Data in the blind spot

Paper in a Nutshell:
Constraint lines and performance envelopes in behavioral physiology: the case of the aerobic dive limit. Markus Horning, Frontiers in Physiology 2012; 3:381

All humans have a blind spot (puntum caecum in medical parlance): if you look directly at something it’s hard to see, but if you look to the side it becomes apparent.  This nutshell is from a slightly older, but unusual, paper that explored what could be called a ‘data blind spot’.

YOUR MISSION SHOULD YOU CHOOSE TO ACCEPT IT— Alright fellow readers, ready to get nerdy with data? This paper in a nutshell explores the data analyses used to understand animal behavior. It is probably more of a challenge than most of our posts, but you got this!!!

Marine Mammal Diving

Let’s start with some background. The study of physiology is dedicated to understanding how organisms maintain homeostasis (dynamic equilibrium) – how our bodies avoid going haywire when we tax them. Diving, air-breathing animals face a particular challenge: vigorous exercise under extended breath-hold depletes life-supporting oxygen stored in tissues, and things can quickly get out of whack.

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When studying marine mammal diving, a core concept is the aerobic dive limit. If you think about how long a mammal can stay underwater, you might think about it in terms of “the size of my SCUBA tank?” In a way, it is related to that. How long one can stay submerged depends on the size of the oxygen tank and on oxygen use. Good divers can eek out longer breath-holds with the same ‘tank size’, through many tricks of the trade collectively referred to as the ‘dive response’. This includes lowering heart- and metabolic rate, shutting down non-essential activities such as digestion, but some animals also use an unusually large tank (more blood, hemoglobin and myoglobin).

In extreme cases, some air-breathing animals can stay submerged even after oxygen in their ‘tank’ has been pretty much used up, by switching to an anaerobic metabolism that does not initially burn oxygen. However, this produces lactic acid and actually uses more fuel, making it less efficient and requiring that “oxygen debt” to be repaid later. Noted physiologist Gerald L. Kooyman defined the breath-hold time when lactate begins to increase in at least some organs as the ‘aerobic dive limit’, or ADL.

So the ADL is not actually the size of the scuba tank, it is the time when you run out of air given the tank’s size and how hard you are breathing. The ADL is thus a useful concept for scientists studying the behavioral ecology of diving animals. But is it a real threshold that limits foraging behavior and energy acquisition, which could ultimately even influence individual fitness?

To answer this question, we need to look at how dive duration (oxygen depletion) relates to the post-dive recovery time (oxygen recovery). Scientists typically do this by exploring how X influences Y—for example, one might expect age (x) influences height (Y) in humans: we get taller as we get older (up to some point in adolescence).

However, this may be difficult to determine in actual diving data. Many factors influence dive duration: tank size, use rate, but also temperature, depth we dive to, and how we feel. We also can’t just look at how long it takes after a dive to recharge the tank – after all, animals could simply decide to hang out at the surface a bit longer than strictly necessary. Similarly, if an animal exceeds its ADL and incurs an oxygen debt, it could decide to defer ‘paying off’ this debt until a later time. At some point, it will definitely have to ‘burn off lactate’ with additional oxygen, but this could be put off until after several partially anaerobic dives.

This disconnect is the data blind-spot: if we look at the data directly we can’t tell where the ADL manifests, or after what dive duration animals have to dramatically increase their post-dive recovery time. When we look at a recovery time (Y) versus dive duration (X), there is no clear effect (Fig. 1), and a bottom contour line added in Fig. 1 shows several possible and not clearly defined times.

Figure 1: Post-dive recovery times (Y) versus dive duration (X), for a 2-year old male Galápagos fur seal. From Horning 2012.

A New Approach

To eliminate these confounding effects, I explored the diving data from the Galápagos fur seal shown in Fig. 1, and simply summed up the dive durations and corresponding recovery times for eight successive dives. This relatively easy approach dramatically sharpens up the fuzzy picture we started with (Fig. 2).

Figure 2: Plotting all possible combinations of the sum of successive recovery times versus the sum of successive dive durations for 2-year old male Galápagos fur seal from Fig. 1. This is done as a moving sum plot, capturing all possible combinations of sequential sums.
(A) The moving sum plot resulting for eight successive recovery times vs dive durations (From Horning 2012)

Can you see a pattern emerging? Look at the edge of the otherwise diffuse point cloud above and see how sharp and defined they are. These edges are called ‘Constraint Lines’ to reflect the idea that they represent the effects of limiting factors (such as how much time you need to refill the scuba tank) more directly than the data in the core of the diffuse point cloud.

The second thing we immediately note when looking this new figure is that there are actually TWO distinct ‘informative edges’ that intersect at a specific point (Figure 3).

Figure 3. The best two regression lines that define the lower edges of Fig 2. How to obtain these regression lines is explained in detail in Horning 2012. Since this plot represents the sum of 8 successive dive/recovery pairs, dividing the value of the intersect of the two edges (1100s) by eight yields the equivalent duration for a single dive, of 2.29 min. This value – called the STI – is shown as a solid black triangle in Fig. 1. From Horning 2012.

This leads us to the question of what information these edges represent, how the two edges differ, and what their intersect could mean? The lower edge is the easiest to explain: how much time does it minimally take to recharge the tank, based on how much time was spent submerged.

But why does this time increase at a greater rate beyond a given underwater time (e.g. why is the second line so much steeper?). The most probable explanation is that this disproportionate increase is related to a greater use of oxygen, most likely from some level of anaerobic metabolism. In other words, for dive set durations past where those two lines intersect, oxygen has been used up at least in some tissues, and anaerobic metabolism starts producing lactate. This lactate needs to be ‘burned off’ – depleting the tank to a greater extent.

Thus, the intersect of the two constraint lines is probably a manifestation of the Aerobic Dive Limit!

However, until we can actually measure lactate in these animals we cannot directly prove that this is the ADL. We can only consider whether the ADL relates to other animal characteristics as we would expect based on prior knowledge. For example, bigger animals are often better divers– as an animal’s size increases, oxygen stores increase at a greater rate than typical oxygen consumption. So when we look at the results of our data (Y) relative to body mass (X), the dive duration that is likely a manifestation of the ADL does increase in a non-linear way with body mass, as shown in (Fig. 4).

Figure 4 All constraint line intercepts are plotted here as the STI – or the likely ADL (see legend to Fig. 3) versus body mass, for 75 Galápagos fur seals ranging in age from 1 year to adult (females). Solid points are actual STI / intercepts, open circles represent the upper end-point of plots with only a single, lower constraint line. From Horning 2012.

Congratulations! You made it through all of that data and analysis…now what does it all mean?

An adult female fur seal with a body mass of about 28 kg, and her male yearling Galapagos fur seal offspring, (about 10 kg) and her dead pup (<2 kg) that starved since the yearling could not feed itself yet and was still suckling. Yearlings and even two-year-olds are more constrained than full grown fur seals, often pushing their physiological limits, and thus may be less able to respond to changes in the environment like warm/cold seasons or environmental fluctuations. If that is the case, very young pups are displaced from suckling and starve. In years of ample food supply a yearling may be able to feed itself, and the young pup may then survive

Well, with this new method, we can use the ADL as a measuring stick. We can use data on dive behaviors that is routinely collected from freely-swimming wild animals to determine whether an animal is ‘pushing its limit’, more than just saying ‘it’s diving pretty long’. From that, we can look at the effects of normal environmental changes in e.g. fish abundance relative to El Niño, or other changes in the environment such as those expected due to Climate change. And that is at the core of what we are interested in studying in the Anthropocene with this data analysis method—under what conditions are animals pushed to their limits, and lack additional behavioral or physiological adaptive capacity?

Written by: Dr. Markus Horning, ASLC Senior Scientist

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