What are the Odds?

April 1, 2015

Through a shroud of mosquito netting I saw the bright light of my ringing alarm. It was 4:30 AM, an ungodly hour, and I felt the lonely pangs of a person who rises before dawn. It seemed like centuries before the first rays of sunlight would emerge over the hills from the east, and as I pulled on my field pants I felt sure that I was the only creature stirring for miles around. Only parts of my body were awake and my stomach, always the last to rise, was displeased to have to accommodate a bowl of Quaker instant oats made thick with a glob of unsweetened peanut butter. I brushed my teeth after a warm cup of Africafe, a little jolt for my sleepy brain, and was out the door. My legs felt heavy and the sluggishness in my step caused me to fumble over a fallen branch on the path outside. I caught myself before hitting the ground, but the reality sunk in– it was going to be a long day. I had been on somewhat of a roll, a series of successful behavioral follows with paired physiological samples, but it was the end of a physically challenging week and as I trudged off towards the south of the park, I knew that I was due for a hard time.

Jumping out of bed in the morning has never been my strong suit. Back at home, I am nowhere near the up-and-at-’em kind of girl, and past roommates would surely describe my pre-caffeinated state as a confusing combination of comatose and cantankerous. But there is something unique to Gombe that incentivizes my early morning activity, and that something is chimpanzee urine. Rousing oneself before sunrise for the sole purpose of pipetting primate effluvia is probably not an experience with which many can identify, but it just so happens that this is an integral component to my doctoral dissertation. Near daily, researchers at Gombe conduct dawn-to-dusk follows of chimpanzees by locating individuals at their sleeping sites from the night before. Finding a group of chimps before they emerge from their nests presents a perfect opportunity to collect a set of samples that facilitate “baseline” measures of individual UGM (urinary glucocorticoid metabolite) concentrations, physiological indicators of stress [1]. Voids collected in the early morning correlate to the animal’s resting state and other endogenous factors such as natural circadian rhythm [2], allowing us to track cortisol levels that do not correspond to social stimuli like aggression or affiliation. With these baselines, we can begin to understand standard stress levels, and report on differences between individuals and even populations.

As a result, early morning urine sampling of the Gombe chimpanzees has become a part of my daily routine, or, more romantically, the reason I get up in the morning. Yet just like any sleep enthusiast, every so often I find myself lying in bed, alarm sounding off in the dark, as I ask myself the fateful question: do I have to? Tired, sore and dreading a bowl of oat paste, I mull over all the arguments that support staying under the covers. My shoes are wet from yesterday’s rain. I’m grumpy. I don’t need that many samples. Fortunately for my dissertation, and for the sciences in general, the best arguments for research protocol do not usually stem from the drowsy fancies of a woman in pajamas, but from a statistical theorem that predates Gombe, chimpanzee research and Quaker oats altogether.

As I stated earlier, one potential function of urine sampling could be to quantify the stress of the Gombe population. But one or two early morning urine samples does not a population make. The basis for this argument, and one of the most compelling reasons to roll out of bed in the morning, comes from Jakob Bernoulli, a theologian turned mathematician who lived in Basel, Switzerland during the 1600’s. His central theorem, presented in 1713 and later modified to be the Law of Large Numbers, was the first to demonstrate the relationship between sample size and the ability to accurately interpret real world phenomena. Using a household urn filled with black and white pebbles of known quantities (e.g., 3,000 black pebbles and 2,000 white, or a 3:2 ratio) Bernoulli examined the ratio of black:white pebbles when a subset of 100 were drawn from the larger population with replacement. He repeated the experiment, drawing next 1,000 pebbles from the urn, and found that as sample size increased (in this case, the number of pebbles drawn), the more closely the ratio in the subset reflected the actual 3:2 ratio found in the urn. This example teaches us an important statistical lesson: the larger the sample, the more likely it is to reflect the population being sampled [For background on Jakob Bernoulli and a review of the Law of Large Numbers, see 3]. Thus, while it would be nice to lounge about in the mornings and meet the chimps before dawn say, once a month, one or two urine samples are likely to reflect the only individuals sampled and the effects of that day, rather than the stress of the population as a whole.

And so as I set out that morning, legs dragging along like anvils, the allure of sample size drew me into the forest, compelling me to continue despite a dread of the day to come. A path appeared in the tall grasses to my left and I followed its steady incline, quickening my pace as the trail wound its way up a steep mountainside. I climbed higher and higher, and with each step felt my legs turn to putty beneath my weight. In the darkness, looking down to steady my footing, I finally met the hard fate that I knew I had coming…

…when I ran headfirst into a tree.

A wave of pain flashed across my face and I cupped my hand to my bleeding forehead*. Turning back towards camp, a fresh lump swelling at my hairline, I couldn’t help but to consider that after over sixty-one injury-free days at Gombe, a good blow to the head was rightfully in my cards. Now it may have been the concussion talking, but this thought process was actually just as flawed as my arguments to stay in bed. In fact, the belief that because I had experienced a “run” of good data, my next follow would likely be bad, was a common violation of logic known as The Gambler’s Fallacy. This error in thinking occurs when we fail to understand statistical independence, or that the frequent occurrence of one event (such as a good field day) does not make the occurrence of another any more or less likely [3]. So while an exciting day of chimpanzee aggression may prompt conciliatory behaviors on the next, neither have much bearing on the likelihood of researchers running themselves into stationary forest objects before dawn.

Sometimes, because events like waking up before sunrise, chasing after chimp urine and crashing into trees can seem a bit chaotic, it’s nice to have a few hard stats to make sense of all the randomness that Gombe has to offer.

*Hogwarts, you can send my acceptance letter at any time.

[1] Sapolsky, R.M., Romero, L.M. and Munck, A.U. (2000). How do glucocorticoids influence stress responses? Integrating permissive, suppressive, stimulatory, and preparative actions. Endocrine Reviews 21:55–89.

[2] Anestis, S.F. and Bribiescas, R.G. (2004) Rapid changes in chimpanzee (Pan troglodytes) urinary cortisol excretion. Hormones and Behavior 45: 209-213.

[3] Mlodinow, L. (2008). The drunkard’s walk: how randomness rules our lives. Pantheon Books: New York.

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