We’re marking Halloween 2017 with some memorably spooky posts from our seven year PLOSBLOGS archive. Here’s one by PLOS Ecology Community Editor, Jeff Atkins. — Victoria Costello, PLOSBLOGS
The neighborhoods and sidewalks of America are going to be full of superheroes, witches, zombies, and princesses across the country as kids (and adults!) celebrate Halloween tonight. The National Retail Federation reports that after an eleven-year reign at the top, princess costumes have fallen to the number two spot on the annual top ten most popular kid’s Halloween costume list:
3) Animal (Cat, Dog, Lion, Monkey, etc.)
4) Batman Character
5) Star Wars Character
6) Tie: Witch AND DC Superhero (excl. Batman)
7) Frozen Character (Anna, Elsa, Olaf)
8) Marvel Superhero (excl. Spiderman)
Source: National Retail Federation
Superheroes, reportedly, will total over three million, followed by 2.9 million princesses, and 2.5 million animals of one kind or another. And while one may take issue with how the list is tabulated or aggregated (i.e. are we counting superheroes twice here?), you too, using a little bit of math and ecology can figure out how many ghost, goblins, or superheroes are in your neighborhood.
First, we need to understand how scientists and researchers count animals in the real world. Most of the time, it is not possible to actually, physically count all of the animals in a place. From squirrels on a city block to whales in the ocean, it would be difficult if not impossible to make a complete census of any wild population. We could just sit in one spot and count as best we can, but as any birder will tell you, it isn’t that simple. But more on that later.
Mark and recapture is one method that attempts to solve this problem. In mark and recapture, a set of animals are captured at one point and are marked in some way (perhaps by a leg band, or some type of identifying paint) and then re-released. At another point or another time (or both!) you recapture a set of animals and see how many of them are marked from the previous capture. This method was pioneered by C. G. Johannes Peterson, a Danish marine biologist working with marine fishes, and Frederick Charles Lincoln, an American ornithologist working with waterfowl. This method has a few assumptions*, but works amazingly well. Let’s apply it to our ghosts and goblins.
***A word of warning, please do not actually try and “mark” or count anyone—these are just examples and any attempt to do this in the real world would likely get you into serious, serious trouble.***
To count our trick or treaters, we have to “mark” them in some way. Obviously we can’t put leg tags on children. That should be a no-brainer. Let’s say that a couple of nights before Halloween, there is a Halloween festival downtown where there is candy and everyone shows up dressed in their costumes. A good time is had by all. We hand out glow stick necklaces to 100 kiddos who can wear those necklaces while they are trick or treating. Not only do we now have a “marked” population, but the kids are safe too. A win-win. We are going to assume 100% of kids who get the necklaces wear them and that they all go trick or treating on Halloween.
Halloween night rolls around. We have our bowl of candy to handout and we are ready to do our “recapture.” Fortunately, in this world we have constructed, exactly 100 kids show up at our door. Of those 100, 20 are wearing those nifty glow in the dark necklaces. That means 80 were not. We “recaptured” 20 of our target population. So how do we figure out how many trick or treaters there are in the entire population, not just how many showed up to either event? Well, we do some math. Let’s walk through it:
Let’s also assume we wanted to know more about the diversity of the different “species” of trick or treaters. In this experiment, we are keeping not only a tally of how many trick or treaters there are, but what type of “species” of trick or treater we are spotting. To do this, we have set up two observation posts. We will use the green and blue houses on our city map:
For this example, we are going to assume these are two separate populations of trick or treaters who do not overlap. Now, since we are not able to do a mark and recapture in this scenario, we may not be able to make accurate estimates of the total number of individuals, but we can compare these two areas of the city and see how they differ in their species composition and diversity. Let’s look at the data:
At the blue house, we got 130 total trick or treaters, while only 90 at the green house. For each “species,” there is a total count, this is the abundance—or the number of individuals of a given species. For superheroes, there is an abundance of 75 at the blue house versus 20 at the green house. This number is informative, but we can dig deeper. If we are interested in diversity, the first thing we want to know is the species richness—the number of different species at a given location. In our example, there were only five different species at the blue house, but seven at the green, giving us a species richness of five and seven, respectively. This gives us a rough estimate that the neighborhood around the green house is more diverse.
But, we can go farther. Just how different is the diversity between these sites? One way is to look at species evenness—a diversity index that uses the proportion of species in an area compared to the total number species in the region. Species evenness is a bit more obtuse. The number ranges from 0 to 1. The higher the value, the more “even” the species distribution. To calculate species evenness, we first have to get the Shannon Diversity Index that accounts for the uncertainty in our sampling and then adjust that to the maximum possible diversity in the system. The math here is a bit more wonky and involved, and uses a log transformation of the proportional species data to make comparisons. A good ecology text book can give you a complete run down. My favorite is Elements of Ecology from Smith and Smith.
If we crunch the numbers on our sites, using a maximum possible species number of 7, we get a species evenness of 0.35 for the blue house, but a much higher value of 0.92 for the green house. And if we look back at our data, we see the green house had a much more “diverse” range of trick or treaters during the evening—including several witches and wizards not found at the blue house. What could be different between these sites? One thing we can look at is the amount of available resources at each site . . . in this case, candy:
We can see that at the green house, there are more available resources in the form of higher quality candy—likely chocolate bars, that fruit candy that comes in the red bag, or even the suckers with gum in the middle. The blue house has less desirable candy—maybe butterscotch, bags of pretzels, or even toothbrushes or erasers. From this data, we could infer if you want to have a more diverse trick or treater population, or even attract those rare wizards and witches, you have to have high quality candy that provides available resources for all species. However, if you are focused on attracting more superheroes to your house, in this example, giving out low quality candy seems to be the best bet. Of course in nature, these comparisons can be much more complex. If we wanted to compare the diversity of two forests, we would want to look at climate, elevation, drainage, available nutrients, proximity to human disturbance, soils, etc. Diversity can be impacted by a slew of factors. While this is a fun and rather ridiculous example of how species counts and diversity works, the leap to how this can inform ecology, management, and conservation is clear.
Have a safe and happy Halloween!
* Mark and recapture relies on a couple of assumptions–that during whatever time interval between when the individuals are marked and then recounted, that nothing has occurred to alter the size of the population (e.g. deaths, births, migration, etc.). Also, that the chance of each individual being caught are both constant and equal during both the initial capture and the recapture. There are also assumptions that whatever mark is used does not come off and that during the period between captures, that all individuals are able to randomly disperse back into the populations. (John Kell from Radford University has an excellent, more detailed guide here.)