Effects of size and temperature on metabolic rate.

We derive a general model, based on principles of biochemical kinetics and allometry, that characterizes the effects of temperature and body mass on metabolic rate. The model fits metabolic rates of microbes, ectotherms, endotherms (including those in hibernation), and plants in temperatures ranging from 0 degrees to 40 degrees C. Mass- and temperature-compensated resting metabolic rates of all organisms are similar: The lowest (for unicellular organisms and plants) is separated from the highest (for endothermic vertebrates) by a factor of about 20. Temperature and body size are primary determinants of biological time and ecological roles.

Reproductive constraints and the evolution of life histories with indeterminate growth.

A prominent feature of comparative life histories in fish (and other indeterminate growers) is the approximate invariance across species of certain dimensionless numbers made up from reproductive and timing variables. The two best known are the age at maturity (alpha) divided by the average adult lifespan (E), and the proportion of a body mass given to reproduction per year (c) multiplied by E. This article uses evolutionary life-history theory for nongrowing populations to predict the numeric value of these numbers for fish and lizards, with several new implications for the dynamics of ontogenetic development.

A resource range invariance rule for optimal offspring size predicts patterns of variability in parental phenotypes.

Previous analysis of the rules regarding how much more a female should invest in a litter of size C rather than producing a litter with one more offspring revealed an invariance relationship between litter size and the range of resources per offspring in any litter size. The rule is that the range of resources per offspring should be inversely proportional to litter size. Here we present a modification of this rule that relates litter size to the total resources devoted to reproduction at that litter size. The result is that the range of resources devoted to reproduction should be the same for all litter sizes. When parental phenotypes covary linearly with resources devoted to reproduction, then those traits should also show equal ranges within each litter size category (except for litters of one). We tested this prediction by examining the range in body size (=total length) of female mosquito fish (Gambusia hubbsi) at different litter sizes. Because resources devoted to reproduction may take many forms (e.g., nest defense), this prediction may have broad applicability.

Grandmothering, menopause, and the evolution of human life histories.

Long postmenopausal lifespans distinguish humans from all other primates. This pattern may have evolved with mother-child food sharing, a practice that allowed aging females to enhance their daughters' fertility, thereby increasing selection against senescence. Combined with Charnov's dimensionless assembly rules for mammalian life histories, this hypothesis also accounts for our late maturity, small size at weaning, and high fertility. It has implications for past human habitat choice and social organization and for ideas about the importance of extended learning and paternal provisioning in human evolution.

Trade-off-invariant rules for evolutionarily stable life histories.

Optimization models have been widely and successfully used in evolutionary ecology to predict the attributes of organisms. Most such models maximize darwinian fitness in the face of trade-offs and constraints; the numerical results usually depend on the exact form of the trade-offs or constraints. But not always: for example, earlier work predicted that the optimal range in offspring size ought to show a - 1 scaling with small litter size, independent of most details of the underlying offspring-survival/ offspring-size trade-off relation. Here I report that in non-growing (stationary), age-structured populations, three major life-history attributes (age at first breeding, size of an offspring in large litters, and reproductive effort) are likely to evolve to equilibrium values that satisfy a universal numerical rule; the underlying trade-off will have a slope of - 1 at the optimum, independent of most other aspects of the trade-off. Each of these three attributes can be viewed as an allocation problem between just two alternatives; the trade-off is then between having more of one alternative and less of the other. The slope of the trade-off is simply the slope of the curve of allowed combinations of the two alternatives. The theory predicts that natural selection will push to an equilibrium where the slope is always - 1. The economic structure is the same as that which underlies evolution of the sex ratio where the two alternatives are sons and daughters.

A trade-off-invariant life-history rule for optimal offspring size.

Optimization models have been widely and successfully used in evolutionary ecology to predict the attributes of organisms. Most such models maximize darwinian fitness (or a component of fitness) in the face of trade-offs and constraints; the numerical results usually depend on the exact form of the trade-offs/constraints. Here we report the first (to our knowledge) numerical optimum for life-history evolution which is independent of the details of the underlying trade-off, for a large array for trade-off forms. The rule is that at small litter sizes, the range in offspring size is inversely proportional to the size of the litter. Details of the offspring-survival/offspring-size trade-off set the value of the proportionality constant, but the -1 exponent, the inverse proportionality itself, is universal. Studies of life histories have yielded many empirical examples of universality for various scaling exponents (for example, adult lifespan scales as approximately 0.25 with adult body mass within many taxa); this is an example of the numerical value of an exponent (here -1) emerging from a life-history model as independent of all but a few general features of the underlying economic structure.

Dimensionless invariants from foraging theory's marginal value theorem.

Copula duration (t) decreases, and proportional rate of sperm transfer (c) increases, with larger male body size in dung flies, so their dimensionless product (c. t) is approximately constant (approximately 2.2). The most recent copulating male fertilizes about 89% of the eggs laid (= 1 - e(-c.t) = 1 - e(-2.2)), independent of his body size. The conditions under which natural selection favors this phenotypic invariance are studied with fitness optimization models. The dimensionless rules for optimal patch residence times are then generalized to cover phenotypic variation in other foraging cases.

Evolution of life history variation among female mammals.

A unified approach is developed for the evolutionary structure of mammalian life histories; it blends together three basic components (individual growth or production rate as a function of body size, natural selection on age of maturity, and stable demography) to predict both the powers and the intercepts of the scaling allometry of life history variables to adult size. The theory also predicts the signs (+, -) of the correlations between life history variables when body size is held constant. Finally, the approach allows us to eliminate body size to predict the dimensionless relationships between the life history variables themselves.

The primary sex ratio under environmental sex determination.

The ESS primary sex ratio (male/female) under environmental sex determination (ESD) is shown to be equal to the ratio of the average fertility of a female to the average fertility of a male. Thus, depending upon how male and female fertility change over the environmental variable causing ESD, the primary sex ratio may be either male or female biased, or neither. The primary sex ratio thus contains information as to how male and female fertilities change with the environment.

Phenotypic evolution under Fisher's Fundamental Theorem of Natural Selection.

Lande's (1982) equations for phenotypic evolution are derived as a linearized version of Fisher's Fundamental Theorem of Natural Selection. In this derivation the genetic covariance matrix is not necessarily a fixed object and is likely to alter as directional selection proceeds. Under stabilizing or equilibrium selection, the mean phenotypes take on values identical to those which would be predicted by an "optimization of fitness in the face of tradeoffs" approach. It is argued that optimization is a more powerful way to understand equilibrium or stabilizing selection.

Some conceptual issues in the origin of eusociality.

Certain issues arising in connection with the evolutionary origins of eusociality are discussed. Previous results about when natural selection favours helping behaviour are generlised, and the differing viewpoints of both parents and offspring are considered. Particular attention is given to the evolutionary implications of different patterns of overlapping generations observed in bivoltine insects. As argued by Seger (1983), these patterns imply different conditions under which a daughter is selected to help her mother rear additional siblings in haplodiploid populations. Other factors that can alter the selective advantages of helping behaviour under haplodiploidy are also discussed, including the possibility of sex ratio manipulation and the novel result that helping behaviour may be locally favoured in populations that are spatially patchy with respect to sex-specific fitness. A new hypothesis is also presented: The fact that sisters are selected to aid their mother to parasitise other sisters may have played an important role in the origins of eusociality. A given offspring benefits from having maternally parasitised siblings because such siblings rear additional siblings (to which the given offspring is more closely related) instead of nieces and nephews. Finally, the importance of haploidiploidy in the origins of eusociality is discounted; the virtually unique biology of aculeate Hymenoptera would seem to be of much greater importance.

Size advantage may not always favor sex change.

A simple application of sex allocation theory to sex reversal suggests that, under Ghiselin's size advantage model, this form of sexuality ought to be common; actually it is quite rare. This note suggests that a sex specific size advantage may not favor sex change if the advantage is offset by other life-history tradeoffs. A few possibilities are discussed.

Sex allocation in a patchy environment: a marginal value theorem.

The ESS sex allocation when male/female fitnesses vary with patch type is a set of values which either equalizes the marginal values of the male/female fitness tradeoffs, or are pure sexes. This is shown for a hermaphrodite; the result is then generalized to other sex allocation cases.

Sex ratio evolution in a variable environment.

We develop a natural selection model for sex ratio control in a spatially variable environment. Predictions of sex ratio alteration as a function of environmental change are tested in laboratory experiments with two parasitic wasps. Field data from a variety of other organisms also support the model. Finally, we discuss possibilities and difficulties for testing this type of evolutionary model.