When Counting Gets Difficult, Part 2

Prion sp., March 22, 2016, seen just west of Heard Island. Image credit: Bill Mitchell.

Earlier I posed a question: suppose a group of 40 birds are identified to genus level (prion sp.). Four photographs of random birds are identified to species level, all of one species that was expected to be in the minority (fulmar prion) and likely would be present in mixed flocks. How many birds of the 40 should be upgraded from genus-level ID to species-level ID?

Clearly there is a minimum of one fulmar prion present, because it was identified in the photographs. With four photographs and 40 birds, the chance of randomly catching the same bird all four times is quite small, so the number of fulmar prions is probably much higher than 1. At the same time, it would not be reasonable from a sample of our photographs to say all 40 were fulmar prions.

If we have four photographs of fulmar prions (A), what is the minimum number of non-fulmar prions (B) needed in a 40-prion flock to have a 95% chance of photographing at least one non-fulmar prion?

To answer this question, I used a Monte Carlo simulation, which I wrote in R. I generated 40-element combinations of A and B ranging from all A to all B. Then for each of those populations, I ran 100,000 trials, sampling 4 random birds from each population (with replacement). By tracking the proportion of trials for each population that had at least one B, it becomes possible to find the 95% confidence limit.

pop_size <- 40  # Set the population size
sample_n <- 4  # Set the number of samples (photographs)
n_trials <- 100000  # Set the number of trials for each population

x <- seq(0:pop_size)  # Create a vector of the numbers from 0 to pop_size (i.e. how many B in population)

sample_from_pop <- function(population, sample_size, n_trials){
	# Run Monte Carlo sampling, taking sample_size samples (with replacement)
                # from population (vector of TRUE/FALSE), repeating n_trials times
	# population: vector of TRUE/FALSE representing e.g. species A (TRUE) and B (FALSE)
	# sample_size: the number of members of the population to inspect
	# n_trials: the number of times to repeat the sampling
	my_count <- 0
	for(k in 1:n_trials){  # Repeat sampling n_trials times
		my_results <- sample(population, sample_size, replace=TRUE)  # Get the samples
		if(FALSE %in% my_results){  # Look for whether it had species B
			my_count <- my_count + 1  # Add one to the count if it did
		}
	}
	return(my_count/n_trials)  # Return the proportion of trials detecting species B
}

create_pop <- function(n,N){  # Make the populations
	return(append(rep(TRUE,N-n),rep(FALSE,n)))  # Populations have N-n repetitions of TRUE (sp. A), n reps of FALSE (sp. B)
}

mypops <- lapply(0:pop_size, create_pop, pop_size)  # Create populations for sampling

# Apply the sampling function to the populations, recording the proportion of trials sampling at least one of species B
my_percentages <- sapply(mypops, sample_from_pop, sample_size=sample_n, n_trials=n_trials)

My simulation results showed that with 22 or more birds of species B (non-fulmar prions), there was a >95% that they would be detected. In other words, from my photographic data, there is a 95% probability that the flock of 40 prions contained no fewer than 19 fulmar prions.

Let’s take a look at it graphically.

library(ggplot2)

mydata <- data.frame(my_percentages, 0:pop_size)  # Make a data.frame with the results and the # of species B
names(mydata) <- c("DetProb", "B")  # Rename the columns to something friendly and vaguely descriptive

p <- ggplot(mydata2, aes(x=B,y=DetProb)) + geom_point() # Create the basic ggplot2 scatterplot
p <- p + geom_hline(yintercept=0.95)  # Add a horizontal line at 95%
p <- p + theme_bw() + labs(x="# of species B (pop. 40)", y="Detection probability of B")  # Tidy up the presentation and labeling
print(p)  # Display it!

Results of the Monte Carlo simulation. At left is all A, while at right is a population with all B. The horizontal line is the 95% probability line. Points above the line have a >95% chance of detecting species B.

With 22 or more non-fulmar prions, there’s a >95% chance one would be photographed. With 19 fulmar prions and 21 non-fulmar prions, there’s a >5% chance the non-fulmar prions would be missed. So our minimum number of fulmar prions is 19. I may have seen a flock of 40 fulmar prions, but there aren’t enough observations to say with statistical confidence that they were all fulmar prions.

When Counting is Difficult

A fulmar prion glides swiftly over the swell of the Southern Ocean. Image credit: Bill Mitchell (CC-BY)

During the Heard Island Expedition, including the nearly three weeks at sea on the Southern Ocean, I made a few observations for a citizen science project: eBird. It’s a pretty simple system: identify and count all the birds you see in a small area and/or time period, then submit your list to a centralized database. That database is used for research, and keeps track of your life/year/county lists. With so few observations in the southern Indian Ocean in March and April (and no penguins on my life list before the expedition), I figured I would make a few counts.

On its face, identifying and counting birds is straightforward. Get a good look, maybe a photograph, and count (or estimate) the number present of that species.

It gets more difficult when you go outside your usual spot, particularly when the biome is much different. Although I have some familiarity with the Sibley Guide for North American birds, I’ve never payed very close attention to the seabird section, and have never birded at sea before. All the birds I expected to see on this expedition would be life birds, and that changes things a bit. I would have to observe very closely, and photograph where I could.

Before the expedition, I read up on the birds I would likely find on the island. In addition to four species of penguins, there were three species of albatross (wandering, black-browed, and light-mantled sooty) and two species of prions (Antarctic and fulmar). Albatrosses are large and the species near Heard are readily distinguished. Prions, however, can be quite difficult even with good observations. They’re not quite to the level of the Empidonax flycatchers, but close.

At sea, we usually had prions flying near the ship. I took pictures, knowing that I might be able to get help with ID if I needed it—and of course I needed it.

That’s where the problem started: I had a count where I had observed 40 prions flying around the ship, which I identified only to genus level. From my reading on Heard Island, I knew that breeding populations for prions on Heard Island were generally larger Antarctic prions than fulmar prions, with an estimate of a 10:1 margin. I had four clear pictures of individual birds, which my helpful eBird reviewer was able to get to an expert for further identification. All four were fulmar prions.

With 40 birds identified to genus level, and four photos of random birds identified to species level as a species expected to be a minor proportion, how many of the original 40 birds can I reasonably assign as fulmar prions?

I have an answer to this question, which I will post next week.

Christmas Bird Count 2015

A red-bellied woodpecker visits a backyard bird feeder. This photo is not from Christmas Bird Count 2015, but red-bellied woodpeckers were observed on my count. Image credit: Bill Mitchell (CC-BY).

Beginning in 1900, the Audubon Society began holding an annual bird population survey at Christmas (in contrast with the earlier tradition of shooting all the birds one could). Over the years, the Christmas Bird Count (CBC) has changed and grown, but still maintains its founding principles: a census of birds, taken around Christmas.

Today, counts are organized into 15-mile diameter circles, with teams of birders tallying not just how many different species they see over the course of a day, but the number of individuals of each species. In many cases, the large circle itself is subdivided, and teams of birders will count in a smaller area. Many groups meet at or before dawn for breakfast and planning. Some finish in time for lunch, others don’t stop for much of anything until it’s too dark to bird.

This weekend, I took part in the count, with a northern section of the Faribault (MN) circle. As a college student at Carleton College, I got involved in the count around Northfield, MN (within the Faribault circle), and have gone back to join the count a handful of times since graduating. One year I was in Berkeley for the CBC, which was a very different experience: no snow, and >100 species recorded.

Our group managed to see 19 species (on the higher side for that area in my experience), and around 1400 individuals. Most of those individuals, due to the relatively warm conditions here, were Canada geese (800) and mallards (450), which could be found on the open water. In years past when cold conditions have frozen over the lake and river, the waterfowl count (and total individuals count) are much lower.

Many of the other regulars were out and about: white-breasted nuthatches, red-bellied woodpeckers, goldfinches, crows, blue jays, and cardinals. We found a few surprises while counting: a belted kingfisher, a hooded merganser (among the 800 geese and 200 mallards on one small pond), a great blue heron, and five eastern bluebirds. The heron, bluebirds, and kingfisher are surprising in that they are quite uncommon in this area at this time of year (i.e. generally expected to migrate further south), but a quick search of eBird shows that they are not unheard of (note that the data include my CBC checklists).

The Christmas Bird Count is a great opportunity for new or newer birders, because you can (and probably will) be placed on a team with more experienced birders. You meet new people, see some birds—possibly adding a species or ten to your life list—and participate in citizen science. Professional scientists alone couldn’t do these detailed counts in this many areas all at once. While in many areas the annual count may have happened already, some areas might be still have a count coming up, so check to see when your local circle does its count.

Of course, if the count already happened and you don’t want to wait for next year, you can always participate in eBird. eBird is a project of the Cornell Ornithology Laboratory, and is a huge database of population counts. Participants submit their lists (including counts of individuals) with time, date, location, and some other information. The database keeps track of your life list (and many other lists), and also can show you data from all the aggregated observations. Are you wondering what birds you might see when you go on vacation? You can check that county/area in eBird, and get a graph showing the relative abundance of different birds seen in that area over the course of a year. Looking for a particular species? A map tool can show you where they have been seen, and at a detailed zoom level will show the individual observations.

To date, there have been no eBird checklists from Heard Island, or the ocean near Heard Island. However, I intend to do what I can (and I may not be alone in birding Heard Island) to get a few lists for eBird when I am there in March and April.