Do Bertalanffy's growth curves result from optimal resource allocation?

Bertalanffy's equation is commonly used to model indeterminate growth. Bertalanffy claimed that this growth pattern results from growth potential decreasing with age. An alternative approach provided by life history theory predicts that indeterminate growth is optimal for organisms in a seasonal environment and results not from decreasing growth potential but from allocating increasingly less energy with age into growth, and more into reproduction. Bertalanffy's curves are the result of evolutionary optimization and should not be used in optimization models as an assumption, but they can be used as a tool to describe the indeterminate growth pattern phenomenologically.     

Can optimal resource allocation models explain why ectotherms grow larger in cold?

Basically all organisms can be classified as determinate growers if their growth stops or almost stops at maturation, or indeterminate growers if growth is still intense after maturation. Adult size for determinate growers is relatively well defined, whereas in indeterminate growers usually two measures are used: size at maturation and asymptotic size. The latter term is in fact not a direct measure but a parameter of a specific growth equation, most often Bertalanffy's growth curve. At a given food level, the growth rate in determinate growers depends under given food level on physiological constraints as well as on investments in repair and other mechanisms that improve future survival. The growth rate in indeterminate growers consists of two phases: juvenile and adult. The mechanisms determining the juvenile growth rate are similar to those in determinate growers, whereas allocation to reproduction (dependent on external mortality rate) seems to be the main factor limiting adult growth. Optimal resource allocation models can explain the temperature-size rule (stating that usually ectotherms grow slower in cold but attain larger size) if the exponents of functions describing the size-dependence of the resource acquisition and metabolic rates change with temperature or mortality increases with temperature. Emerging data support both assumptions. The results obtained with the aid of optimization models represent just a rule and not a law: it is possible to find the ranges of production parameters and mortality rates for which the temperature-size rule does not hold.     

Integrating Thermal Physiology and Ecology of Ectotherms: A Discussion of Approaches

An understanding of interactions between the thermal physiologyand ecology of ectotherms remains elusive, partly because informationon the relative performance of whole-animal physiological systemsat ecologically relevant body temperatures is limited. Afterdiscussing physiological systems that have direct links to ecology(e.g., growth, locomotor ability), we review analytical methodsof describing and comparing certain aspects of performance (includingoptimal temperature range, thermal performance breadth), applythese techniques in an example on the thermal sensitivity oflocomotion in frogs, and evaluate potential applications.     

Plasticity of life-cycle, physiological thermal traits and Hsp70 gene expression in an insect along the ontogeny: Effect of temperature variability

It is considered that extreme environmental temperature, rather than mean temperatures exert a selective pressure in ectotherms. Consequently, it is important to understand how the predicted increase in temperature variance with a higher frequency of extreme events in climate change is likely to impact on organisms. Thermal tolerance traits (i.e. chill-coma, recovery time, Hsp70 expression) are directly linked with performance in ectotherms and have consequences in life-history traits. We examined the effects of temperature variability on thermal tolerance and life-history traits through ontogeny of an insect with a complex life-cycle: the yellow mealworm beetle Tenebrio molitor. We established two common gardens with 100 recently ovoposited eggs each. Larvae were reared from hatching to adult on either a variable (mean=18 °C and a variance of 6.8 °C) or constant (18±1 °C) thermal environment. Development rate and growth rate were similar between thermal environments. Results indicate that larvae reared in a variable environment are more cold-tolerant than larvae of a constant environment. Interestingly, these results are reversed in the adult stage, outlining an inter-stage physiological cost. Gene expression pattern of an Hsp70 gene was well correlated with larval thermotolerance to cold in the variable environment but higher gene expression in adults is not correlated with individual's thermotolerance. We conclude that chill-coma, recovery time and Hsp70 gene expression are plastic in response to a thermal environment but also change significantly their responses depending on the ontogenetic stage, implying that the response of adult individuals is linked to early stages of the life-cycle.     

A comparison of dynamic-state-dependent models of the trade-off between growth, damage, and reproduction

Fast growth can be costly, so trade-offs between growth and fitness are to be predicted when organisms adjust their growth to compensate for earlier environmental conditions. We developed four generic models of increasing complexity with different processes to predict the indeterminate growth of vertebrate ectotherms, which is sensitive to ambient temperature even when food is not limiting. We contrast the predictions of the models with observed experimental data on growth trajectories, feeding activity, and reproductive investment of three-spined sticklebacks and inferred patterns of accumulation of biomolecular damage arising from activity and growth. All models predicted observed patterns of compensatory growth (both accelerating and decelerating) in response to earlier temperature perturbations, but the more complex models provided the best fit to experimental data. Growth trajectories influenced future reproductive investment regardless of final body size at breeding. Our findings suggest that while models with fewer parameters can predict basic patterns of growth in stable conditions, they cannot capture the costly long-term effects of deviations from steady growth trajectories. In contrast, models in which foraging activity is assumed to carry costs are capable of predicting the complex patterns of feeding, growth, and reproductive investment seen in animals, with the cost of a heightened mortality risk (e.g., through predation) being more important than the cost of increased physiological damage.     

Influences of thermal environment on fish growth

Thermoregulation in ectothermic animals is influenced by the ability to effectively respond to thermal variations. While it is known that ectotherms are affected by thermal changes, it remains unknown whether physiological and/or metabolic traits are impacted by modifications to the thermal environment. Our research provides key evidence that fish ectotherms are highly influenced by thermal variability during development, which leads to important modifications at several metabolic levels (e.g., growth trajectories, microstructural alterations, muscle injuries, and molecular mechanisms). In Atlantic salmon (Salmo salar), a wide thermal range (Δ_T 6.4°C) during development (posthatch larvae to juveniles) was associated with increases in key thermal performance measures for survival and growth trajectory. Other metabolic traits were also significantly influenced, such as size, muscle cellularity, and molecular growth regulators possibly affected by adaptive processes. In contrast, a restricted thermal range (Δ_T 1.4°C) was detrimental to growth, survival, and cellular microstructure as muscle growth could not keep pace with increased metabolic demands. These findings provide a possible basic explanation for the effects of thermal environment during growth. In conclusion, our results highlight the key role of thermal range amplitude on survival and on interactions with major metabolism‐regulating processes that have positive adaptive effects for organisms.     

A Flexible Growth Function for Empirical Use

The application of an extended form of von Bertalanffy's growthfunction to plant data is considered; the equation has considerableflexibility, but is used only to supply an empirical fit. Inorder to aid the biological analysis of such growth data asare capable of representation by the function, general rateparameters are deduced which are related in a simple mannerto its constants.     

Could the intrinsic rate of increase represent the fitness in terrestrial ectotherms?

The intrinsic rate of increase (r_m) has been considered as an important indicator of fitness in terrestrial ectotherms since long. It is actually an equivalent to the instantaneous growth rate of the exponential equation for describing the density-independent population growth. In terrestrial ectotherms, r_m has been demonstrated to be temperature-dependent. The temperature at which r_m was maximal, was considered to be the “optimal” temperature for fitness in Amarasekare and Savage (2012), but this definition needs further analysis. Only r_m cannot provide thorough representation of fitness. Because body size can affect the competitive abilities in many terrestrial ectotherms, both population size and body size should be considered in measuring the fitness of ectotherms. The rule of “bigger is better” requires relatively low temperature to increase in body size, whereas relatively high temperature is required for a rapid increase in population size. Thus, there is presumably a trade-off in temperature for adjusting individual body size and population size to achieve maximum fitness. We hypothesized that this temperature could be reflected by the intrinsic optimum temperature for developmental rate in the Sharpe–Schoolfield–Ikemoto model, and it led to a temperature estimate around 20 °C. However, the traditional viewpoint based on the temperature corresponding to the maximal intrinsic rate of increase provides a temperature estimate around 30 °C. This study suggests that a low temperature around 20 °C might authentically represent the optimal ambient temperature for fitness in terrestrial ectotherms. It implies that thermal biologists who are interested in the effect of temperature on the fitness in terrestrial ectotherms should pay more attention to their performance at low temperature rather than high temperature.     

Growth,stress, and acclimation responses to fluctuating temperatures in field and domesticated populations of Manduca sexta

Diurnal fluctuations in temperature are ubiquitous in terrestrial environments, and insects and other ectotherms have evolved to tolerate or acclimate to such fluctuations. Few studies have examined whether ectotherms acclimate to diurnal temperature fluctuations, or how natural and domesticated populations differ in their responses to diurnal fluctuations. We examine how diurnally fluctuating temperatures during development affect growth, acclimation, and stress responses for two populations of Manduca sexta: a field population that typically experiences wide variation in mean and fluctuations in temperature, and a laboratory population that has been domesticated in nearly constant temperatures for more than 300 generations. Laboratory experiments showed that diurnal fluctuations throughout larval development reduced pupal mass for the laboratory but not the field population. The differing effects of diurnal fluctuations were greatest at higher mean temperature (30°C): Here diurnal fluctuations reduced pupal mass and increased pupal development time for the laboratory population, but had little effect for the field population. We also evaluated how mean and fluctuations in temperature during early larval development affected growth rate during the final larval instar as a function of test temperature. At an intermediate (25°C) mean temperature, both the laboratory and field population showed a positive acclimation response to diurnal fluctuations, in which subsequent growth rate was significantly higher at most test temperatures. In contrast at higher mean temperature (30°C), diurnal fluctuations significantly reduced subsequent growth rate at most test temperatures for the laboratory population, but not for the field population. These results suggest that during domestication in constant temperatures, the laboratory population has lost the capacity to tolerate or acclimate to high and fluctuating temperatures. Population differences in acclimation capacity in response to temperature fluctuations have not been previously demonstrated, but they may be important for understanding the evolution of reaction norms and performance curves.     

The temperature-size rule in ectotherms: simple evolutionary explanations may not be general

In many organisms, individuals in colder environments grow more slowly but are larger as adults. This widespread pattern is embodied by two well-established rules: Bergmann's rule, which describes the association between temperature and body size in natural environments, and the temperature-size rule, which describes reaction norms relating temperature to body size in laboratory experiments. Theory predicts that organisms should grow to be larger in colder environments when growth efficiency decreases with increasing environmental temperature. Using data from 97 laboratory experiments, including 58 species of ectotherms, we found little evidence that growth efficiency is negatively related to environmental temperature within the thermal range that is relevant to the temperature-size rule. Instead, growth efficiency was either positively related or insensitive to environmental temperature in the majority of cases (73 of 89 cases for gross growth efficiency and 18 of 24 cases for net growth efficiency). Two possibilities merit consideration. First, high temperatures may impose constraints on growth that only arise late during ontogeny; this simple and potentially general explanation is supported by the fact that thermal optima for growth efficiency and growth rate decrease as individuals grow. Alternatively, the general explanation for relationships between temperature and body size may not be simple. If the latter view is correct, the best approach might be to generate and test theories that are tailored specifically to organisms with similar behavior and physiology.     

Effect of the critical thermal maximum on the preferred temperatures of Ictalurus punctatus exposed to constant and fluctuating temperatures

No significant differences were found in the temperature of the onset of behavioural response spasms and equilibrium loss in Ictalurus punctatus maintained in constant and fluctuating temperatures. The preferred temperature was determined in an aquatic gradient to be 29.0°C and the temperatures avoided were 21.7–34.1°C. The temperature that causes the loss of equilibrium of acclimation at constant or fluctuating temperatures changes the organisms final preferendum and the avoided temperatures were significantly different (p<0.05) if compared with the control group. The behavioural response that should be considered as the critical thermal maximum (CTMax) of I. punctatus is the equilibrium loss that reflects a major deep core reaction.     

From cells to colonies: at what levels of body organization does the ‘temperature‐size rule’ apply?

SUMMARY An inverse relationship between temperature during ontogeny and final body size is widespread in ectotherms, but poorly understood. Evidence suggests that within organs, this “temperature‐size rule” (TSR) may also apply to cell size with no change in numbers. So how closely do reductions in size and number of cells and other repeated structures correlate with size reduction at higher levels of organization? We examine this in the context of a proposal that size and/or number changes at various organizational levels are adaptive responses to temperature‐ and size‐dependent oxygen supply. We subjected two clones of the modular colonial bryozoan, Celleporella hyalina, to orthogonal combinations of two temperatures and two oxygen concentrations during ontogeny, observing effects on sizes of colonies and larvae, and sizes and numbers of cells, tentacles, and modules (autozooids). We found that the size:number responses varied among cell types and among structures at different levels of organization, with the inverse temperature‐size relationship applying only to larval parenchymal cells and colony modules. Using our findings and other evidence we propose a unifying adaptive hypothesis that predicts how temperature affects the sizes of mitochondria, cells, organs, modules and organisms, and their relationships with processes that determine the functional capacity of aerobic metabolism.     

Breaking the temperature-size rule: Thermal effects on growth,development and fecundity of a crustacean from temporary waters

The temperature-size rule (TSR) is a well-established phenomenon to describe the growth response of ectotherms to temperature by which individuals maintained at low temperatures grow more slowly, but attain a larger size upon maturity. Although there are adaptive and non-adaptive theories about the plasticity of body size in response to temperature, these cannot be applied to all ectotherms, and little is known about the changes in growth and development rates through ontogeny. The ostracod species Heterocypris bosniaca, an inhabitant of freshwater temporary ponds, was used to examine the growth and development rates of its nine growth stages and female fecundity at four different temperatures (15 °C, 20 °C, 25 °C and 30 °C). The development rate of this species accelerates with increasing temperature, reaching a maximum value at 25 °C. The growth factor has a reverse-TSR in younger instars, and the typical TSR is followed only in the last two moults, resulting in non-monotonic response of adult size to temperature. Fecundity (total offspring per female) was not directly related to adult size and was generally higher at lower temperatures. Our results agree with recent research showing that the TSR may vary during ontogeny, and may not be a general trend in ostracod species from temporary waters. Indeed, adult carapace size seems to follow the pattern of a thermal reaction norm, probably influenced by the reduction of oxygen bioavailability at low temperature and the drastic increase in metabolic demand at the upper extreme of the thermal gradient.     

Comparative Physiological Studies on Hyperthermophilic Archaea Isolated from Deep-Sea Hot Vents with Emphasis on Pyrococcus Strain GB-D

Three new sulfur- or non-sulfur-dependent archaeal isolates, including a Pyrococcus strain, from Guaymas Basin hydrothermal vents (Gulf of California; depth, 2,010 m) were characterized and physiologically compared with four known hyperthermophiles, previously isolated from other vent sites, with an emphasis on growth and survival under the conditions particular to the natural habitat. Incubation under in situ pressure (200 atm [1 atm = 101.29 kPa]) did not increase the maximum growth temperature by more than 1°C for any of the organisms but did result in increases in growth rates of up to 15% at optimum growth temperatures. At in situ pressure, temperatures considerably higher than those limiting growth (i.e., > 105°C) were survived best by isolates with the highest maximum growth temperatures, but none of the organisms survived at temperatures of 150°C or higher for 5 min. Free oxygen was toxic to all isolates at growth range temperatures, but at ambient deep-sea temperature (3 to 4°C), the effect varied in different isolates, the non-sulfur-dependent isolate being the most oxygen tolerant. Hyperthermophiles could be isolated from refrigerated and oxygenated samples after 5 years of storage. Cu, Zn, and Pb ions were found to be toxic under nongrowth conditions (absence of organic substrate), with the non-sulfur-dependent isolate again being the most tolerant.     

Ontogenetic Variation in the Thermal Biology of Yarrow's Spiny Lizard,Sceloporus jarrovii

Climate change is rapidly altering the way current species interact with their environment to satisfy life-history demands. In areas anticipated to experience extreme warming, rising temperatures are expected to diminish population growth, due either to environmental degradation, or the inability to tolerate novel temperature regimes. Determining how at risk ectotherms, and lizards in particular, are to changes in climate traditionally emphasizes the thermal ecology and thermal sensitivity of physiology of adult members of a population. In this study, we reveal ontogenetic differences in thermal physiological and ecological traits that have been used to anticipate how ectotherms will respond to climate change. We show that the thermal biological traits of juvenile Yarrow’s Spiny Lizards (Sceloporus jarrovii) differ from the published estimates of the same traits for adult lizards. Juvenile S. jarrovii differ in their optimal performance temperature, field field-active body temperature, and critical thermal temperatures compared to adult S. jarrovii. Within juvenile S. jarrovii, males and females exhibit differences in field-active body temperature and desiccation tolerance. Given the observed age- and sex-related variation in thermal physiology, we argue that not including physiological differences in thermal biology throughout ontogeny may lead to misinterpretation of patterns of ecological or evolutionary change due to climate warming. Further characterizing the potential for ontogenetic changes in thermal biology would be useful for a more precise and accurate estimation of the role of thermal physiology in mediating population persistence in warmer environments.     

The impacts of extreme and fluctuating temperatures on trait‐mediated indirect aphid–parasitoid interactions

1. Global climate change models predict an increase in the frequency and magnitude of extreme temperature events. These temperature events, heatwaves for example, will impact a wide range of physiological and behavioural processes, particularly in ectotherms, and may therefore influence interactions between species. 2. Anti‐predator responses may be more costly under more severe temperature regimes and therefore trait‐mediated disturbance could lead to high mortality or reduced reproduction under extreme and fluctuating temperature regimes. 3. We examined the impacts of extreme and fluctuating temperatures on trait‐mediated indirect interactions in an aphid–parasitoid community. 4. In treatments that isolated the effects of trait‐mediated disturbance from the effects of foraging parasitoids we found that an increase in both the amplitude and frequency of peak temperatures reduced aphid numbers and provided evidence that the cost of trait‐mediated disturbance could increase under frequent periods of high temperature. Aphid dispersal also increased with more frequent periods of high temperature. 5. In treatments where female wasps were allowed to freely forage (direct + trait‐mediated effects), there was no evidence that extreme and fluctuating temperatures influenced the wasp's foraging ability. Exposure to extreme fluctuating temperatures did not influence the offspring production of exposed wasps or the position of the mummies within the plots.     

Kleptothermy: an additional category of thermoregulation,and a possible example in sea kraits (Laticauda laticaudata,Serpentes)

Lacking the capacity for thermogenesis, most ectotherms inhabiting thermally heterogeneous environments rely instead upon exploiting that ambient heterogeneity. In many cases they maintain body temperatures within a narrow range despite massive spatial and temporal variation in ambient conditions. Reliance on diverse thermal opportunities is reflected in specific terms for organisms that bask in sunlight to regulate their temperature (heliotherms), or that press their bodies against warm substrates to facilitate heat flow (thigmotherms), or that rely on large body mass to maintain thermal constancy (gigantothermy). We propose an additional category of thermoregulators: kleptotherms, which regulate their own temperature by ‘stealing’ heat from other organisms. This concept involves two major conditions: the thermal heterogeneity created by the presence of a warm organism in a cool environment and the selective use of that heterogeneity by another animal to maintain body temperatures at higher (and more stable) levels than would be possible elsewhere in the local area. Kleptothermy occurs in endotherms also, but is usually reciprocal (rather than unilateral as in ectotherms). Thermal monitoring on a small tropical island documents a possible example of kleptothermy, based on high stable temperatures of a sea snake (Laticauda laticaudata) inside a burrow occupied by seabirds.     

Thermally mediated body temperature, water content and aggregation behaviour in the intertidal gastropod Nerita atramentosa

Intertidal organisms are vulnerable to global warming as they already live at, or near to, the upper limit of their thermal tolerance window. The behaviour of ectotherms could, however, dampen their limited physiological abilities to respond to climate change (e.g. drier and warmer environmental conditions) which could substantially increase their survival rates. The behaviour of ectotherms is still mostly overlooked in climate change studies. Here, we investigate the potential of aggregation behaviour to compensate for climate change in an intertidal gastropod species (Nerita atramentosa) in South Australia. We used thermal imaging to investigate (1) the heterogeneity in individual snail water content and body temperature and surrounding substratum temperature on two topographically different habitats (i.e. rock platform and boulders) separated by 250 m at both day- and night-times, (2) the potential relationship between environment temperature (air and substratum) and snail water content and body temperature, and (3) the potential buffering effect of aggregation behaviour on snail water content and body temperature. Both substratum and snail temperature were more heterogeneous at small spatial scales (a few centimetres to a few metres) than between habitats. This reinforces the evidence that mobile intertidal ectotherms could survive locally under warmer conditions if they can locate and move behaviourally in local thermal refuges. N. atramentosa behaviour, water content and body temperature during emersion seem to be related to the thermal stability and local conditions of the habitat occupied. Aggregation behaviour reduces both desiccation and heat stresses but only on the boulder field. Further investigations are required to identify the different behavioural strategies used by ectothermic species to adapt to heat and dehydrating conditions at the habitat level. Ultimately, this information constitutes a fundamental prerequisite to implement conservation management plans for ectothermic species identified as vulnerable in the warming climate.     

Rapid shifts in the thermal sensitivity of growth but not development rate causes temperature–size response variability during ontogeny in arthropods

Size at maturity in ectotherms commonly declines with warming. This near‐universal phenomenon, formalised as the temperature–size rule, has been observed in over 80% of tested species, from bacteria to fish. The proximate cause has been attributed to the greater temperature dependence of development rate than growth rate, causing individuals to develop earlier but mature smaller in the warm. However, few studies have examined the ontogenetic progression of the temperature–size response at high resolution. Using marine planktonic copepods, we experimentally determined the progression of the temperature–size response over ontogeny. Temperature–size responses were not generated gradually from egg to adult, contrary to the predictions of a naïve model in which development rate was assumed to be more temperature‐dependent than growth rate, and the difference in the temperature dependence of these two rates remained constant over ontogeny. Instead, the ontogenetic progression of the temperature–size response in experimental animals was highly episodic, indicating rapid changes in the extent to which growth and development rates are thermally decoupled. The strongest temperature–size responses occurred temporally mid‐way through ontogeny, corresponding with the point at which individuals reached between ~5 and 25% of their adult mass. Using the copepod Oithona nana, we show that the temperature‐dependence of growth rate varied substantially throughout ontogeny, whereas the temperature dependence of development rate remained constant. The temperature‐dependence of growth rate even exceeded that of development rate in some life stages, leading to a weakening of the temperature–size response. Our analyses of arthropod temperature–size responses from the literature, including crustaceans and insects, support these conclusions more broadly. Overall, our findings provide a better understanding of how the temperature–size rule is produced over ontogeny. Whereas we find support for the generality of developmental rate isomorphy in arthropods (shared temperature dependence of development rate across life stages), this concept appears not to apply to growth rates.     

High temperature intensifies negative density dependence of fitness in red flour beetles

Competition for food, space, or other depletable resources has strong impacts on the fitness of organisms and can lead to a pattern known as negative density dependence, where fitness decreases as population density increases. Yet, many resources that have strong impacts on fitness are nondepletable (e.g., moisture or temperature). How do these nondepletable resources interact with depletable resources to modify negative density dependence? We tested the hypothesis that negative density dependence is modulated by temperature in red flour beetles and tested the prediction that the strength of negative density dependence should decrease as temperature decreases. We measured the number of eggs laid, offspring development time, and the number of offspring that reached maturity at three temperatures and two food treatment combinations as we simultaneously manipulated adult population density. We demonstrated that low temperatures weaken negative density dependence in the number of eggs laid; this pattern was most evident when food was abundant. Density had no effect on development time, but low temperatures increased development time. The percent of eggs that emerged as adults decreased with both density and temperature and increased with food. Temperature, an abiotic driver, can thus modulate density-dependent processes in ectotherms. Therefore, models of population growth for ectotherms should incorporate the effects of temperature.