Animals are different. An elephant differs from a mouse, both in shape and size. Size is one of the most important aspects of an animal's endowment, and yet size differences are so obvious that often we give no further thought to them. We know that the elephant is much bigger than the mouse, but we rarely think about how much bigger; in fact, an elephant weighs 100 000 times more than a mouse. The smallest shrew, when fully grown, is only one-tenth the size of a mouse, or one-millionth the size of an elephant.

The world we live in is governed by the laws of chemistry and physics, and animals must live within the bounds set by those laws. We shall see that body size has profound consequences for structure and function and that the size of an organism is of crucial importance to the question of how it manages to survive.

Let us take a closer look at the enormous size differences among living organisms (Table 1.1). Each single step in this table represents a 1000-fold difference in size, and the total difference between the smallest and largest organism listed is 1021. The blue whale, which may exceed 100 tons, is the largest living animal, but the giant sequoia trees of California outweigh the largest whales by 10-or 15-fold.

Definition of scaling

It is regrettable that we cannot study the effects of scaling by building super-sized elephants. Nevertheless, we can approach the problem in a different way, and in this regard we have much to learn from the engineer who continually solves the problems of building taller skyscrapers, longer bridges, bigger ships, and so on. Indeed, the need for changes in the size or scale of things has given rise to an entire branch of engineering known as scaling. For our purposes here, we shall use the definition that scaling deals with the structural and functional consequences of changes in size or scale among otherwise similar organisms.

If we increase the size of a brick house, we know that we need heavier foundations and thicker walls. There are practical limits to the size of brick houses, however, for the walls must be made thicker and thicker as house size increases. Eventually we meet an ultimate limit to further increases, dictated by the strength of brick. In the design of a skyscraper the engineer therefore changes the material in the main supporting structures; he uses steel rather than brick. In this case the constraint on a further increase in size is overcome by a change in material.

Another avenue is also open to the engineer: He can change to a new design. The construction of long bridges gives an example.

The circulatory system consists of a pump, the heart, and the attached plumbing of blood vessels. The dimensions of both pump and plumbing must be scaled to the demands, and it seems evident that in vertebrates the transport of gases is the most important consideration. If this demand is met, it appears that most or all other functional requirements on the circulatory system will be satisfied. This applies to the transport of nutrients, metabolic intermediates, excretory products, hormones, heat, and so on.

The circulatory system serves also in the transmission of force; blood is used as a hydraulic fluid to achieve, for example, ultrafiltration (in the kidney and in fluid exchange in the capillaries) and volume changes (e.g., erection of the penis). The needed force is supplied by the heart, as reflected in the blood pressure; we shall see that blood pressure appears to be a scale-independent physiological parameter.

The mammalian heart

The rate of oxygen consumption in mammals, relative to body size, decreases with increasing body size. It is therefore somewhat surprising to find that the relative size of the heart of small and large mammals is similar, that both mouse and elephant have hearts that are around 0.6% of their body mass. There is a great deal of information available on the size of the mammalian heart (e.g., Clark, 1927; Crile and Quiring, 1940; Grande and Taylor, 1965; Holt et al., 1968).

Birds and mammals maintain their body temperatures more or less constant and independent of variations in environmental temperature. To maintain a constant body temperature, there is one fundamental requirement: The rate of heat loss must equal the rate of heat production. This simple fact is basic to all considerations of temperature regulation.

Both heat production and heat loss can be varied through a number of physiological mechanisms. Most mammals and birds are very successful in achieving balance and maintaining a constant core temperature with only minor fluctuations. One regular fluctuation is the change in core temperature with the day-and-night cycle, the night temperature being a couple of degrees lower than the day temperature in diurnal animals, and vice versa for nocturnal animals. The body temperature is also increased during physical activity, but we shall not be concerned with any of these fluctuations.

What do we mean by body temperature? This is by no means a simple question, because the different parts of the organism are not all at the same temperature. Body temperature in mammals and birds is usually taken to mean the temperature of the deeper abdominal organs, sometimes referred to as the core temperature, and often measured as the deep rectal temperature.

Scaling of heat loss

We saw earlier that various groups of warm-blooded vertebrates have characteristic ranges of body core temperatures, without any obvious relationship to body size (Table 16.1). In each group, the body temperature is maintained within a few degrees as a scale-independent variable.

Real animals were not meant to sit still and patiently let a physiologist measure their “basal” metabolic rates. Animals eat, drink, sleep, run, chase, mate, and play. When their physical exertion is maximal, parts of the system, such as lungs and heart, must perform at a maximal level. Therefore, the limits on maximal performance are much more informative about animal design and much more interesting than the resting or idling level. Think of a racing car or an airplane sitting still with the engine running; the idling speed gives little information about maximal performance.

Maximal performance

During heavy physical work, such as running at top speed, oxygen is taken up in the lungs at a maximal rate and diffuses into the red blood cells of the lung capillaries, where it binds to the hemoglobin. The heart pumps the blood to the muscles, where oxygen diffuses from the capillaries to the cells and the mitochondria, which serve as the final oxygen sink. At each point in this chain, the flow rate of oxygen must equal the rate at which it is consumed in the sink.

Carbon dioxide, produced at a rate corresponding to the oxygen consumed, traverses the same pathway but in the opposite direction. At each step, the flow rate must equal the rate of production as CO2 flows from the mitochondria into the capillaries, is circulated to the lungs, diffuses into the alveoli, and is dumped to the outside atmosphere.

Animals running on land are supported by a solid substratum. Animals that swim and fly move in fluid media and have no solid support; they are supported by the medium through which they move. Fish have nearly the same density as water, and the energy they use for locomotion goes into overcoming the resistance of the medium. A flying bird must also overcome the resistance of the medium, but in addition it must keep from falling to the ground; that is, it must provide lift equal to its body weight.

Fish

Because fish are nearly neutrally buoyant, they expend little or no energy to support themselves, but energy is needed to overcome the resistance of the medium. The resistance that a swimming fish encounters is called the drag. To overcome the drag, the fish must provide thrust that equals the drag. There are two components to the drag on a fish moving through the water: pressure drag and friction drag.

Friction drag can be thought of as the drag on a thin, flat plate being pulled through a fluid parallel to its plane. Pressure drag can be thought of as the drag on the plate if it is moved through the fluid in a direction vertical to its plane.

Pressure drag is difficult to calculate accurately. It comes from the necessity to displace water during forward movement, and it is determined by the frontal area (the projected body area onto a plane normal to the direction of swimming) and by the shape of the body.

For all vertebrates and many invertebrates, the blood plays a major role in gas transport. In vertebrate blood, oxygen is carried by hemoglobin, which is located within the red blood cells. Carbon dioxide, in contrast, is carried mainly as the bicarbonate ion, dissolved in the blood plasma. It is commonly agreed that the supply of oxygen is more critical than the elimination of carbon dioxide and that whenever the oxygen supply is adequate, there is no difficulty in eliminating carbon dioxide at the rate at which it is formed.

The main parameters that are of interest in connection with oxygen transport and scaling are (1) the concentration of hemoglobin, which determines how much oxygen can be carried by one unit volume of blood, (2) the total volume of blood in the body and thus the total amount of hemoglobin in the blood, (3) the size of the red blood cell, and (4) the affinity of hemoglobin for oxygen, which is of interest both for the uptake of oxygen in the lung and for its delivery in the tissues.

Hemoglobin concentration

The hemoglobin concentration and oxygen capacity of blood have been surveyed by Larimer (1959) and Burke (1966) for a wide range of mammals. As could be expected, the oxygen-carrying capacity of the blood is strictly proportional to its hemoglobin concentration. The average hemoglobin concentration in 18 mammals, ranging in size from a small bat to the horse, was 128.7 g hemoglobin per liter blood.

A bird egg is a mechanical structure strong enough to hold the chick securely during development, yet weak enough to break out of. The shell must let oxygen in and carbon dioxide out, yet be sufficiently impermeable to water to keep the contents from drying out.

Bird eggs

Eggs are interesting structures. They are beautifully designed, self-contained life-support systems for the developing bird. All the nutrients, minerals, and water needed during incubation, as well as the necessary energy supply, are present in the freshly laid egg. This well-designed microcosmos contains everything needed for the growth and production of the hatchling chick, with one crucial exception: Oxygen. Furthermore, the shell of the avian egg is a simple physical system that is exceptionally well suited to considerations of scaling.

A hummingbird egg may weigh less than 0.3 g, and an ostrich egg over 1 kg, a 3000-fold range. The birds that lay these eggs range in size from 3-g hummingbirds to 100-kg ostriches, a 30000-fold range. The largest bird that has ever lived, the elephant bird (Aepyornis) from Madagascar, was a sizable animal, standing perhaps 3 m tall and weighing over 500 kg (Feduccia, 1980). Its giant egg weighed about 10 kg, 10 times as much as an ostrich egg and 30000 times as much as a hummingbird egg.

This book is about the importance of animal size. Although it is informative and tells a great deal about what we know today, it is not encyclopedic. It should therefore be easy to read and use.

When we try to find the rules that govern animal function, we tend to think in terms of chemistry. We think of water, salts, proteins, enzymes, oxygen, energy, and so on – a whole world of chemistry. We should not forget that physical laws are equally important; they determine rates of diffusion and heat transfer, transfer of force and momentum, the strength of structures, the dynamics of locomotion, and so on. Physical laws provide possibilities and opportunities, yet they impose constraints and set limits to what is physically possible. It is our purpose to understand these rules because of their profound implications when we deal with organisms of widely different size and scale.

The book requires a minimum of basic numerical skills. It turns out that body size relationships are best expressed with logarithms and powers. These are simple enough to require familiarity with no more than a few easy algebraic operations. The entire book has been made as simple as possible, and most arguments are intuitively understandable. Although I use equations, which are useful for calculations, the conclusions are presented verbally, so that a minimum of effort is required to read the book from cover to cover.

Let us return to the warm-blooded vertebrates, birds and mammals. We have seen that for these the empirical relationship between metabolic rate and body size is known with much greater certainty than for cold-blooded vertebrates and invertebrates, and the reason is undoubtedly related to their relatively constant body temperature. To understand the regular relationship to body size, we should examine those groups that are best known, also in regard to related physiological information.

Body temperature

First of all, the regularity of metabolic rates in warm-blooded vertebrates is undoubtedly related to their relatively constant body temperatures. This eliminates temperature as a variable here, whereas in cold-blooded animals it causes innumerable difficulties in determining a definite metabolic rate, both for the short term and for the long term (acute effects of a temperature change as well as long-term acclimatization).

How constant is the body temperature of birds and mammals? For the moment, let us disregard the small number of mammals and even smaller number of birds that in connection with periods of torpor or hibernation can undergo profound decreases in body temperature. Here we are concerned with the normal or usual temperature of active animals.

Do small and large mammals have similar temperatures, or is the body temperature of mammals related to body size? This question was discussed by Morrison and Ryser (1952), who examined published material supplemented with a considerable number of observations of their own, especially on smaller animals.

In earlier chapters we were concerned with the scaling of structures; in this and later chapters we shall deal mostly with function. The first subject will be the metabolic rates of animals. Energy is needed for maintenance and for all the normal functions of the living animal: for moving about, for feeding, for escaping, and so on. The energy an animal needs for all this comes from the chemical energy contained in food. The total use or turnover of chemical energy is frequently referred to as the metabolic rate, and for reasons that we shall not discuss here, it is convenient as well as reasonably accurate to measure the rate of energy metabolism as the rate of oxygen consumption.

The determination of oxygen consumption is technically easy, and it is so commonly used for estimation of metabolic rate that the two terms often are used interchangeably. This is not correct; for example, an anaerobic organism that depends on nonoxidative metabolic processes has zero oxygen consumption, but it certainly does not have a zero metabolic rate. In the following, however, we shall be concerned mostly with the rate of oxidative metabolism as it almost universally is measured as the rate of oxygen consumption.

In the absence of external activity, metabolism, or oxygen consumption, continues at a rate that can be called the resting or maintenance rate.