of data (through and including 2023) submitted to HawkCount.org. We will include count sites lacking data for 2014-2023 in future analyses as they meet the 10 recent year threshold. We also exclude species with fewer than 10 individuals counted on average per year at a site as trends from these rarely counted species provide dubious information about population status.

We ask users to recognize that the RPI partners lack the resources or staff for exhaustive quality control of raw data and subsequent results. We rely on contributing sites to provide accurate data in HawkCount.org and to alert us to problems. Any questions about datasets or results can be sent to brown@hawkmigration.org. Site locations, descriptions and protocols are posted within the site profiles on hawkcount.org.

We present results 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 2014 to 2023 (see trend maps).

How to read the population index and trend graphs

The following example shows the long-term trend for Northern Harrier at Hawk Mountain Sanctuary in fall. The 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 each annual index. 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 values for different time periods. We report these trends as percent change in counts per year along with the lower and upper limits of 95% credible interval for the trend.  We assume a linear change in migration counts among years over the time period examined. In the example shown, the CI does not include zero for 2009-2019, offering strong support for the observed decline in migration counts for this species over the past 10 years. Additional reported trend results for 1999-2019 and 1989-2019 support that this decline extends back several decades (see species assessment).

RPI Trend maps

Maps display the trends calculated for each RPI count site with sufficient data for a given species. Users can select species, season (spring/fall), period (10-yr, 20-yr, all years of data for a site, and the published three-generation timespan for a given species), and map type using drop-down menus. Maps effectively visualize the spatial variation in trends for a species over a large geographic area. Consistent trends across sites within a region supports that our results represent trends in the underlying regional population, and not the result of site-specific variation. The example below represents the 10-year trends of Bald Eagle counts fall count from 2014-2023 for sites that see at least 10 migrating eagles each year on average. Green upward arrows indicate positive trends, red downward arrows indicate negative trends supported (95% credible interval excludes zero) at a site. Blue dots indicate sites with no supported trend i.e., 95% credible intervals included zero, and the posterior probability < 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 count site 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 count sites, such as along the Appalachian Mountains. The example map clearly shows that Bald Eagles are doing very well across North America with some stable counts mixed in.

Data Collection

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

HMA established various data recording standards for use at hawk watch sites. As part of the RPI project, HMA created a generalized site data collection protocol that may be used by individual count sites as a starting point to create their own operating protocols.

Hawkcount.org is an online raptor migration database established by HMA as a repository for raptor migration count data. It also allows count 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 HMA 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 are stored in hawkcount.org, and data use as part of RPI is governed by HMA 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. We aggregated hourly data to daily totals, following the recommendations in Crewe et al. 2016.

Regression analysis

We estimated trends in raptor migration counts 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). We included number of observation hours in day j as an offset to account for variable daily effort.

We fit models with either a negative binomial or Poisson distribution depending on the distribution of counts. For both data distributions, we back-transformed year estimates and 95% credible intervals to annual rates of population change using 100*exp(estimate)-1. We calculated trends 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. We calculated the trend 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, and 20 year time periods following Oleyar et. al 2023:

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. Gray symbols indicate TSI’s for species with trends from < 10 count sites.

References

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

Oleyar, D., L.J. Goodrich, D.Ethier, D.Brandes, R.Smith, J.Brown, and J.Sodergren. 2023. Thirty years of migration and winter count data indicate regional differences in population trajectories for American Kestrels in North America. Journal of Raptor Research 57(2):146-153. https://doi.org/10.3356/JRR-22-17

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.