A Matter of Scale

Q:  I know that sealife comes in all sizes, from plankton to whales. What I'd like to know is, relatively speaking, how big are divers? Are we sort of medium-sized, small, or large?

- Laurel
Vancouver, BC

A:  Interesting question, Laurel. Of course, strictly speaking, divers are not 'sealife', but scuba enables us to come closer to being aquatic than most mammals and certainly closer than any other primate.

Size is a fundamental quality of organisms. The marine environment affords unique opportunities and challenges for living creatures. Water is about 775 times as dense as air, conducts heat more than 20 times faster, but contains a much lower concentration of oxygen compared with the atmosphere (from a maximum of only 4.5% in very cold water to nearly 0% in very warm water). How successfully a creature exploits the resources of the sea depends in part on being the 'right' size.

Tiny photosynthetic creatures, such as diatoms, hardly sink at all and thus do not need to invest much energy in staying afloat (these plankters bristle with structures to further reduce their rate of sinking). Huge creatures, such as the great whales, are less affected by surface drag and heat loss than smaller creatures (these creatures have relatively little surface area to form a boundary layer or radiate heat). Small creatures can absorb dissolved oxygen directly through the body surface, but low oxygen concentration places firm limitations on how large a gill-breathing animal can grow. With these factors in mind, let's consider the size range of marine creatures.

How can one represent the amazing size spectrum from plankton to whales in such a way that we can conveniently compare them with our own dimensions? This is not an easy problem. The smallest plankton (a single-celled alga, Micromonas pusilla) is some 19 billion times smaller than the largest whale (the Blue Whale, Balaenoptera musculus). Even if we include only multicellular animals, the smallest marine rotifer is some 840,000 times smaller than the largest whale. Body weight shows a similar size range: the smallest rotifer weighs in at about two ten billionths of an ounce, the largest whale weighed just over six million ounces. Too awkward. Besides, the weight of marine creatures in air or of humans in water is biologically out-of-context and seems rather meaningless. Representing size by the number of cells is an interesting idea, reflecting complexity as well as sheer size. The smallest marine rotifer has fewer than 100 cells. So far so good. A human being is typically composed of about 50 trillion cells; the largest Blue Whale 100 quadrillion. Not so good.

Mass is probably the most elegant measure of physical entity. But here we run up against unfamiliar units. Mass is defined as resistance to acceleration; the more mass, the more energy required to accelerate it. Most importantly, mass does not change no matter how buoyant the medium or how strong the gravitational field so it provides a uniform standard of comparison. The imperial system used in the United States has no unit expressly for mass, so ounces, pounds, and tons are squeezed into double duty. The metric system provides a logical solution, the gram. One gram is equal to a mass of one cubic centimeter of water (roughly the same dimensions as a sugar cube). One thousand grams is a kilogram (roughly the same dimensions as a quart of milk). One thousand kilograms is a metric ton (or about four bathtubs full), often spelled 'tonne' to distinguish it from the imperial ton. But a gram isn't very massive, and as we move up the scale of marine creatures the numbers are sure to get disconcertingly large. So what's a dedicated marine biologist to do?

Logarithms provide a convenient means to compare a wide range of numbers. Recall that the logarithm of a given number is the exponent to which a standard base number must be raised to produce that number. The most common system of logarithms is based on the number 10. Under this system, the logarithm of 10 is 1, of 100 is 2, and of 1000 is 3 as these numbers are equivalent to the base raised to the exponents 1, 2, and 3, respectively. It is possible to express any number, positive or negative even very awkward numbers as exponents of base 10. The utility of all this is that logarithms allow us to compare ratios through simple subtraction of relatively simple numbers.

The Richter Scale, used to measure energy released through seismic activity, provides a familiar example of a logarithmic scale based on 10. An earthquake measuring 7 on the Richter Scale is ten times more energetic than one measuring 6 (since 7 minus 6 is 1 and 10 raised to the exponent 1 is 10), and one hundred times as energetic as one rating 5 (7 - 5 = 2, 10 raised to the exponent 2 is 100). Similarly, an earthquake measuring 6.8 on the Richter Scale is 398 times as energetic as one measuring 4.2, as 6.8 - 4.2 = 2.6 and 10 raised to the exponent 2.6 is 398. From such simple numbers precise ratios can be easily attained. Consider the following table:

Animal Claim to Fame

Logarithm
of Mass

Blue Whale  (Balaenoptera musculus) Largest Animal 8.08
Sperm Whale (Physeter macrocephalus) Largest Carnivore  7.74
Whale Shark (Rhincodon typus) Largest Fish  7.65
White Shark (Carcharodon carcharias) Largest Predatory Fish  6.36
Giant Squid (Architeuthis dux) Largest Invertebrate  6.26
Sturgeon (Huso huso) Largest Bony Fish  6.13
Leatherback (Dermochelys coriacea) Largest Turtle  5.93
Giant Clam (Tridacna gigas) Largest Mollusc  5.50
Human (Homo sapiens) Most Aquatic Primate  4.96
Lobster (Homarus americanus) Largest Crustacean 4.20
Dwarf Goby (Trimmatom nanus) Smallest Vertebrate -0.52
Rotifer (Phylum Rotifera) Smallest Multicelled  Creature -8.22

So what does all this mean? Well, for openers, it means that the size spectrum of marine creatures, measured in grams, spans 16.3 (8.08 + 8.22) orders of magnitude that is, the largest marine creature is more than ten quadrillion (10,000,000,000,000,000 or 10 to the exponent 16.3) times more massive than the smallest. It also means we (4.96) are much, much closer in size to the largest marine creature (8.08) than we are to the smallest (-8.22); an average human just over 1000 times smaller than a Blue Whale (a difference of 3.12 orders of magnitude) but over a trillion times larger than the smallest (a difference of 12.38 orders of magnitude). Therefore, in absolute terms we are very large compared with most marine creatures.

That the largest predatory shark is about 25 times (1.4 orders of magnitude) bigger than the average human is a scary thought. But the White Shark does not seek us out as food. The average human is some 5.75 times (0.76 orders of magnitude) as big as the largest lobster. Relax and pass the garlic butter! Evolutionarily speaking, we may be the newest kid on the block, but we're also one of the biggest.

 

Originally published in Underwater Sports World, June 1993

 
 

ReefQuest Centre for Shark Research
Text and illustrations R. Aidan Martin
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