Estimating physiological tolerances - a comparison of traditional approaches to nonlinear regression techniques

Per capita sperm metabolism is density dependent

From bacteria to metazoans, higher density populations have lower per capita metabolic rates than lower density populations. The negative covariance between population density and metabolic rate is thought to represent a form of adaptive metabolic plasticity. A relationship between density and metabolism was actually first noted 100 years ago, and was focused on spermatozoa; even then, it was postulated that adaptive plasticity drove this pattern. Since then, contemporary studies of sperm metabolism specifically assume that sperm concentration has no effect on metabolism and that sperm metabolic rates show no adaptive plasticity. We did a systematic review to estimate the relationship between sperm aerobic metabolism and sperm concentration, for 198 estimates spanning 49 species, from protostomes to humans from 88 studies. We found strong evidence that per capita metabolic rates are concentration dependent: both within and among species, sperm have lower metabolisms in dense ejaculates, but increase their metabolism when diluted. On average, a 10-fold decrease in sperm concentration increased per capita metabolic rate by 35%. Metabolic plasticity in sperm appears to be an adaptive response, whereby sperm maximize their chances of encountering eggs.

Interactive effects of food deprivation state and hypoxia on the respiratory responses of postprandial rock crabs, Cancer irroratus

Under the background of climate change, increasing attention has focused on the effects of ocean deoxygenation on marine organisms. However, few studies address the effects of different food deprivation states on hypoxia tolerance. We therefore investigated the metabolic responses of the Atlantic rock crab, Cancer irroratus (starved 28-35 days, fasted 3-5 days and recently fed). Starved-crab exhibited the lowest critical oxygen saturation (S_crit)_, while fed-crab had the highest S_crit. The fed-crab maintained an elevated postprandial oxygen consumption (MO₂) even below the S_crit of fasted-crab indicating reserved aerobic scopes for critical activities in severe hypoxia. Following feeding, hypoxia (50% and 20% oxygen saturation, S_O2) retarded the specific dynamic action resulting in lower peak MO₂ and longer duration. The starved-crab exhibited a lower peak MO₂, prolonged duration and higher energy expenditure than fasted-crab after feeding. The decline in arterial P_O2 was most pronounced below the S_crit for both fasted- and starved-crab. The higher hemocyanin concentration ([Hc]) of fasted-crab (than starved-crab) suggested they had improved oxygen transport capacity, but hypoxia did not increase [Hc] during the 72-h experiment. Following feeding, the fasted-crab significantly increased L-lactate concentration ([L-lactate]) in 20% S_O2, which was not observed in starved-crab. These results suggest starvation may trigger a cross-tolerance to hypoxia. Because crabs can undergo long periods of food deprivation in their natural environment, future studies should consider how this may affect their ability to deal with environmental perturbations.

Biological scaling analyses are more than statistical line fitting

The magnitude of many biological traits relates strongly and regularly to body size. Consequently, a major goal of comparative biology is to understand and apply these 'size-scaling' relationships, traditionally quantified by using linear regression analyses based on log-transformed data. However, recently some investigators have questioned this traditional method, arguing that linear or non-linear regression based on untransformed arithmetic data may provide better statistical fits than log-linear analyses. Furthermore, they advocate the replacement of the traditional method by alternative specific methods on a case-by-case basis, based simply on best-fit criteria. Here, I argue that the use of logarithms in scaling analyses presents multiple valuable advantages, both statistical and conceptual. Most importantly, log-transformation allows biologically meaningful, properly scaled (scale-independent) comparisons of organisms of different size, whereas non-scaled (scale-dependent) analyses based on untransformed arithmetic data do not. Additionally, log-based analyses can readily reveal biologically and theoretically relevant discontinuities in scale invariance during developmental or evolutionary increases in body size that are not shown by linear or non-linear arithmetic analyses. In this way, log-transformation advances our understanding of biological scaling conceptually, not just statistically. I hope that my Commentary helps students, non-specialists and other interested readers to understand the general benefits of using log-transformed data in size-scaling analyses, and stimulates advocates of arithmetic analyses to show how they may improve our understanding of scaling conceptually, not just statistically.

Oxygen supply capacity breathes new life into critical oxygen partial pressure (Pcrit)

The critical oxygen partial pressure (Pcrit), typically defined as the PO2 below which an animal's metabolic rate (MR) is unsustainable, is widely interpreted as a measure of hypoxia tolerance. Here, Pcrit is defined as the PO2 at which physiological oxygen supply (α0) reaches its maximum capacity (α; µmol O2 g-1 h-1 kPa-1). α is a species- and temperature-specific constant describing the oxygen dependency of the maximum metabolic rate (MMR=PO2×α) or, equivalently, the MR dependence of Pcrit (Pcrit=MR/α). We describe the α-method, in which the MR is monitored as oxygen declines and, for each measurement period, is divided by the corresponding PO2 to provide the concurrent oxygen supply (α0=MR/PO2). The highest α0 value (or, more conservatively, the mean of the three highest values) is designated as α. The same value of α is reached at Pcrit for any MR regardless of previous or subsequent metabolic activity. The MR need not be constant (regulated), standardized or exhibit a clear breakpoint at Pcrit for accurate determination of α. The α-method has several advantages over Pcrit determination and non-linear analyses, including: (1) less ambiguity and greater accuracy, (2) fewer constraints in respirometry methodology and analysis, and (3) greater predictive power and ecological and physiological insight. Across the species evaluated here, α values are correlated with MR, but not Pcrit. Rather than an index of hypoxia tolerance, Pcrit is a reflection of α, which evolves to support maximum energy demands and aerobic scope at the prevailing temperature and oxygen level.

Thermal reaction norms of key metabolic enzymes reflect divergent physiological and behavioral adaptations of closely related amphipod species

Lake Baikal is inhabited by more than 300 endemic amphipod species, which are narrowly adapted to certain thermal niches due to the high interspecific competition. In contrast, the surrounding freshwater fauna is commonly represented by species with large-scale distribution and high phenotypic thermal plasticity. Here, we investigated the thermal plasticity of the energy metabolism in two closely-related endemic amphipod species from Lake Baikal (Eulimnogammarus verrucosus; stenothermal and Eulimnogammarus cyaneus; eurythermal) and the ubiquitous Holarctic amphipod Gammarus lacustris (eurythermal) by exposure to a summer warming scenario (6-23.6 °C; 0.8 °C d^-1). In concert with routine metabolic rates, activities of key metabolic enzymes increased strongly with temperature up to 15 °C in E. verrucosus, whereupon they leveled off (except for lactate dehydrogenase). In contrast, exponential increases were seen in E. cyaneus and G. lacustris throughout the thermal trial (Q₁₀-values: 1.6-3.7). Cytochrome-c-oxidase, lactate dehydrogenase, and 3-hydroxyacyl-CoA dehydrogenase activities were found to be higher in G. lacustris than in E. cyaneus, especially at the highest experimental temperature (23.6 °C). Decreasing gene expression levels revealed some thermal compensation in E. cyaneus but not in G. lacustris. In all species, shifts in enzyme activities favored glycolytic energy generation in the warmth. The congruent temperature-dependencies of enzyme activities and routine metabolism in E. verrucosus indicate a strong feedback-regulation of enzymatic activities by whole organism responses. The species-specific thermal reaction norms reflect the different ecological niches, including the spatial distribution, distinct thermal behavior such as temperature-dependent migration, movement activity, and mating season.

Are acute and acclimated thermal effects on metabolic rate modulated by cell size? A comparison between diploid and triploid zebrafish larvae

Being composed of small cells may carry energetic costs related to maintaining ionic gradients across cell membranes as well as benefits related to diffusive oxygen uptake. Here, we test the hypothesis that these costs and benefits of cell size in ectotherms are temperature dependent. To study the consequences of cell size for whole-organism metabolic rate, we compared diploid and triploid zebrafish larvae differing in cell size. A fully factorial design was applied combining three different rearing and test temperatures that allowed us to distinguish acute from acclimated thermal effects. Individual oxygen consumption rates of diploid and triploid larvae across declining levels of oxygen availability were measured. We found that both acute and acclimated thermal effects affected the metabolic response. In comparison with triploids, diploids responded more strongly to acute temperatures, especially when reared at the highest temperature. These observations support the hypothesis that animals composed of smaller cells (i.e. diploids) are less vulnerable to oxygen limitation in warm aquatic habitats. Furthermore, we found slightly improved hypoxia tolerance in diploids. By contrast, warm-reared triploids had higher metabolic rates when they were tested at acute cold temperature, suggesting that being composed of larger cells may provide metabolic advantages in the cold. We offer two mechanisms as a potential explanation of this result, related to homeoviscous adaptation of membrane function and the mitigation of developmental noise. Our results suggest that being composed of larger cells provides metabolic advantages in cold water, while being composed of smaller cells provides metabolic advantages in warm water.

The utility and determination of P crit in fishes

The critical O₂ tension (P _crit) is the lowest P _O2  at which an animal can maintain some benchmark rate of O₂ uptake (Ṁ _O2 ). This P _O2  has long served as a comparator of hypoxia tolerance in fishes and aquatic invertebrates, but its usefulness in this role, particularly when applied to fishes, has recently been questioned. We believe that P _crit remains a useful comparator of hypoxia tolerance provided it is determined using the proper methods and hypoxia tolerance is clearly defined. Here, we review the available methods for each of the three steps of P _crit determination: (1) measuring the most appropriate benchmark Ṁ _O2  state for P _crit determination (Ṁ _O2,std, the Ṁ _O2  required to support standard metabolic rate); (2) reducing water P _O2 ; and (3) calculating P _crit from the Ṁ _O2  versus P _O2  curve. We make suggestions on best practices for each step and for how to report P _crit results to maximize their comparative value. We also discuss the concept of hypoxia tolerance and how P _crit relates to a fish's overall hypoxia tolerance. When appropriate methods are used, P _crit provides useful comparative physiological and ecological information about the aerobic contributions to a fish's hypoxic survival. When paired with other hypoxia-related physiological measurements (e.g. lactate accumulation, calorimetry-based measurements of metabolic depression, loss-of-equilibrium experiments), P _crit contributes to a comprehensive understanding of how a fish combines aerobic metabolism, anaerobic metabolism and metabolic depression in an overall strategy for hypoxia tolerance.

The osmorespiratory compromise: physiological responses and tolerance to hypoxia are affected by salinity acclimation in the euryhaline Atlantic killifish (Fundulus heteroclitus)

The characteristics of the fish gill that maximize gas exchange are the same that promote diffusion of ions and water to and from the environment; therefore, physiological trade-offs are likely to occur. Here, we investigated how salinity acclimation affects whole-animal respiratory gas exchange during hypoxia using Fundulus heteroclitus, a fish that inhabits salt marshes where salinity and oxygen levels vary greatly. Salinity had marked effects on hypoxia tolerance, with fish acclimated to 11 and 35 ppt showing much longer time to loss of equilibrium (LOE) in hypoxia than 0 ppt-acclimated fish. Fish acclimated to 11 ppt (isosmotic salinity) exhibited the greatest capacity to regulate oxygen consumption rate (Ṁ _O2 ) under hypoxia, as measured through the regulation index (RI) and P _crit At 35 ppt, fish had a higher routine metabolic rate (RMR) but a lower RI than fish at 11 ppt, but there were no differences in gill morphology, ventilation or blood O₂ transport properties between these groups. In contrast, 0 ppt-acclimated fish had the highest ventilation and lowest O₂ extraction efficiency in normoxia and hypoxia, indicating a higher ventilatory workload in order to maintain similar levels of Ṁ _O2 These differences were related to alterations in gill morphology, where 0 ppt-acclimated fish had the smallest lamellar surface area with the greatest epithelial cell coverage (i.e. thicker lamellae, longer diffusion distance) and a larger interlamellar cell mass, contrasting with 11 ppt-acclimated fish, which had overall the highest respiratory surface area. The alteration of an array of physiological parameters provides evidence for a compromise between salinity and hypoxia tolerance in killifish acclimated to freshwater.

Standardizing the determination and interpretation of P crit in fishes

The critical oxygen tension (P _crit) for fishes is the oxygen level below which the rate of oxygen consumption (Ṁ _O2 ) becomes dependent upon ambient oxygen partial pressure (P _O2 ). We compare multiple curve-fitting approaches to estimate P _crit of the Gulf killifish, Fundulus grandis, during closed and intermittent-flow respirometry. Fitting two line segments of Ṁ _O2  versus P _O2  produced high and variable estimates of P _crit, as did nonlinear regression using a hyperbolic (Michaelis-Menten) function. Using nonlinear regression fit to an exponential (modified Weibull) function, or linear regression of Ṁ _O2 versus P _O2  at low P _O2 , and determining P _crit as the P _O2  when Ṁ _O2 equals standard metabolic rate (SMR) yielded values that were consistent across fish and among experimental trials. The magnitude of the difference in P _crit determined by alternative calculation methods exceeded the differences determined in closed and intermittent-flow respirometry, highlighting the need to standardize analytical as well as experimental approaches in determining P _crit.

Will giant polar amphipods be first to fare badly in an oxygen-poor ocean? Testing hypotheses linking oxygen to body size

It has been suggested that giant Antarctic marine invertebrates will be particularly vulnerable to declining O₂ levels as our ocean warms in line with current climate change predictions. Our study provides some support for this oxygen limitation hypothesis, with larger body sizes being generally more sensitive to O₂ reductions than smaller body sizes. However, it also suggests that the overall picture is a little more complex. We tested predictions from three different, but overlapping, O₂-related hypotheses accounting for gigantism, using four Antarctic amphipod species encompassing a wide range of body sizes. We found a significant effect of body size, but also of species, in their respiratory responses to acutely declining O₂ tensions. The more active lifestyle of intermediate-sized Prostebbingia brevicornis was supported by a better respiratory performance than predicted by the oxygen limitation hypothesis alone, but consistent with the symmorphosis hypothesis. We suggest that giant polar amphipods are likely to be some of the first to fare badly in an O₂-poor ocean. However, the products of past evolutionary innovation, such as respiratory pigments that enhance O₂-transport and novel gas exchange structures, may in some species offset any respiratory disadvantages of either large or small body size. This article is part of the theme issue 'Physiological diversity, biodiversity patterns and global climate change: testing key hypotheses involving temperature and oxygen'.

Phenotypic flexibility in respiratory traits is associated with improved aerial respiration in an amphibious fish out of water

Amphibious fishes have evolved multiple adaptive strategies for respiring out of water, but there has been less focus on reversible plasticity. We tested the hypothesis that when amphibious fishes leave water, enhanced respiratory performance on land is the result of rapid functional phenotypic flexibility of respiratory traits. We acclimated four isogenic strains of Kryptolebias marmoratus to air for 0, 1, 3 or 7 days. We compared respiratory performance out of water with traits linked to the O₂ cascade. Aerial O₂ consumption rate was measured over a step-wise decrease in O₂ levels. There were significant differences between strains, but time out of water had the largest impact on measured parameters. K ryptolebias marmoratus had improved respiratory performance [lower aerial critical oxygen tension (P _crit), higher regulation index (RI)] after only 1 day of air exposure, and these changes were strongly associated with the change in hematocrit and dorsal cutaneous angiogenesis. Additionally, we found that 1 h of air exposure induced the expression of four angiogenesis-associated genes - vegfa, angpt2, pecam-1 and efna1 - in the skin. After 7 days in air, respiratory traits were not significantly linked to the variation in either aerial P _crit or RI. Overall, our data indicate that there are two phases involved in the enhancement of aerial respiration: an initial rapid response (1 day) and a delayed response (7 days). We found evidence for the hypothesis that respiratory performance on land in amphibious fishes is the result of rapid flexibility in both O₂ uptake and O₂ carrying capacity.

Assessment of oxygen consumption in response to progressive hypoxia

A new method is presented for describing the rate of oxygen consumption in response to progressive hypoxia. The method consists of screening candidate functions describing the relationship between Vo₂ (oxygen consumption rate) and Po₂ (ambient oxygen concentration) by testing each for fit to observed data for a single curve and the function that best fits is chosen using lowest AICc value as the criterion. Descriptive statistics are then extracted from the selected function that best describes the pattern present in the curve. Several new descriptive statistics for the pattern of response are proposed which are based on the null model of simple diffusion and no regulation. The method quantifies deviation from the null model at each point on the curve and measures both positive and negative deviation which occur when the curve changes more slowly or more rapidly than the null model predicts, respectively. The new descriptive statistics generalize the traditional one used in the past, the critical oxygen tension (P_c), and allow interpretation of a variety of shapes of curves which cannot be analyzed with conventional methods. Because the method is descriptive, it does not implicate any specific mechanisms in generating the response. The method is applied to data from 68 animals in 14 different species groups reported in the literature. The overall results suggest the existence of substantial diversity in response types among animals, which requires a more complex description than has traditionally been used.

The fallacy of the P crit - are there more useful alternatives?

P _crit - generally defined as the P _O2  below which the animal can no longer maintain a stable rate of O₂ consumption (Ṁ _O2 ), such that Ṁ _O2  becomes dependent upon P _O2  - provides a single number into which a vast amount of experimental effort has been invested. Here, with specific reference to water-breathers, I argue that this focus on the P _crit is not useful for six reasons: (1) calculation of P _crit usually involves selective data editing; (2) the value of P _crit depends greatly on the way it is determined; (3) there is no good theoretical justification for the concept; (4) P _crit is not the transition point from aerobic to anaerobic metabolism, and it disguises what is really going on; (5) P _crit is not a reliable index of hypoxia tolerance; and (6) P _crit carries minimal information content. Preferable alternatives are loss of equilibrium (LOE) tests for hypoxia tolerance, and experimental description of full Ṁ _O2  versus P _O2  profiles accompanied by measurements of ventilation, lactate appearance and metabolic rate by calorimetry. If the goal is to assess the ability of the animal to regulate Ṁ _O2  from this profile in a mathematical fashion, promising, more informative alternatives to P _crit are the regulation index and Michaelis-Menten or sigmoidal allosteric analyses.

Differences in the respiratory response to temperature and hypoxia across four life-stages of the intertidal porcelain crab Petrolisthes laevigatus

For aquatic breathers, hypoxia and warming can act synergistically causing a mismatch between oxygen supply (reduced by hypoxia) and oxygen demand (increased by warming). The vulnerability of these species to such interactive effects may differ during ontogeny due to differing gas exchange systems. This study examines respiratory responses to temperature and hypoxia across four life-stages of the intertidal porcelain crab Petrolisthes laevigatus. Eggs, megalopae, juveniles and adults were exposed to combinations of temperatures from 6 to 18 °C and oxygen tensions from 2 to 21 kPa. Metabolic rates differed strongly across life-stages which could be partly attributed to differences in body mass. However, eggs exhibited significantly lower metabolic rates than predicted for their body mass. For the other three stages, metabolic rates scaled with a mass exponent of 0.89. Mass scaling exponents were similar across all temperatures, but were significantly influenced by oxygen tension (the highest at 9 and 14 kPa, and the lowest at 2 kPa). Respiratory responses across gradients of oxygen tension were used to calculate the response to hypoxia, whereby eggs, megalopae and juveniles responded as oxyconformers and adults as oxyregulators. The thermal sensitivity of the metabolic rates (Q₁₀) were dependent on the oxygen tension in megalopae, and also on the interaction between oxygen tension and temperature intervals in adults. Our results thus provide evidence on how the oxygen tension can modulate the mass dependence of metabolic rates and demonstrate changes in respiratory control from eggs to adults. In light of our results indicating that adults show a good capacity for maintaining metabolism independent of oxygen tension, our study highlights the importance of assessing responses to multiple stressors across different life-stages to determine how vulnerability to warming and hypoxia changes during development.

Emersion behaviour underlies variation in gill morphology and aquatic respiratory function in the amphibious fish Kryptolebias marmoratus

Fishes acclimated to hypoxic environments often increase gill surface area to improve O₂ uptake. In some species, surface area is increased via reduction of an interlamellar cell mass (ILCM) that fills water channels between gill lamellae. Amphibious fishes, however, may not increase gill surface area in hypoxic water because these species can, instead, leave water and breathe air. To differentiate between these possibilities, we compared wild amphibious mangrove rivulus Kryptolebias marmoratus from two habitats that varied in O₂ availability - a hypoxic freshwater pool versus nearly anoxic crab burrows. Fish captured from crab burrows had less gill surface area (as ILCMs were enlarged by ∼32%), increased rates of normoxic O₂ consumption and increased critical O₂ tension compared with fish from the freshwater pool. Thus, wild mangrove rivulus do not respond to near-anoxic water by decreasing metabolism or increasing O₂ extraction. Instead, fish from the crab burrow habitat spent three times longer out of water, which probably caused the observed changes in gill morphology and respiratory phenotype. We also tested whether critical O₂ tension is influenced by genetic heterozygosity, as K. marmoratus is one of only two hermaphroditic vertebrate species that can produce both self-fertilized (inbred) or out-crossed (more heterozygous) offspring. We found no evidence for inbreeding depression, suggesting that self-fertilization does not impair respiratory function. Overall, our results demonstrate that amphibious fishes that inhabit hypoxic aquatic habitats can use a fundamentally different strategy from that used by fully aquatic water-breathing fishes, relying on escape behaviour rather than metabolic depression or increased O₂ extraction ability.

Do low oxygen environments facilitate marine invasions? Relative tolerance of native and invasive species to low oxygen conditions

Biological invasions are one of the biggest threats to global biodiversity. Marine artificial structures are proliferating worldwide and provide a haven for marine invasive species. Such structures disrupt local hydrodynamics, which can lead to the formation of oxygen-depleted microsites. The extent to which native fauna can cope with such low oxygen conditions, and whether invasive species, long associated with artificial structures in flow-restricted habitats, have adapted to these conditions remains unclear. We measured water flow and oxygen availability in marinas and piers at the scales relevant to sessile marine invertebrates (mm). We then measured the capacity of invasive and native marine invertebrates to maintain metabolic rates under decreasing levels of oxygen using standard laboratory assays. We found that marinas reduce water flow relative to piers, and that local oxygen levels can be zero in low flow conditions. We also found that for species with erect growth forms, invasive species can tolerate much lower levels of oxygen relative to native species. Integrating the field and laboratory data showed that up to 30% of available microhabitats within low flow environments are physiologically stressful for native species, while only 18% of the same habitat is physiologically stressful for invasive species. These results suggest that invasive species have adapted to low oxygen habitats associated with manmade habitats, and artificial structures may be creating niche opportunities for invasive species.

Estimating monotonic rates from biological data using local linear regression

Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research, and is applicable to a wide variety of research disciplines in the biological sciences.

Cold tolerance is unaffected by oxygen availability despite changes in anaerobic metabolism

Insect cold tolerance depends on their ability to withstand or repair perturbations in cellular homeostasis caused by low temperature stress. Decreased oxygen availability (hypoxia) can interact with low temperature tolerance, often improving insect survival. One mechanism proposed for such responses is that whole-animal cold tolerance is set by a transition to anaerobic metabolism. Here, we provide a test of this hypothesis in an insect model system (Thaumatotibia leucotreta) by experimental manipulation of oxygen availability while measuring metabolic rate, critical thermal minimum (CT_min), supercooling point and changes in 43 metabolites in moth larvae at three key timepoints (before, during and after chill coma). Furthermore, we determined the critical oxygen partial pressure below which metabolic rate was suppressed (c. 4.5 kPa). Results showed that altering oxygen availability did not affect (non-lethal) CT_min nor (lethal) supercooling point. Metabolomic profiling revealed the upregulation of anaerobic metabolites and alterations in concentrations of citric acid cycle intermediates during and after chill coma exposure. Hypoxia exacerbated the anaerobic metabolite responses induced by low temperatures. These results suggest that cold tolerance of T. leucotreta larvae is not set by oxygen limitation, and that anaerobic metabolism in these larvae may contribute to their ability to survive in necrotic fruit.

A new analysis of hypoxia tolerance in fishes using a database of critical oxygen level (P crit)

Hypoxia is a common occurrence in aquatic habitats, and it is becoming an increasingly frequent and widespread environmental perturbation, primarily as the result of anthropogenic nutrient enrichment and climate change. An in-depth understanding of the hypoxia tolerance of fishes, and how this varies among individuals and species, is required to make accurate predictions of future ecological impacts and to provide better information for conservation and fisheries management. The critical oxygen level (P crit) has been widely used as a quantifiable trait of hypoxia tolerance. It is defined as the oxygen level below which the animal can no longer maintain a stable rate of oxygen uptake (oxyregulate) and uptake becomes dependent on ambient oxygen availability (the animal transitions to oxyconforming). A comprehensive database of P crit values, comprising 331 measurements from 96 published studies, covering 151 fish species from 58 families, provides the most extensive and up-to-date analysis of hypoxia tolerance in teleosts. Methodologies for determining P crit are critically examined to evaluate its usefulness as an indicator of hypoxia tolerance in fishes. Various abiotic and biotic factors that interact with hypoxia are analysed for their effect on P crit, including temperature, CO2, acidification, toxic metals and feeding. Salinity, temperature, body mass and routine metabolic rate were strongly correlated with P crit; 20% of variation in the P crit data set was explained by these four variables. An important methodological issue not previously considered is the inconsistent increase in partial pressure of CO2 within a closed respirometer during the measurement of P crit. Modelling suggests that the final partial pressure of CO2 reached can vary from 650 to 3500 µatm depending on the ambient pH and salinity, with potentially major effects on blood acid-base balance and P crit itself. This database will form part of a widely accessible repository of physiological trait data that will serve as a resource to facilitate future studies of fish ecology, conservation and management.

Oxygen safety margins set thermal limits in an insect model system

A mismatch between oxygen availability and metabolic demand may constrain thermal tolerance. While considerable support for this idea has been found in marine organisms, results from insects are equivocal and raise the possibility that mode of gas exchange, oxygen safety margins and the physico-chemical properties of the gas medium influence heat tolerance estimates. Here, we examined critical thermal maximum (CTmax) and aerobic scope under altered oxygen supply and in two life stages that varied in metabolic demand in Bombyx mori (Lepidoptera: Bombycidae). We also systematically examined the influence of changes in gas properties on CTmax. Larvae have a lower oxygen safety margin (higher critical oxygen partial pressure at which metabolism is suppressed relative to metabolic demand) and significantly higher CTmax under normoxia than pupae (53°C vs 50°C). Larvae, but not pupae, were oxygen limited with hypoxia (2.5 kPa) decreasing CTmax significantly from 53 to 51°C. Humidifying hypoxic air relieved the oxygen limitation effect on CTmax in larvae, whereas variation in other gas properties did not affect CTmax. Our data suggest that oxygen safety margins set thermal limits in air-breathing invertebrates and the magnitude of this effect potentially reconciles differences in oxygen limitation effects on thermal tolerance found among diverse taxa to date.

Gross mismatch between thermal tolerances and environmental temperatures in a tropical freshwater snail: climate warming and evolutionary implications

The relationship between acute thermal tolerance and habitat temperature in ectotherm animals informs about their thermal adaptation and is used to assess thermal safety margins and sensitivity to climate warming. We studied this relationship in an equatorial freshwater snail (Clea nigricans), belonging to a predominantly marine gastropod lineage (Neogastropoda, Buccinidae). We found that tolerance of heating and cooling exceeded average daily maximum and minimum temperatures, by roughly 20°C in each case. Because habitat temperature is generally assumed to be the main selective factor acting on the fundamental thermal niche, the discordance between thermal tolerance and environmental temperature implies trait conservation following 'in situ' environmental change, or following novel colonisation of a thermally less-variable habitat. Whereas heat tolerance could relate to an historical association with the thermally variable and extreme marine intertidal fringe zone, cold tolerance could associate with either an ancestral life at higher latitudes, or represent adaptation to cooler, higher-altitudinal, tropical lotic systems. The broad upper thermal safety margin (difference between heat tolerance and maximum environmental temperature) observed in this snail is grossly incompatible with the very narrow safety margins typically found in most terrestrial tropical ectotherms (insects and lizards), and hence with the emerging prediction that tropical ectotherms, are especially vulnerable to environmental warming. A more comprehensive understanding of climatic vulnerability of animal ectotherms thus requires greater consideration of taxonomic diversity, ecological transition and evolutionary history.

Fitting statistical models in bivariate allometry: scaling metabolic rate to body mass in mustelid carnivores

The ongoing debate about methods for fitting the two-parameter allometric equation y=ax(b) to bivariate data seemed to be resolved recently when three groups of investigators independently reported that statistical models fitted by the traditional allometric method (i.e., by back-transforming a linear model fitted to log-log transformations) typically are superior to models fitted by standard nonlinear regression. However, the narrow focus for the statistical analyses in these investigations compromised the most important of the ensuing conclusions. All the investigations focused on two-parameter power functions and excluded from consideration other simple functions that might better describe pattern in the data; and all relied on Akaike's Information Criterion instead of graphical validation to identify the better statistical model. My re-analysis of data from one of the studies (BMR vs. body mass in mustelid carnivores) revealed (1) that the best descriptor for pattern in the dataset is a straight line and not a two-parameter power function; (2) that a model with additive, normal, heteroscedastic error is superior to one with multiplicative, lognormal, heteroscedastic error; and (3) that Akaike's Information Criterion is not a generally reliable metric for discriminating between models fitted to different distributions. These findings have apparent implications for interpreting the outcomes of all three of the aforementioned studies. Future investigations of allometric variation should adopt a more holistic approach to analysis and not be wedded to the traditional allometric method.