Stand up and be counted

Imagine. You’re a consulting company hired by Kluane National Park in the Yukon Territory to conduct a survey of the Grizzly Bear population in the park by the Canadian Government. You have been given one summer to conduct the field data collection and a fixed amount of helicopter time – no you cannot just go and count every individual!  You need to provide a population estimate.

grizzly-bear-861962_1280

Now imagine, that the bears are Pom-Bears (crisps) in a bowl rather than a National Park and the tools you have to hand are a coloured pen and your own mathematical knowhow.  That is the scenario that each of the Edinburgh Conservation Science students were faced with a few weeks back.

pombears

Not only did the Cons. Sci. students need to figure out how to sample a population to estimate the total population of individuals. They had to figure out the mathematical formula to make their estimates without the aid of the internet. There were moments of struggle as numbers were jotted down, then crossed out, and sums done by hand, then checked with a calculator and minorly adjusted. But in the end six different tutorial groups came up with six different estimates with error for their populations of Grizzly Bears using a technique known as mark-recapture.

mark-recapture

How close did each group come to the true number of bears in the park?  I will let the numbers speak for themselves!

markrecapture

Lots of samples or more marked individuals increases the accuracy of your estimate, but in the real world tagging extra bears is expensive. Most groups came quite close to estimating their populations, but some were farther off and some (Sandra’s group) forgot to count their bears to see how close they got! What did we learn – that precision and accuracy aren’t necessarily the same thing. Emiel’s group’s estimates are pretty precise, but not super accurate!

mrformula

In summary, Pom bears are tasty and coming up with accurate population estimates can be challenging, if field sampling of real populations is limited by resources and time.

By Isla

Data for figure:

Group Tutor Estimate Error Actual Marked Samples
Group 1 Isla 114 34.81 105 20 4
Group 2 Zac 156.82 38.57 133 18.57 7
Group 3 Emiel 102.37 6.31 154 21.14 7
Group 4 Haydn 224 72.03 134 NA 4
Group 5 Sandra 130 14 NA NA 4
Group 6 Rose 129 24.72 134 21 5

Code for figure:

library(ggplot2)

data

ggplot() +
geom_point(data=data, aes(x=Tutor, y=Actual, colour=”Actual Pop.”), size=6, pch = 17, show.legend=TRUE) +
geom_errorbar(data=data, aes(x=Tutor, ymin=Estimate-Error, ymax=Estimate+Error), width=.1, colour = “black”, show.legend=FALSE) +
geom_point(data=data, aes(x=Tutor, y=Estimate, colour=”Est. Pop.”, shape = 2), pch = 19, size=6, show.legend=TRUE) +
labs(y = “Population Estimate\n”, x = “\nTutorial Leader”) +
theme_bw() +
theme_classic() +
theme(legend.title = element_blank(), legend.text=element_text(size=25), axis.line.x = element_line(colour = ‘black’), axis.line.y = element_line(colour = ‘black’), axis.title.x = element_text(size=25), axis.text.x = element_text(size=25), axis.title.y = element_text(size=25), axis.text.y = element_text(size=25), axis.ticks.length = unit(0.3, “cm”)) +
scale_colour_manual(values = c(“Est. Pop.” = “black”, “Actual Pop.” = “red”), name = “Legend”) +
guides(colour = guide_legend(override.aes = list(size=6, shape = c(17,19))))

# Code credit to Anne for figuring out the tricky stuff to make the legend work!

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