Invariants combinations and comparative studies

Researchers studying particular groups of organisms have long known that certain traits are correlated in very specific ways with other traits across species. The most famous of these correlations are those in the mammals, which display the so-called 'fast-slow continuum' (Promislow and Harvey 1990). Large-bodied mammals, such as elephants and buffalo, have long adult lifespans, take a long time to mature, have small litters of large offspring. In contrast, small-bodied mammals, such as mice and shrews, have short adult lifespans, mature very rapidly, and have large litters of small offspring. They therefore 'live fast and die young'. All mammals fit relatively neatly somewhere onto this continuum. We will examine how widespread this pattern is in other groups later on.

The differences just described are known because of comparative studies (Harvey and Pagel 1991), and much of the rest of this chapter relies on comparative studies. Comparative studies take variation among different species as their source of data. This variation has evolutionary origins, and much of the time the forces causing the variation we see among species have

TRAITS, INVARIANTS, AND THEORIES OF EVERYTHING 41 Speciesl -»-Species2 Species3 -► Species4

TRAITS, INVARIANTS, AND THEORIES OF EVERYTHING 41 Speciesl -»-Species2 Species3 -► Species4

Fig. 4.4 Four species plotted onto an evolutionary tree, or phylogeny, showing their evolutionary relationships. The comparison between species 1 and species 2 is evolutionarily independent of the comparison between species 3 and 4. Both may be used as data in a comparative study.

been ecological ones. We can use the variation we see therefore as the results of some grand experiment in evolution played out over time, and ask what factors correlate with the variation. We have been using comparative data in a rather loose sense throughout the previous chapters: for example, we compared the species richness of different cichlid groups with different traits, the rates of recombination among species of different size, and the fecundities of annual verses perennial plants. More formally, comparative biologists like to use their data in some kind of statistical analysis, and the power of such analyses increases with the quantity of data. Normally, this means finding many different taxonomic groups that have changed independently of other groups. To ensure this is the case, comparative biologists often include in their study a 'phylogeny' that describes the relationships between the species in the dataset, and helps to identify independent evolutionary events (Figure 4.4).

Comparative studies on mammals have revealed the fast-slow continuum just described. The more specific details of this continuum are also interesting. First, many of the life history traits are related to body size across species by a characteristic power function, known as an allometric exponent (Figure 4.5). The birth rate of a mammal species, for example, is proportional to its body size to the power of —0.25 (thus, birth rate declines with body size across species). Amazingly, all of the allometric exponents for mammalian life history traits are close to some multiple of a quarter. This seems to require explanation. Furthermore,but rather less surprisingly given what we have just seen, certain traits, when multiplied together have values that are unrelated to body size. For example, if one trait with the exponent 0.25 is multiplied by another trait with the exponent —0.25, the result is a number that is not related to the body size of the species, and may be relatively constant. Eric Charnov, who has done most to bring these facts

Linear plots Log-log plots

Fig. 4.5 Allometry. Traits are allometric if they are related to body mass by a power function (linear plot, numbers indicate the exponent). If both the trait and body mass are logged, the relationship is a straight line where the slope of the line is equal to the exponent. Both 0.25 and -0.25 exponents are common in mammals. If a trait with an exponent of 0.25 is multiplied by a trait with an exponent of -0.25, the resulting product is an 'invariant' because it is unrelated to body mass (exponent of zero).

Body size Log body size

Fig. 4.5 Allometry. Traits are allometric if they are related to body mass by a power function (linear plot, numbers indicate the exponent). If both the trait and body mass are logged, the relationship is a straight line where the slope of the line is equal to the exponent. Both 0.25 and -0.25 exponents are common in mammals. If a trait with an exponent of 0.25 is multiplied by a trait with an exponent of -0.25, the resulting product is an 'invariant' because it is unrelated to body mass (exponent of zero).

to the attention of other researchers, called these interesting numbers 'invariants'. In mammals, for example, one invariant is age at maturity times the adult annual mortality rate (this is in fact, relatively invariant within many groups of organisms but varies across groups). These strange facts seem to be telling us something pretty fundamental about life history evolution; the trouble is in knowing exactly what.

Charnov (1991) was the first to build a theoretical evolutionary model that would be able to predict these relationships. The basis of the model was natural selection on age at maturity governed primarily by adult mortality. One of the studies that most influenced this assumption is a study by Harvey and Zammuto (1985) using data on mortality rates of mammal species in their natural habitats. Getting data on that rather tricky variable for enough species has entailed centuries of man-hours in the field by dedicated researchers. Rather interestingly, the data showed that adult mortality rates in the wild strongly predicted where a mammal stood on the fast-slow continuum. Small-bodied mammals suffered high adult mortality and large-bodied mammals low mortality. Even more interesting, when body size was controlled for statistically, adult mortality rate was still related to most other life history traits: for example, mammals with low adult mortality for their size also had low fecundity for their size. This seemed to suggest that adult mortality might be a controlling selective force in shaping the fast-slow continuum.

In mammals offspring reach independence from their mothers at a certain size but then grow further until, when mature, they stop growing (Figure 4.6). Charnov then reasoned that the mortality rates they experienced after independence would govern when would be the best time to mature: if

Fig. 4.6 Charnov's (1991) model. The solid line represents a mammal suffering heavy mortality after independence. It is best for it to mature early even though this means it can devote fewer resources to reproduction (vertical arrows). A mammal suffering lower mortality (dotted line) can afford to wait longer before maturing. As a result, it lives longer, is bigger when mature, and can devote more resources to reproduction. This model oversimplifies mammalian growth and metabolism (see Figure 4.8), yet makes accurate predictions across species.

Fig. 4.6 Charnov's (1991) model. The solid line represents a mammal suffering heavy mortality after independence. It is best for it to mature early even though this means it can devote fewer resources to reproduction (vertical arrows). A mammal suffering lower mortality (dotted line) can afford to wait longer before maturing. As a result, it lives longer, is bigger when mature, and can devote more resources to reproduction. This model oversimplifies mammalian growth and metabolism (see Figure 4.8), yet makes accurate predictions across species.

they matured late, the benefit would be achieving a bigger body size, and consequent larger reproductive resources per unit time. However, this had to be traded-off against the risk of death before maturity. In general then, a late maturation time would only be selected if adult mortality was low.

Where do the allometric slopes in the model all come from? Charnov assumed a within-species allometry of metabolic rate on body size of 0.75. Before maturity, this metabolism causes growth, after maturity the metabolism is channelled into reproduction. Charnov had to make two more assumptions: first, about offspring size. He assumed that size at weaning is a constant proportion of maturation size across species. Finally, he assumed that the populations of mammals were of constant size, so that juvenile mortality balances fecundity. Density-dependent mortality acts only after the strategies have been decided on, so this does not contradict the idea of optimization. These assumptions are the origins of all the quarter-power scalings in the model.

The model can successfully predict the fast-slow continuum. For example, imagine an organism with low adult mortality. As a result of this, it lives a long adult life. It is selected to mature late and large because it can afford to delay reproduction to gain reproductive power due to the low risk of mortality before maturation (Figure 4.6). Since offspring size at weaning scales with body size to the power 1 in the model, but reproductive power only 0.75, it leaves fewer but larger offspring, which have a low risk of mortality prior to

Table 4.1 Scaling exponents, relationships between variables and invariants predicted or assumed by Charnov (1991) and observed by Purvis and Harvey (1995)

Variables

Theory

Observed

Assumptions

Allometric exponent

Growth rate

0.75

0.82/

Biomass offspring per year

0.75

0.66/'

Size at weaning to size at maturity

1

0.89X

Predictions

Allometric exponent

Age at maturity

0.25

0.24/

Annual fecundity

-0.25

-0.24/

Adult mortality rate

-0.25

-0.24/

Juvenile mortality rate

-0.25

-0.32/

Pairs of traits

Relationship

Adult mortality, age at maturity

Negative

Negative/

Juvenile mortality, age at maturity

Negative

Negative/

Juvenile mortality, adult mortality

Positive

Positive/

Birth rate, adult mortality

Positive

Positive/

Birth rate, juvenile mortality

Positive

Positive/

Age at maturity times adult mortality

Size invariant

Size invariant/

Age at maturity times juvenile mortality

Size invariant

Size invariant/

Age at maturity times fecundity

Size invariant

Size invariant/

Note: Ticks indicate that the data match the prediction, crosses indicate a mismatch.

Note: Ticks indicate that the data match the prediction, crosses indicate a mismatch.

independence. The model manages, via a bit of algebra, to predict nearly all of the allometric exponents and invariants seen in the data (see Table 4.1).

If we were to accept the model as an approximate description of the evolutionary forces at work, it would be a major achievement. It might, for example, explain the human life history (large body size, long adult lifespan, late maturation, few large offspring) in terms of low adult mortality in our evolutionary past. Other curious facts would be explicable. The longest lifespans of any mammal are achieved by the bowhead whale which typically lives to over one hundred years, and several may well have lived over 200 years (George etal. 1999). Such findings have raised some public interest: why do they live so long? If Charnov is right, then the answer is ridiculously simple: they live long because they experience low adult mortality. The model, of course, makes a number of simplifying assumptions, and several developments have since been made (Kozlowski and Weiner 1997; Charnov 2001,2004).

How far do other organisms fit the Charnov model? One would think not many. For example, in many organisms, body size is not determined by a decision on when to mature, but by the size of a food patch allocated to them by their parents and the number of offspring with which they share it. Many insects, such as parasitic wasps and seed eating beetles, possess such a life history (Mayhew and Glaizot 2001). In others, such as altricial birds (which feed their offspring at the nest until fledging), offspring do not grow after independence at all but are raised to maturation size by their parents. In still others, such as most perennial plants, growth is not determinate, so organisms not only grow after maturation but also do not divert all their metabolic effort away from growth and into reproduction.

It would seem therefore that so many organisms break the assumptions of the model that it could not possibly be general. However, some of the model's predictions are turning out to be sufficiently general to suppose that some of the principles are common to many superficially different life histories. Flowering plants, for example, show many features of the fast-slow continuum predicted by Charnov's model, such as a negative relationship between adult mortality and age at maturity, despite breaking the assumption of deterministic growth (Franco and Silvertown 1997). Enquist et al. (1999) have even used Charnov's results for mammals to derive relationships between adult lifespan, age and size at maturity, and the density of wood across tropical forest tree species. These relationships are positive as predicted by the theory. Many indeterminate growers show some of Charnov's predicted invariants; parasitic nematodes for example, display an invariant maturation time multiplied by adult mortality rate, indicating that these are negatively related to each other with exponents of equal magnitude but opposite sign (Gemmil etal. 1999).

In contrast however, it is equally clear that it would not be valid to view all organisms as possessing mammal-like life histories. In birds, there is a general dichotomy between species that nest in safe places, such as albatrosses on offshore islands, and those that nest in dangerous places, such as grouse on the ground. The former suffer only low juvenile mortality, display low annual fecundity, grow slowly, breed late, and survive well as adults, while the latter display opposite traits. However, adult size is not consistently correlated with adult survival or with fecundity, but is robustly related to age at first breeding (Bennett and Owens 2002). These relationships are readily understood from the theory of single trait optimization. For example, high pre-breeding mortality, when maturation and growth are flexible, has long been known to select for high growth rates and early maturation, and early maturation selects for increased investment in reproduction and decreased investment in survival. In parasitoid wasps, there is no association between adult body size and either development time, adult lifespan, or fecundity (Blackburn 1991). Instead, these variables are correlated with traits specific to parasitoids: whether they develop as endo- or ectoparasitoids, and whether or not they permanently paralyze their host (Mayhew and Blackburn 1999). These traits probably exert their influence through constraints, such as on host range and egg size (Godfray 1994). Body size is related instead to host size and clutch size (see Mayhew and Hardy 1998). Thus, one of the exciting prospects of the next few years in life history evolution will be how many fundamentally different life histories there really are, and what the major selective influences are. Trying to understand invariant relationships, where they exist, is likely to be valuable.

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