About the analyses and illustrated trends
Canadian Migration Monitoring Network trends are displayed only for species at each site that meet the following criteria:
- The species is a regular migrant with minimal stopover (i.e. excluding partial, irruptive and non-migrants, and roosting or staging species).
- Standardized count protocols are followed consistently through time.
- At least 75% of the species? migratory period is well-sampled in 2/3 or more of all years.
- Relatively few individuals are detected before or after clearly recognizable migratory influxes, such that trends are minimally affected by wintering or locally breeding species recorded regularly outside the migratory period.
- The species is regularly observed within and between seasons (averaging 10+ detections/season and detection on 5+ days/season).
Trends for species meeting these criteria can be interpreted as representing change in population size within a large area of the stations' catchment area
(the portion of breeding range sampled by that station).
Trend maps show the estimated population trend over the most recent ten-year period for sites that meet the
criteria for that species.
About seasonal abundance
Seasonal abundance graphs are plots of information showing phenology and abundance of all species regularly sampled at the selected location.
Migration windows show the boundaries of the spring and fall migration window used in analyses (only for species with trends displayed on website). The bounds
of spring and fall migration windows were restricted to those days of the year when the station operated during at least two-thirds of total years in operation,
and are in some cases restricted further (e.g. to omit likely summer residents from analysis).
˜ 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
Analysis methods for Annual Indices and Population Trends
Long-term trends in count were estimated independently for each species, site and season using a Bayesian framework with Integrated Nested Laplace Approximation
(R-INLA, Rue et al. 2014) in R (version 3.1.3; R Core Team 2014). We estimated trends using log-linear regression, which included 1) a continuous effect for year (i)
to estimate log-linear change in population size over time, 2) first and second order effects for day of year (j) to model the seasonal distribution of counts, and 3)
hierarchical terms to account for random variation in counts among years and among days. Number of observation days each year was included as an offset to account for
variation in daily effort:
where γ_i is a first-order autoregressive (AR1) random effect for year to account for temporal autocorrelation among years, and η_jis an independent and
identically distributed (IID) hierarchical term to account for random variation in counts among days of the year. For monitoring stations with more than one site
(e.g., Long Point Bird Observatory), the regression also included a fixed site effect, as well as interactions between site and the first and second-order day of
year effects. While we recognize that an AR1 random effect for day of year nested within year might have been more appropriate to account for temporal
autocorrelation among daily counts, we found that specifying the random day effect as IID had no noticeable effect on trend bias or on probability of
estimating a precise trend (probability that the simulated trend fell within confidence limits of the estimated trend; T. L. Crewe, unpublished data).
Specifying the random day effect as IID did, however, significantly increase the speed of analysis, and reduced the probability of errors using INLA.
We assumed a Poisson distribution of counts, unless the proportion of 0-observation days across years was >= 0.65. This cut-off is somewhat arbitrary,
and should be examined in greater detail, but see Crewe et al. 2016. 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., where appropriate) trends for comparison among years over time. Trends are presented as %/year with lower and upper 95% credible intervals,
which suggest that there is a 95% probability that the true trend falls within that range. A posterior distribution was also calculated to estimate the support
for an increasing or declining trend. A value near 0.5 would suggest equal probability for an increasing and declining trend (little evidence for a change in
migration counts over time), whereas a posterior probability near 1 will suggest strong support for the observed change in counts. The posterior probability
can be used as a pseudo p-value, such that trends with a posterior probability > 0.9 could be considered to have strong support. Annual indices of population
size were estimated as the mean daily count from the posterior distribution of the above model. Plots of annual indices show 95% credible intervals (vertical lines),
and the black line and grey shading display a loess fit across indices and upper and lower credible intervals.
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 11(2): 8. <http://dx.doi.org/10.5751/ACE-00907-110208>
R Core Team. 2014. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. [online] URL:
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.