The illusion of invariant quantities in life histories

The Relevance of Time in Biological Scaling

Various phenotypic traits relate to the size of a living system in regular but often disproportionate (allometric) ways. These "biological scaling" relationships have been studied by biologists for over a century, but their causes remain hotly debated. Here, I focus on the patterns and possible causes of the body-mass scaling of the rates/durations of various biological processes and life-history events, i.e., the "pace of life". Many biologists have regarded the rate of metabolism or energy use as the master driver of the "pace of life" and its scaling with body size. Although this "energy perspective" has provided valuable insight, here I argue that a "time perspective" may be equally or even more important. I evaluate various major ways that time may be relevant in biological scaling, including as (1) an independent "fourth dimension" in biological dimensional analyses, (2) a universal "biological clock" that synchronizes various biological rates/durations, (3) a scaling method that uses various biological time periods (allochrony) as scaling metrics, rather than various measures of physical size (allometry), as traditionally performed, (4) an ultimate body-size-related constraint on the rates/timing of biological processes/events that is set by the inevitability of death, and (5) a geological "deep time" approach for viewing the evolution of biological scaling patterns. Although previously proposed universal four-dimensional space-time and "biological clock" views of biological scaling are problematic, novel approaches using allochronic analyses and time perspectives based on size-related rates of individual mortality and species origination/extinction may provide new valuable insights.

A simple explanation for declining temperature sensitivity with warming

Recently, multiple studies have reported declining phenological sensitivities (∆ days per ℃) with higher temperatures. Such observations have been used to suggest climate change is reshaping biological processes, with major implications for forecasts of future change. Here, we show that these results may simply be the outcome of using linear models to estimate nonlinear temperature responses, specifically for events that occur after a cumulative thermal threshold is met-a common model for many biological events. Corrections for the nonlinearity of temperature responses consistently remove the apparent decline. Our results show that rising temperatures combined with linear estimates based on calendar time produce the observations of declining sensitivity-without any shift in the underlying biology. Current methods may thus undermine efforts to identify when and how warming will reshape biological processes.

Macroevolution of dimensionless life-history metrics in tetrapods

Life-history traits represent organisms' strategies to navigate the fitness trade-offs between survival and reproduction. Eric Charnov developed three dimensionless metrics to quantify fundamental life-history trade-offs. Lifetime reproductive effort (LRE), relative reproductive lifespan (RRL) and relative offspring size (ROS), together with body mass can be used to classify life-history strategies across the four major classes of tetrapods: amphibians, reptiles, mammals and birds. First, we investigate how the metrics have evolved in concert with body mass within tetrapod lineages. In most cases, we find evidence for correlated evolution among body mass and the three dimensionless metrics. Second, we compare life-history strategies across the four classes of tetrapods and find that LRE, RRL and ROS delineate a space in which the major tetrapod classes occupy mostly unique subspaces. These distinct combinations of life-history strategies provide us with a framework to understand the impact of major evolutionary transitions in energetics, physiology and ecology.

An identification of invariants in life history traits of amphibians and reptiles

While many morphological, physiological, and ecological characteristics of organisms scale with body size, some do not change under size transformation. They are called invariant. A recent study recommended five criteria for identifying invariant traits. These are based on that a trait exhibits a unimodal central tendency and varies over a limited range with body mass (type I), or that it does not vary systematically with body mass (type II). We methodologically improved these criteria and then applied them to life history traits of amphibians, Anura, Caudata (eleven traits), and reptiles (eight traits). The numbers of invariant traits identified by criteria differed across amphibian orders and between amphibians and reptiles. Reproductive output (maximum number of reproductive events per year), incubation time, length of larval period, and metamorphosis size were type I and II invariant across amphibians. In both amphibian orders, reproductive output and metamorphosis size were type I and II invariant. In Anura, incubation time and length of larval period and in Caudata, incubation time were further type II invariant. In reptiles, however, only number of clutches per year was invariant (type II). All these differences could reflect that in reptiles body size and in amphibians, Anura, and Caudata metamorphosis (neotenic species go not through it) and the trend toward independence of egg and larval development from water additionally constrained life history evolution. We further demonstrate that all invariance criteria worked for amphibian and reptilian life history traits, although we corroborated some known and identified new limitations to their application.

Density-dependent offspring interactions do not explain macroevolutionary scaling of adult size and offspring size

Most life forms exhibit a correlated evolution of adult size (AS) and size at independence (SI), giving rise to AS-SI scaling relationships. Theory suggests that scaling arises because relatively large adults have relatively high reproductive output, resulting in strong density-dependent competition in early life, where large size at independence provides a competitive advantage to juveniles. The primary goal of our study is to test this density hypothesis, using large datasets that span the vertebrate tree of life (fishes, amphibians, reptiles, birds, and mammals). Our secondary goal is to motivate new hypotheses for AS-SI scaling by exploring how subtle variation in life-histories among closely related species is associated with variation in scaling. Our phylogenetically informed comparisons do not support the density hypothesis. Instead, exploration of AS-SI scaling among life-history variants suggests that steeper AS-SI scaling slopes are associated with evolutionary increases in size at independence. We suggest that a positive association between size at independence and juvenile growth rate may represent an important mechanism underlying AS-SI scaling, a mechanism that has been underappreciated by theorists. If faster juvenile growth is a consequence of evolutionary increases in size at independence, this may help offset the cost of delayed maturation, leading to steeper AS-SI scaling slopes.

Adaptive significance of critical weight for metamorphosis in holometabolous insects

Holometabolous insect larvae become committed to metamorphosis when they reach a critical weight. Although the physiological mechanisms involved in this process have been well-studied, the adaptive significance of the critical weight remains unclear. Here, we developed a life history model for holometabolous insects and evaluated it from the viewpoint of optimal energy allocation. We found that, without a priori assumptions about critical weight, the optimal growth schedule is always biphasic: larval tissues grow predominately until they reach a certain threshold, after which the imaginal tissues begin rapid growth, suggesting that the emergence of a critical weight as a phase-transition point is a natural consequence of optimal growth scheduling. Our model predicts the optimal timing of critical-weight attainment, in agreement with observations in phylogenetically-distinct species. Furthermore, it also predicts the scaling of growth scheduling against environmental change, i.e., the relative value and timing of the critical weight should be constant, thus providing a general interpretation of observed phenotypic plasticity. This scaling relationship allows the classification of adaptive responses in critical weight into five possible types that reflect the ecological features of focal insects. In this manner, our theory and its consistency with experimental observations demonstrate the adaptive significance of critical weight.

Great cities look small

Great cities connect people; failed cities isolate people. Despite the fundamental importance of physical, face-to-face social ties in the functioning of cities, these connectivity networks are not explicitly observed in their entirety. Attempts at estimating them often rely on unrealistic over-simplifications such as the assumption of spatial homogeneity. Here we propose a mathematical model of human interactions in terms of a local strategy of maximizing the number of beneficial connections attainable under the constraint of limited individual travelling-time budgets. By incorporating census and openly available online multi-modal transport data, we are able to characterize the connectivity of geometrically and topologically complex cities. Beyond providing a candidate measure of greatness, this model allows one to quantify and assess the impact of transport developments, population growth, and other infrastructure and demographic changes on a city. Supported by validations of gross domestic product and human immunodeficiency virus infection rates across US metropolitan areas, we illustrate the effect of changes in local and city-wide connectivities by considering the economic impact of two contemporary inter- and intra-city transport developments in the UK: High Speed 2 and London Crossrail. This derivation of the model suggests that the scaling of different urban indicators with population size has an explicitly mechanistic origin.

How does biomass distribution change with size and differ among species? An analysis for 1200 plant species from five continents

We compiled a global database for leaf, stem and root biomass representing c. 11 000 records for c. 1200 herbaceous and woody species grown under either controlled or field conditions. We used this data set to analyse allometric relationships and fractional biomass distribution to leaves, stems and roots. We tested whether allometric scaling exponents are generally constant across plant sizes as predicted by metabolic scaling theory, or whether instead they change dynamically with plant size. We also quantified interspecific variation in biomass distribution among plant families and functional groups. Across all species combined, leaf vs stem and leaf vs root scaling exponents decreased from c. 1.00 for small plants to c. 0.60 for the largest trees considered. Evergreens had substantially higher leaf mass fractions (LMFs) than deciduous species, whereas graminoids maintained higher root mass fractions (RMFs) than eudicotyledonous herbs. These patterns do not support the hypothesis of fixed allometric exponents. Rather, continuous shifts in allometric exponents with plant size during ontogeny and evolution are the norm. Across seed plants, variation in biomass distribution among species is related more to function than phylogeny. We propose that the higher LMF of evergreens at least partly compensates for their relatively low leaf area : leaf mass ratio.

The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes

Ecosystems exhibit surprising regularities in structure and function across terrestrial and aquatic biomes worldwide. We assembled a global data set for 2260 communities of large mammals, invertebrates, plants, and plankton. We find that predator and prey biomass follow a general scaling law with exponents consistently near ¾. This pervasive pattern implies that the structure of the biomass pyramid becomes increasingly bottom-heavy at higher biomass. Similar exponents are obtained for community production-biomass relations, suggesting conserved links between ecosystem structure and function. These exponents are similar to many body mass allometries, and yet ecosystem scaling emerges independently from individual-level scaling, which is not fully understood. These patterns suggest a greater degree of ecosystem-level organization than previously recognized and a more predictive approach to ecological theory.

Applying Quantitative Genetic Methods to Primate Social Behavior

Increasingly, behavioral ecologists have applied quantitative genetic methods to investigate the evolution of behaviors in wild animal populations. The promise of quantitative genetics in unmanaged populations opens the door for simultaneous analysis of inheritance, phenotypic plasticity, and patterns of selection on behavioral phenotypes all within the same study. In this article, we describe how quantitative genetic techniques provide studies of the evolution of behavior with information that is unique and valuable. We outline technical obstacles for applying quantitative genetic techniques that are of particular relevance to studies of behavior in primates, especially those living in noncaptive populations, e.g., the need for pedigree information, non-Gaussian phenotypes, and demonstrate how many of these barriers are now surmountable. We illustrate this by applying recent quantitative genetic methods to spatial proximity data, a simple and widely collected primate social behavior, from adult rhesus macaques on Cayo Santiago. Our analysis shows that proximity measures are consistent across repeated measurements on individuals (repeatable) and that kin have similar mean measurements (heritable). Quantitative genetics may hold lessons of considerable importance for studies of primate behavior, even those without a specific genetic focus.

The marginal valuation of fertility

Substantial theoretical and empirical evidence demonstrates that fertility entails economic, physiological, and demographic trade-offs. The existence of trade-offs suggests that fitness should be maximized by an intermediate level of fertility, but this hypothesis has not had much support in the human life-history literature. We suggest that the difficulty of finding intermediate optima may be a function of the way fitness is calculated. Evolutionary analyses of human behavior typically use lifetime reproductive success as their fitness criterion. This fitness measure implicitly assumes that women are indifferent to the timing of reproduction and that they are risk-neutral in their reproductive decision-making. In this paper, we offer an alternative, easily-calculated fitness measure that accounts for differences in reproductive timing and yields clear preferences in the face of risky reproductive decision-making. Using historical demographic data from a genealogically-detailed dataset from 19th century Utah, we show that this measure is highly concave with respect to reproductive effort. This result has three major implications: (1) if births are properly timed, a lower-fertility reproductive strategy can have the same fitness as a high-fertility strategy, (2) intermediate optima are far more likely using fitness measures that are strongly concave with respect to effort, (3) we expect mothers to have strong investment preferences with respect to the risk inherent in reproduction.

Simple life-history traits explain key effective population size ratios across diverse taxa

Effective population size (Ne) controls both the rate of random genetic drift and the effectiveness of selection and migration, but it is difficult to estimate in nature. In particular, for species with overlapping generations, it is easier to estimate the effective number of breeders in one reproductive cycle (Nb) than Ne per generation. We empirically evaluated the relationship between life history and ratios of Ne, Nb and adult census size (N) using a recently developed model (agene) and published vital rates for 63 iteroparous animals and plants. Nb/Ne varied a surprising sixfold across species and, contrary to expectations, Nb was larger than Ne in over half the species. Up to two-thirds of the variance in Nb/Ne and up to half the variance in Ne/N was explained by just two life-history traits (age at maturity and adult lifespan) that have long interested both ecologists and evolutionary biologists. These results provide novel insights into, and demonstrate a close general linkage between, demographic and evolutionary processes across diverse taxa. For the first time, our results also make it possible to interpret rapidly accumulating estimates of Nb in the context of the rich body of evolutionary theory based on Ne per generation.

How do leaf veins influence the worldwide leaf economic spectrum? Review and synthesis

Leaf vein traits are implicated in the determination of gas exchange rates and plant performance. These traits are increasingly considered as causal factors affecting the 'leaf economic spectrum' (LES), which includes the light-saturated rate of photosynthesis, dark respiration, foliar nitrogen concentration, leaf dry mass per area (LMA) and leaf longevity. This article reviews the support for two contrasting hypotheses regarding a key vein trait, vein length per unit leaf area (VLA). Recently, Blonder et al. (2011, 2013) proposed that vein traits, including VLA, can be described as the 'origin' of the LES by structurally determining LMA and leaf thickness, and thereby vein traits would predict LES traits according to specific equations. Careful re-examination of leaf anatomy, published datasets, and a newly compiled global database for diverse species did not support the 'vein origin' hypothesis, and moreover showed that the apparent power of those equations to predict LES traits arose from circularity. This review provides a 'flux trait network' hypothesis for the effects of vein traits on the LES and on plant performance, based on a synthesis of the previous literature. According to this hypothesis, VLA, while virtually independent of LMA, strongly influences hydraulic conductance, and thus stomatal conductance and photosynthetic rate. We also review (i) the specific physiological roles of VLA; (ii) the role of leaf major veins in influencing LES traits; and (iii) the role of VLA in determining photosynthetic rate per leaf dry mass and plant relative growth rate. A clear understanding of leaf vein traits provides a new perspective on plant function independently of the LES and can enhance the ability to explain and predict whole plant performance under dynamic conditions, with applications towards breeding improved crop varieties.

Long-term climate forcing in loggerhead sea turtle nesting

The long-term variability of marine turtle populations remains poorly understood, limiting science and management. Here we use basin-scale climate indices and regional surface temperatures to estimate loggerhead sea turtle (Caretta caretta) nesting at a variety of spatial and temporal scales. Borrowing from fisheries research, our models investigate how oceanographic processes influence juvenile recruitment and regulate population dynamics. This novel approach finds local populations in the North Pacific and Northwest Atlantic are regionally synchronized and strongly correlated to ocean conditions--such that climate models alone explain up to 88% of the observed changes over the past several decades. In addition to its performance, climate-based modeling also provides mechanistic forecasts of historical and future population changes. Hindcasts in both regions indicate climatic conditions may have been a factor in recent declines, but future forecasts are mixed. Available climatic data suggests the Pacific population will be significantly reduced by 2040, but indicates the Atlantic population may increase substantially. These results do not exonerate anthropogenic impacts, but highlight the significance of bottom-up oceanographic processes to marine organisms. Future studies should consider environmental baselines in assessments of marine turtle population variability and persistence.

Maternal investment, life histories, and the costs of brain growth in mammals

Brain size variation in mammals correlates with life histories: larger-brained species have longer gestations, mature later, and have increased lifespans. These patterns have been explained in terms of developmental costs (larger brains take longer to grow) and cognitive benefits (large brains enhance survival and increase lifespan). In support of the developmental cost hypothesis, we show that evolutionary changes in pre- and postnatal brain growth correlate specifically with duration of the relevant phases of maternal investment (gestation and lactation, respectively). We also find support for the hypothesis that the rate of fetal brain growth is related to the energy turnover of the mother. In contrast, we find no support for hypotheses proposing that costs are accommodated through direct tradeoffs between brain and body growth, or between brain growth and litter size. When the duration of maternal investment is taken into account, adult brain size is uncorrelated with other life history traits such as lifespan. Hence, the general pattern of slower life histories in large-brained species appears to be a direct consequence of developmental costs.

Age at the onset of senescence in birds and mammals is predicted by early-life performance

Life-history theory predicts that traits involved in maturity, reproduction and survival correlate along a fast-slow continuum of life histories. Evolutionary theories and empirical results indicate that senescence-related traits vary along this continuum, with slow species senescing later and at a slower pace than fast species. Because senescence patterns are typically difficult to estimate from studies in the wild, here we propose to predict the associated trait values in the frame of life-history theory. From a comparative analysis based on 81 free-ranging populations of 72 species of birds and mammals, we find that a nonlinear combination of fecundity, age at first reproduction and survival over the immature stage can account for ca two-thirds of the variance in the age at the onset of actuarial senescence. Our life-history model performs better than a model predicting the onset based on generation time, and it only includes life-history traits during early life as explanatory variables, i.e. parameters that are both theoretically expected to shape senescence and are measurable within relatively short studies. We discuss the good-fit of our life-history model to the available data in the light of current evolutionary theories of senescence. We further use it to evaluate whether studies that provided no evidence for senescence lasted long enough to include the onset of senescence.

The seven deadly sins of comparative analysis

Phylogenetic comparative methods are extremely commonly used in evolutionary biology. In this paper, I highlight some of the problems that are frequently encountered in comparative analyses and review how they can be fixed. In broad terms, the problems boil down to a lack of appreciation of the underlying assumptions of comparative methods, as well as problems with implementing methods in a manner akin to more familiar statistical approaches. I highlight that the advent of more flexible computing environments should improve matters and allow researchers greater scope to explore methods and data.

Distilling free-form natural laws from experimental data

For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We propose a principle for the identification of nontriviality. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the "alphabet" used to describe those systems.

Distilling Free-Form Natural Laws from Experimental Data

For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We propose a principle for the identification of nontriviality. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the “alphabet” used to describe those systems.

Evaluation of offspring size-number invariants in 12 species of lizard

The optimal division of resources into offspring size vs. number is one of the classic problems in life-history evolution. Importantly, models that take into account the discrete nature of resource division at low clutch sizes suggest that the variance in offspring size should decline with increasing clutch size according to an invariant relationship. We tested this prediction in 12 species of lizard with small clutch sizes. Contrary to expectations, not all species showed a negative relationship between variance in offspring size and clutch size, and the pattern significantly deviated from quantitative predictions in five of the 12 species. We suggest that the main limitation of current size-number models for small clutch sizes is that they rely on assumptions of hierarchical allocation strategies with independence between allocation decisions. Indeed, selection may favour alternative mechanisms of reproductive allocation that avoid suboptimal allocation imposed by the indivisible fraction at low clutch sizes.

Life history costs and benefits of encephalization: a comparative test using data from long-term studies of primates in the wild

The correlation between brain size and life history has been investigated in many previous studies, and several viable explanations have been proposed. However, the results of these studies are often at odds, causing uncertainties about whether these two character complexes underwent correlated evolution. These disparities could arise from the mixture of wild and captive values in the datasets, potentially obscuring real relationships, and from differences in the methods of controlling for phylogenetic non independence of species values. This paper seeks to resolve these difficulties by (1) proposing an overarching hypothesis that encompasses many of the previously proposed hypotheses, and (2) testing the predictions of this hypothesis using rigorously compiled data and utilizing multiple methods of analysis. We hypothesize that the adaptive benefit of increased encephalization is an increase in reproductive lifespan or efficiency, which must be sufficient to outweigh the costs due to growing and maturing the larger brain. These costs and benefits are directly reflected in the length of life history stages. We tested this hypothesis on a wide range of primate species. Our results demonstrate that encephalization is significantly correlated with prolongation of all stages of developmental life history except the lactational period, and is significantly correlated with an extension of the reproductive lifespan. These results support the contention that the link between brain size and life history is caused by a balance between the costs of growing a brain and the survival benefits the brain provides. Thus, our results suggest that the evolution of prolonged life history during human evolution is caused by increased encephalization.

The allometry of host-pathogen interactions

Background

Understanding the mechanisms that control rates of disease progression in humans and other species is an important area of research relevant to epidemiology and to translating studies in small laboratory animals to humans. Body size and metabolic rate influence a great number of biological rates and times. We hypothesize that body size and metabolic rate affect rates of pathogenesis, specifically the times between infection and first symptoms or death.

Methods and Principal Findings

We conducted a literature search to find estimates of the time from infection to first symptoms (t_S) and to death (t_D) for five pathogens infecting a variety of bird and mammal hosts. A broad sampling of diseases (1 bacterial, 1 prion, 3 viruses) indicates that pathogenesis is controlled by the scaling of host metabolism. We find that the time for symptoms to appear is a constant fraction of time to death in all but one disease. Our findings also predict that many population-level attributes of disease dynamics are likely to be expressed as dimensionless quantities that are independent of host body size.

Conclusions and Significance

Our results show that much variability in host pathogenesis can be described by simple power functions consistent with the scaling of host metabolic rate. Assessing how disease progression is controlled by geometric relationships will be important for future research. To our knowledge this is the first study to report the allometric scaling of host/pathogen interactions.

Growth?size scaling relationships of woody plant species differ from predictions of the Metabolic Ecology Model

The Metabolic Ecology Model predicts that tree diameter (D) growth (dD/dt) scales with D(1/3). Using data on diameter growth and height-diameter relationships for 56 and 40 woody species, respectively, from forests throughout New Zealand, we tested one prediction and two assumptions of this model: (i) the exponent of the growth-diameter scaling relationship equals 1/3 and is invariant among species and growth forms, (ii) small and large individuals are invariant in their exponents and (iii) tree height scales with D(2/3). We found virtually no support for any prediction or assumption: growth-diameter scaling exponents varied substantially among species and growth forms, correlated positively with species' maximum height, and shifted significantly with increasing individual size. Tree height did not scale invariantly with diameter. Based on a quantitative test, violation of these assumptions alone could not explain the model's poor fit to our data, possibly reflecting multiple, unsound assumptions, as well as unaccounted-for variation that should be incorporated.

Life history theory and dental development in four species of catarrhine primates

Dental development was reconstructed in several individuals representing four species of catarrhine primates--Symphalangus syndactylus, Hylobates lar, Semnopithecus entellus priam, and Papio hamadryas--using the techniques of dental histology. Bar charts assumed to represent species-typical dental development were constructed from these data and estimated ages at first and third molar emergence were plotted on them along with ages at weaning, menarche, and first reproduction from the literature. The estimated age at first molar emergence appears to occur at weaning in the siamang, lar gibbon, and langur, and just after weaning in the baboon. Age at menarche and first reproduction occur earlier relative to dental development in both cercopithecoids than in the hylobatids, suggesting that early reproduction may be a derived trait in cercopithecoids. The results are examined in the context of life history theory.

The fast-slow continuum in mammalian life history: an empirical reevaluation

Many life-history traits co-vary across species, even when body size differences are controlled for. This phenomenon has led to the concept of a "fast-slow continuum," which has been influential in both empirical and theoretical studies of life-history evolution. We present a comparative analysis of mammalian life histories showing that, for mammals at least, there is not a single fast-slow continuum. Rather, both across and within mammalian clades, the speed of life varies along at least two largely independent axes when body size effects are removed. One axis reflects how species balance offspring size against offspring number, while the other describes the timing of reproductive bouts.

The causes and consequences of variation in offspring size: a case study using Daphnia

Offspring size can have large and direct fitness implications, but we still do not have a complete understanding of what causes offspring size to vary. Daphnia (water fleas) generally produce fewer and larger offspring when food is limited. Here, we use a mathematical model to show that this could be explained by either: (1) an advantage of producing larger eggs when food is limited; or (2) a lower boundary on egg volume (below which eggs do not have sufficient resources to be viable), that is similar in volume to the evolutionarily stable egg volume predicted by standard clutch size models. We tested the first possibilities experimentally by placing offspring from mothers kept at two food treatments (high and low - leading to relatively small and large eggs respectively) into two food treatments (same as maternal treatments, in a fully factorial design) and measuring their fitness (reproduction, age at maturity, and size at maturity). We also tested survival under starvation conditions of offspring produced from mothers at low and high food treatments. We found that (larger) offspring produced by low-food mothers actually had lower fitness as they took longer to reproduce, regardless of their current food treatment. Additionally, we found no survival advantage to being born of a food-stressed mother. Consequently, our results do not support the hypothesis that there is an advantage to producing larger eggs when food is limited. In contrast, data from the literature support the importance of a lower boundary on egg size.

Cerebral vasodilatation to exogenous NO is a measure of fitness for life at altitude

BACKGROUND AND PURPOSE

Andean highlanders, unlike Ethiopians, develop chronic mountain sickness (CMS), a maladaptation to their native land. Ambient hypoxia induces NO-mediated vasodilatation. Fitness for life at altitude might be revealed by cerebrovascular responses to NO.

METHODS

Nine altitude-native men were examined at 3622 and 794 m in Ethiopia and compared with 9 altitude-native Andean men tested at 4338 and 150 m in Peru. We assessed CMS scores, hematocrits, end-tidal pressure of carbon dioxide (P(ET)co2), oxygen saturations, and cerebral blood flow velocity (CBV). We evaluated fitness for life at altitude from the cerebrovascular response to an exogenous NO donor.

RESULTS

At high altitude, CMS scores and hematocrits were higher in Andeans, and they had lower oxygen saturations. Ethiopians had higher P(ET)co2 at all study sites. At low altitude, saturations were similar in both groups. Responsiveness of the cerebral circulation to NO was minimal in Ethiopians at low altitude, whereas Andeans had a large response. In contrast, at high altitude, Ethiopians showed large responses, and Peruvians had minimal responses.

CONCLUSIONS

By our measure, high altitude-native Peruvians were well-adapted lowlanders, whereas Ethiopian highlanders were well adapted to altitude life. Environmental pressures were sufficient for human adaptation to chronic hypoxia in Africa but not South America. The mechanisms underlying these differences are unknown, although studies of neurovascular diseases suggest that this may be related to a NO receptor polymorphism.

Comment on "On the regulation of populations of mammals, birds, fish, and insects" III

Stochasticity in time series explains concave responses of per capita growth rate to population size. The gradients with the natural log of population size have more biological importance because they measure strength of density compensation. Its weakening with increasing body size across taxa (Sibly et al., Reports, 22 July 2005, p. 607) is consistent with slower responses in ascent than descent toward carrying capacity. Time series therefore suggest that populations of large-bodied animals underfill their environments.