Body size, scaling, and allometry - Fishes

Body size, scaling, and allometry

As emphasized repeatedly, body size has an overriding influence on most aspects of fish biology. During ontogeny, fish can grow from a larva a few millimeters long to an adult several meters long. An individual must perform all life functions at all sizes in order to reach the next stage; hence size-related phenomena are constant selection pressures on growing fish. Central to discussions of size are the concepts of scale and allometry, the latter topic forming the basis of a quantitative science of size (Gould 1966; Calder 1984; Schmidt-Nielsen 1983). Scaling refers to the structural and functional consequences of differences in size among organisms; allometry quantifi es size differences among structures and organisms.

Changes in scale, whether over ontogenetic or evolutionary time, involve alterations in the dimensions, materials, and design of structures. A good example of scaling and its ramifi cations involves how an increase in body size affects the swimming speed and ability of large and small members of a species. The pelagic larvae of many marine fishes are small, elongate, and highly fl exible, whereas adults take on a variety of shapes and swimming modes (see  Locomotion: movement and shape). The larvae of many herrings are almost eel-like and swim slowly, but adults have much deeper bodies and swim faster via the carangiform mode, in which the tail is the primary propulsive region. An increase in overall body mass, a dimensional change, requires the reworking of components. The internal skeleton changes from cartilage to bone, a material change. This corresponds to an increase in body musculature and a shift from anguilliform to carangiform swimming to take advantage of the stiffer nature of bone and the more efficient transfer of energy from contracting muscles to the propulsive tail. This shift also corresponds to a design change from elongate with a rounded tail to a deeper, streamlined body with a forked tail, which is a more efficient morphology for a carangiform swimmer.

Allometry as a concept underscores a basic fact of growth and scaling, namely that the change in quantitative relationship between the sizes and functions of growing body parts is seldom linear. Linear relationships take the form:

y =ax,

indicating that structure y changes as a constant function of structure x, with a being the proportionality constant. A doubling of the size of a fish will not necessarily lead to a doubling of its swimming speed.

The relationship is more complex and depends on the measure of body size in question. For salmon, swimming speed increases approximately with the square root of the fish’s length and with the 1/5th power of its mass (i.e., length0.5, mass0.2). Allometric relationships are described by equations of the nature

y =ax^b

or

log y =log a +blog x.

The exponent b describes the slope of the line that results when the relationship between the structures is plotted on log-log paper. For simple, linear proportionalities, b =1, which is biologically rare. More often, b will take on positive or negative values for regression slopes greater or less than 1, respectively, indicating that a structure is increasing in size faster or slower than the increase in the trait to which it is being compared. The equations for swimming as a function of body size in Sockeye Salmon have exponents of 0.5 for body length and 0.17 for body mass (Schmidt-Nielsen 1983).

Numerous examples of allometric relationships in fishes can be given, emphasizing the far-reaching implications of size in fishes as well as convergence in selection pressures and solutions among disparate taxa. Focusing on locomotion and activity, the relative cost of swimming decreases with body size in most fishes, both within and among species. Such a relation indicates that it is more expensive for a small fish to move 1 g of body mass a given distance than it is for a larger fish to do the same (measured as oxygen consumed/g body mass/km, b =−0.3). Heart size in fishes increases with body size in an almost linear fashion, taking on values of about 0.2% of body mass and having a slightly positive exponent (heart mass =0.002 xbody mass1.03).

Not surprisingly, surface area of the gills relates to activity level. Very active fishes such as tunas have comparatively more gill surface than sluggish species such as toadfishes. But within species and even among species, the surface area of the gills (m2) increases allometrically and positively with body size (kg), with an exponent of 0.8–0.9. Locomotion and respiration relate to feeding activity, which is eventually translated into growth. Gut length increases allometrically with body length in many species, with an exponent of >1. Growth rate also scales with size, being faster in larger species, with an exponent of 0.61 (measured as change in mass/day relative to adult body mass) (Schmidt-  Nielsen 1983; Calder 1984; Wootton 1999).

Questions about size, scaling, and allometry are often linked to the idea of trade-offs. What constraints are imposed on an animal by changing its size, both ontogenetically and evolutionarily? What are the advantages and disadvantages of being very small as opposed to being very large? Large size may confer many advantages, but an individual must be small before it is large. During growth, an individual must incur the costs of small size early in ontogeny as well as the energetic and efficiency costs of reworking its size and shape during growth. Juveniles of a large species are often inferior competitors to small adults of a small species. Rapid growth requires rapid feeding and high metabolic rate, which exposes a young fish to more predators and also often carries an increased risk of starvation. Size-related constraints also influence life history attributes such as whether a species will produce many small versus few large young, how extensive the parental care offered will be, and whether adults will mature quickly at small size or slowly

at larger size.

One final topic with respect to size deserves mention. Fishes are supported by a dense medium and their support structures do not reflect the constraints of gravity as much as the necessity to overcome drag. The shapes of fishes then become explainable in terms of drag reduction and which area of the body is used in propulsion. Both are intimately related to the mode of locomotion used. An important sizerelated attribute is the Reynolds number, a dimensionless calculation that accounts for the size of an object, its speed, and the viscosity and density of the fluid through which it moves (see  Larval behavior and physiology).

Calculations of Reynolds numbers help explain swimming speed, body shape, and locomotory type. In very small fishes, including larvae, the effects of drag are so great and the Reynolds numbers so small that inertia is impossible to overcome. Larvae seldom glide because their mass relative to water viscosity prevents them from developing inertia as they swim. They must continue to expend effort to gain any forward progress. However, their problems associated with overcoming inertia also mean that they are less likely to sink. Large fishes such as billfishes or pelagic sharks have high Reynolds numbers. They can use inertia to advantage and literally soar through the water, using their momentum to carry them forward.