Inclusive fitness theory and eusociality.

Arising from M. A. Nowak, C. E. Tarnita & E. O. Wilson 466, 1057-1062 (2010); Nowak et al. reply. Nowak et al. argue that inclusive fitness theory has been of little value in explaining the natural world, and that it has led to negligible progress in explaining the evolution of eusociality. However, we believe that their arguments are based upon a misunderstanding of evolutionary theory and a misrepresentation of the empirical literature. We will focus our comments on three general issues.

A life-history approach to the late Pleistocene megafaunal extinction.

A major criticism of the "overkill" theory for the late Pleistocene extinction in the Americas has been the seeming implausibility of a relatively small number of humans selectively killing off millions of large-bodied mammals. Critics argue that early Paleoindian hunters had to be extremely selective to have produced the highly size-biased extinction pattern characteristic of this event. Here, we derive a probabilistic extinction model that predicts the extinction risk of mammals at any body mass without invoking selective human harvest. The new model systematically analyzes the variability in life-history characteristics, such as the instantaneous mortality rate, age of first reproduction, and the maximum net reproductive rate. It captures the body size-biased extinction pattern in the late Pleistocene and precisely predicts the percentage of unexpectedly persisting large mammals and extinct small ones. A test with a global late Quaternary mammal database well supports the model. The model also emphasizes that quantitatively analyzing patterns of variability in ecological factors can shed light on diverse behaviors and patterns in nature. From a macro-scale conservation perspective, our model can be modified to predict the fate of biota under the pressures from both climate change and human impacts.

Dinosaur fossils predict body temperatures.

Perhaps the greatest mystery surrounding dinosaurs concerns whether they were endotherms, ectotherms, or some unique intermediate form. Here we present a model that yields estimates of dinosaur body temperature based on ontogenetic growth trajectories obtained from fossil bones. The model predicts that dinosaur body temperatures increased with body mass from approximately 25 degrees C at 12 kg to approximately 41 degrees C at 13,000 kg. The model also successfully predicts observed increases in body temperature with body mass for extant crocodiles. These results provide direct evidence that dinosaurs were reptiles that exhibited inertial homeothermy.

Reproductive allometry and the size-number trade-off for lizards.

Fundamental to life-history theory is the assumed inverse proportionality between the number of offspring and the resource allocation per offspring. Lizards have been model organisms for empirical tests of this theory for decades; however, the expected negative relationship between clutch size and offspring size is often not detected. Here we use the approach developed by Charnov and Ernest to demonstrate that this often concealed trade-off can be made apparent in an interspecific comparison by correcting for size-dependent resource allocation. Our data set also shows a tight allometry for annual production that is consistent with life-history models for indeterminate growers. To account for nonindependence of species data we also compare the fit of nonphylogenetic and phylogenetic regression models to test for phylogenetic signal in these allometry and trade-off patterns. When combined, these results demonstrate that the offspring size/clutch size trade-off is not isolated to a single clutch but is shaped by the resource investment made over an entire year. We conclude that, across diverse lizard species, there is strong evidence for the predicted trade-off between offspring size and the annual number of eggs produced.

Lifetime reproductive effort.

In a 1966 American Naturalist article, G. C. Williams initiated the study of reproductive effort (RE) with the prediction that longer-lived organisms ought to expend less in reproduction per unit of time. We can multiply RE, often measured in fractions of adult body mass committed to reproduction per unit time, by the average adult life span to get lifetime reproductive effort (LRE). Williams's hypothesis (across species, RE decreases as life span increases) can then be refined to read "LRE will be approximately constant for similar organisms." Here we show that LRE is a key component of fitness in nongrowing populations, and thus its value is central to understanding life-history evolution. We then develop metabolic life-history theory to predict that LRE ought to be approximately 1.4 across organisms despite extreme differences in production and growth rates. We estimate LRE for mammals and lizards that differ in growth and production by five- to tenfold. The distributions are approximately normal with means of 1.43 and 1.41 for lizards and mammals, respectively (95% confidence intervals: 1.3-1.5 and 1.2-1.6). Ultimately, therefore, a female can only produce a mass of offspring approximately equal to 1.4 times her own body mass during the course of her life.

The offspring-size/clutch-size trade-off in mammals.

The Smith-Fretwell model for optimal offspring size assumes the existence of an inverse proportional relationship (i.e., trade-off) between the number of offspring and the amount of resources invested in an individual offspring; virtually all of the many models derived from theirs make the same trade-off assumption. Over the last 30 years it has become apparent that the predicted proportionality is often not observed when evaluated across species. We develop a general allometric approach to correct for size-related differences in the resources available for reproduction. Using data on mammals, we demonstrate that the predicted inverse proportional relationship between number of offspring and offspring size is closely approached after correcting for allocation, though there is a slight curvature in the relationship. We discuss applications for this approach to other organisms, possible causes for the curvature, and the usefulness of allometries for estimating life-history variables that are difficult to measure.

Maternal condition and facultative sex ratios in populations with overlapping generations.

Facultative investment in offspring sex is related to maternal condition in many organisms. In mammals, empirical support for condition-dependent sex allocation is equivocal, and there is some doubt as to theoretical expectations. Much theory has been developed to make predictions for condition-dependent sex ratios in populations with discrete generations. However, the extension of these predictions to populations with overlapping generations (OLGs; e.g., mammals) has been limited, leaving doubt as to the specific prediction for maternal-condition-dependent sex ratios in mammals. We develop a population genetics model that incorporates maternal effects on multiple offspring fitness components in a population with OLGs. Using a rare-gene and evolutionarily stable strategy approach, we demonstrate that sex ratio predictions of this model are identical to those for equivalent discrete generations models. We show that the predicted sex ratios depend on the sex-specific ratio of R(o) (offspring lifetime fitness) for offspring of good and poor mothers. This offspring lifetime fitness rule indicates that empirical research on conditional sex ratios should consider all three components of offspring R(o) (juvenile survival, adult life span, and fertility).

Sex-specific survival to maturity and the evolution of environmental sex determination.

Four decades ago, it was proposed that environmental sex determination (ESD) evolves when individual fitness depends on the environment in a sex-specific fashion--a form of condition-dependent sex allocation. Many biological processes have been hypothesized to drive this sex asymmetry, yet a general explanation for the evolution of sex-determining mechanisms remains elusive. Here, we develop a mathematical model for a novel hypothesis of the evolution of ESD, and provide a first empirical test using data across turtles. ESD is favored when the sex-determining environment affects annual survival rates equivalently in males and females, and males and females mature at different ages. We compare this hypothesis to alternative hypotheses, and demonstrate how it captures a crucially different process. This maturation process arises naturally from common life histories and applies more broadly to condition-dependent sex allocation. Therefore, it has widespread implications for animal taxa. Across turtle species, ESD is associated with greater sex differences in the age at maturity compared to species without ESD, as predicted by our hypothesis. However, the effect is not statistically significant and will require expanded empirical investigation. Given variation among taxa in sex-specific age at maturity, our survival-to-maturity hypothesis may capture common selective forces on sex-determining mechanisms.

A dimensionless invariant for relative size at sex change in animals: explanation and implications.

Recent comparative studies across sex-changing animals have found that the relative size and age at sex change are strikingly invariant. In particular, 91%-97% of the variation in size at sex change across species can be explained by the simple rule that individuals change sex when they reach 72% of their maximum body size. However, this degree of invariance is surprising and has proved controversial. In particular, it is not clear why this result should hold, given that there is considerable biological variation across species in factors that can influence the evolutionarily stable timing of sex change. Our overall aim here is to explain this result and determine the implications for other life-history variables. Specifically, we use a combination of approaches to formalize and make explicit previous analytical theory in this area, examine the robustness of the empirical invariance result, and carry out sensitivity analyses to determine what the empirical data imply about the mean value and variation in several key life-history variables.

Effects of body size and temperature on population growth.

For at least 200 years, since the time of Malthus, population growth has been recognized as providing a critical link between the performance of individual organisms and the ecology and evolution of species. We present a theory that shows how the intrinsic rate of exponential population growth, rmax, and the carrying capacity, K, depend on individual metabolic rate and resource supply rate. To do this, we construct equations for the metabolic rates of entire populations by summing over individuals, and then we combine these population-level equations with Malthusian growth. Thus, the theory makes explicit the relationship between rates of resource supply in the environment and rates of production of new biomass and individuals. These individual-level and population-level processes are inextricably linked because metabolism sets both the demand for environmental resources and the resource allocation to survival, growth, and reproduction. We use the theory to make explicit how and why rmax exhibits its characteristic dependence on body size and temperature. Data for aerobic eukaryotes, including algae, protists, insects, zooplankton, fishes, and mammals, support these predicted scalings for rmax. The metabolic flux of energy and materials also dictates that the carrying capacity or equilibrium density of populations should decrease with increasing body size and increasing temperature. Finally, we argue that body mass and body temperature, through their effects on metabolic rate, can explain most of the variation in fecundity and mortality rates. Data for marine fishes in the field support these predictions for instantaneous rates of mortality. This theory links the rates of metabolism and resource use of individuals to life-history attributes and population dynamics for a broad assortment of organisms, from unicellular organisms to mammals.

Similarity of mammalian body size across the taxonomic hierarchy and across space and time.

Although it is commonly assumed that closely related animals are similar in body size, the degree of similarity has not been examined across the taxonomic hierarchy. Moreover, little is known about the variation or consistency of body size patterns across geographic space or evolutionary time. Here, we draw from a data set of terrestrial, nonvolant mammals to quantify and compare patterns across the body size spectrum, the taxonomic hierarchy, continental space, and evolutionary time. We employ a variety of statistical techniques including "sib-sib" regression, phylogenetic autocorrelation, and nested ANOVA. We find an extremely high resemblance (heritability) of size among congeneric species for mammals over approximately 18 g; the result is consistent across the size spectrum. However, there is no significant relationship among the body sizes of congeneric species for mammals under approximately 18 g. We suspect that life-history and ecological parameters are so tightly constrained by allometry at diminutive size that animals can only adapt to novel ecological conditions by modifying body size. The overall distributions of size for each continental fauna and for the most diverse orders are quantitatively similar for North America, South America, and Africa, despite virtually no overlap in species composition. Differences in ordinal composition appear to account for quantitative differences between continents. For most mammalian orders, body size is highly conserved, although there is extensive overlap at all levels of the taxonomic hierarchy. The body size distribution for terrestrial mammals apparently was established early in the Tertiary, and it has remained remarkably constant over the past 50 Ma and across the major continents. Lineages have diversified in size to exploit environmental opportunities but only within limits set by allometric, ecological, and evolutionary constraints.

Sexual systems and life history of barnacles: a theoretical perspective.

Thoracican barnacles show one of the most diverse sexual systems in animals: hermaphroditism, dioecy (males and females), and androdioecy (males and hermaphrodites). In addition, when present, male barnacles are very small and are called "dwarf males". The diverse sexual systems and male dwarfism in this taxon have attracted both theoretical and empirical biologists. In this article, we review the theoretical studies on barnacles' sexual systems in the context of sex allocation and life history theories. We first introduce the sex allocation models by Charnov, especially in relation to the mating group size, and a new expansion of his models is also proposed. We then explain three studies by Yamaguchi et al., who have studied the interaction between sex allocation and life history in barnacles. These studies consistently showed that limited mating opportunity favors androdioecy and dioecy over hermaphroditism. In addition, other factors, such as rates of survival and availability of food, are also important. We discuss the importance of empirical studies testing these predictions and how empirical studies interact with theoretical constructs.

Comment on "The illusion of invariant quantities in life histories".

Nee et al. (Reports, 19 August 2005, p. 1236) used a null model to argue that life history invariants are illusions. We show that their results are largely inconsequential for life history theory because the authors confound two definitions of invariance, and rigorous analysis of their null model demonstrates that it does not match observed data.

Size and temperature in the evolution of fish life histories.

Body size and temperature are the two most important variables affecting nearly all biological rates and times, especially individual growth or production rates. By favoring an optimal maturation age and reproductive allocation, natural selection links individual growth to the mortality schedule. A recent model for evolution of life histories for species with indeterminate growth, which includes most fish, successfully predicts the numeric values of two key dimensionless numbers and the allometry of the average reproductive allocation versus maturation size across species. Here we use this new model to predict the relationships of age-at-maturity, adult mortality and reproductive effort to environmental temperature and maturation size across species. Age-at-maturity, adult mortality and the proportion of the body mass given to reproduction per year are predicted to show ±0.25 power allometries with mass at maturity, and an exponential (Boltzmann) temperature dependence. Temperature is assumed to affect only body size growth, so the temperature linkages of maturation, mortality and reproductive effort are indirect via life history optimization; this is briefly contrasted with the idea that (for example) temperature directly affects mortality.

Effects of size and temperature on developmental time.

Body size and temperature are the two most important variables affecting nearly all biological rates and times. The relationship of size and temperature to development is of particular interest, because during ontogeny size changes and temperature often varies. Here we derive a general model, based on first principles of allometry and biochemical kinetics, that predicts the time of ontogenetic development as a function of body mass and temperature. The model fits embryonic development times spanning a wide range of egg sizes and incubation temperatures for birds and aquatic ectotherms (fish, amphibians, aquatic insects and zooplankton). The model also describes nearly 75% of the variation in post-embryonic development among a diverse sample of zooplankton. The remaining variation is partially explained by stoichiometry, specifically the whole-body carbon to phosphorus ratio. Development in other animals at other life stages is also described by this model. These results suggest a general definition of biological time that is approximately invariant and common to all organisms.