Modeling the temperature effect on the specific growth rate of phytoplankton: a review

Phytoplankton are key components of ecosystems. Their growth is deeply influenced by temperature. In a context of global change, it is important to precisely estimate the impact of temperature on these organisms at different spatial and temporal scales. Here, we review the existing deterministic models used to represent the effect of temperature on microbial growth that can be applied to phytoplankton. We first describe and provide a brief mathematical analysis of the models used in constant conditions to reproduce the thermal growth curve. We present the mechanistic assumptions concerning the effect of temperature on the cell growth and mortality, and discuss their limits. The coupling effect of temperature and other environmental factors such as light are then shown. Finally, we introduce the models taking into account the acclimation needed to thrive with temperature variations. The need for new thermal models, coupled with experimental validation, is argued.     

Variation in Thermal Sensitivity and Thermal Tolerances in an Invasive Species across a Climatic Gradient: Lessons from the Land Snail Cornu aspersum

The ability of organisms to perform at different temperatures could be described by a continuous nonlinear reaction norm (i.e., thermal performance curve, TPC), in which the phenotypic trait value varies as a function of temperature. Almost any shift in the parameters of this performance curve could highlight the direct effect of temperature on organism fitness, providing a powerful framework for testing thermal adaptation hypotheses. Inter-and intraspecific differences in this performance curve are also reflected in thermal tolerances limits (e.g., critical and lethal limits), influencing the biogeographic patterns of species’ distribution. Within this context, here we investigated the intraspecific variation in thermal sensitivities and thermal tolerances in three populations of the invasive snail Cornu aspersum across a geographical gradient, characterized by different climatic conditions. Thus, we examined population differentiation in the TPCs, thermal-coma recovery times, expression of heat-shock proteins and standard metabolic rate (i.e., energetic costs of physiological differentiation). We tested two competing hypotheses regarding thermal adaptation (the “hotter is better” and the generalist-specialist trade-offs). Our results show that the differences in thermal sensitivity among populations of C. aspersum follow a latitudinal pattern, which is likely the result of a combination of thermodynamic constraints (“hotter is better”) and thermal adaptations to their local environments (generalist-specialist trade-offs). This finding is also consistent with some thermal tolerance indices such as the Heat-Shock Protein Response and the recovery time from chill-coma. However, mixed responses in the evaluated traits suggest that thermal adaptation in this species is not complete, as we were not able to detect any differences in neither energetic costs of physiological differentiation among populations, nor in the heat-coma recovery.     

Thermal Reaction Norms and the Scale of Temperature Variation: Latitudinal Vulnerability of Intertidal Nacellid Limpets to Climate Change

The thermal reaction norms of 4 closely related intertidal Nacellid limpets, Antarctic (Nacella concinna), New Zealand (Cellana ornata), Australia (C. tramoserica) and Singapore (C. radiata), were compared across environments with different temperature magnitude, variability and predictability, to test their relative vulnerability to different scales of climate warming. Lethal limits were measured alongside a newly developed metric of “duration tenacity”, which was tested at different temperatures to calculate the thermal reaction norm of limpet adductor muscle fatigue. Except in C. tramoserica which had a wide optimum range with two break points, duration tenacity did not follow a typical aerobic capacity curve but was best described by a single break point at an optimum temperature. Thermal reaction norms were shifted to warmer temperatures in warmer environments; the optimum temperature for tenacity (T_opt) increased from 1.0°C (N. concinna) to 14.3°C (C. ornata) to 18.0°C (an average for the optimum range of C. tramoserica) to 27.6°C (C. radiata). The temperature limits for duration tenacity of the 4 species were most consistently correlated with both maximum sea surface temperature and summer maximum in situ habitat logger temperature. Tropical C. radiata, which lives in the least variable and most predictable environment, generally had the lowest warming tolerance and thermal safety margin (WT and TSM; respectively the thermal buffer of CT_max and T_opt over habitat temperature). However, the two temperate species, C. ornata and C. tramoserica, which live in a variable and seasonally unpredictable microhabitat, had the lowest TSM relative to in situ logger temperature. N. concinna which lives in the most variable, but seasonally predictable microhabitat, generally had the highest TSMs. Intertidal animals live at the highly variable interface between terrestrial and marine biomes and even small changes in the magnitude and predictability of their environment could markedly influence their future distributions.     

Ecological differences influence the thermal sensitivity of swimming performance in two co-occurring mysid shrimp species with climate change implications

Temperature strongly affects performance in ectotherms. As ocean warming continues, performance of marine species will be impacted. Many studies have focused on how warming will impact physiology, life history, and behavior, but few studies have investigated how ecological and behavioral traits of organisms will affect their response to changing thermal environments. Here, we assessed the thermal tolerances and thermal sensitivity of swimming performance of two sympatric mysid shrimp species of the Northwest Atlantic. Neomysis americana and Heteromysis formosa overlap in habitat and many aspects of their ecological niche, but only N. americana exhibits vertical migration. In temperate coastal ecosystems, temperature stratification of the water column exposes vertical migrators to a wider range of temperatures on a daily basis. We found that N. americana had a significantly lower critical thermal minimum (CT_min) and critical thermal maximum (CT_max). However, both mysid species had a buffer of at least 4 °C between their CT_max and the 100-year projection for mean summer water temperatures of 28 °C. Swimming performance of the vertically migrating species was more sensitive to temperature variation, and this species exhibited faster burst swimming speeds. The generalist performance curve of H. formosa and specialist curve of N. americana are consistent with predictions based on the exposure of each species to temperature variation such that higher within-generation variability promotes specialization. However, these species violate the assumption of the specialist-generalist tradeoff in that the area under their performance curves is not constant. Our results highlight the importance of incorporating species-specific responses to temperature based on the ecology and behavior of organisms into climate change prediction models.     

Thermal parameters and locomotor performance in juvenile of Pleurodema nebulosum (Anura: Leptodactylidae) from the Monte Desert

We studied a combination of thermal parameters (critical thermal maximum, selected body temperature, and field body temperature) and locomotor performance capacities (laboratory and field conditions) of juveniles of Pleurodema nebulosum. We found that field body temperature was determined largely by the temperature of the micro-environment. Field body temperatures of juveniles of P. nebulosum were below selected body temperature. The locomotor performance curve was maximized and reaches a plateau between 30 and 35 °C, with 35 °C being the temperature at which maximum performance was obtained for analyzed individuals. The plateau values were close to the selected body temperature (T_sel) obtained for the studied frogs. In field conditions the locomotor performance was determinated by the substrate temperature. Apparently, juveniles of P. nebulosum show thermal coadaptation because the selected body temperature and the optimum temperature for locomotion had close values. We believe that the temperatures prevailing during the early hours of activity would allow frogs to explore the micro-environment, covering larger areas in search of food.     

Reaction Norms in Natural Conditions: How Does Metabolic Performance Respond to Weather Variations in a Small Endotherm Facing Cold Environments?

Reaction norms reflect an organisms'' capacity to adjust its phenotype to the environment and allows for identifying trait values associated with physiological limits. However, reaction norms of physiological parameters are mostly unknown for endotherms living in natural conditions. Black-capped chickadees (Poecile atricapillus) increase their metabolic performance during winter acclimatization and are thus good model to measure reaction norms in the wild. We repeatedly measured basal (BMR) and summit (Msum) metabolism in chickadees to characterize, for the first time in a free-living endotherm, reaction norms of these parameters across the natural range of weather variation. BMR varied between individuals and was weakly and negatively related to minimal temperature. Msum varied with minimal temperature following a Z-shape curve, increasing linearly between 24°C and −10°C, and changed with absolute humidity following a U-shape relationship. These results suggest that thermal exchanges with the environment have minimal effects on maintenance costs, which may be individual-dependent, while thermogenic capacity is responding to body heat loss. Our results suggest also that BMR and Msum respond to different and likely independent constraints.     

Coping with temperature at the warm edge--patterns of thermal adaptation in the microbial eukaryote Paramecium caudatum

Background

Ectothermic organisms are thought to be severely affected by global warming since their physiological performance is directly dependent on temperature. Latitudinal and temporal variations in mean temperatures force ectotherms to adapt to these complex environmental conditions. Studies investigating current patterns of thermal adaptation among populations of different latitudes allow a prediction of the potential impact of prospective increases in environmental temperatures on their fitness.

Methodology/Principal Findings

In this study, temperature reaction norms were ascertained among 18 genetically defined, natural clones of the microbial eukaryote Paramecium caudatum. These different clones have been isolated from 12 freshwater habitats along a latitudinal transect in Europe and from 3 tropical habitats (Indonesia). The sensitivity to increasing temperatures was estimated through the analysis of clone specific thermal tolerances and by relating those to current and predicted temperature data of their natural habitats.All investigated European clones seem to be thermal generalists with a broad thermal tolerance and similar optimum temperatures. The weak or missing co-variation of thermal tolerance with latitude does not imply local adaptation to thermal gradients; it rather suggests adaptive phenotypic plasticity among the whole European subpopulation. The tested Indonesian clones appear to be locally adapted to the less variable, tropical temperature regime and show higher tolerance limits, but lower tolerance breadths.

Conclusions/Significance

Due to the lack of local temperature adaptation within the European subpopulation, P. caudatum genotypes at the most southern edge of their geographic range seem to suffer from the predicted increase in magnitude and frequency of summer heat waves caused by climate change.     

Sex cells in changing environments: can organisms adjust the physiological function of gametes to different temperatures?

Over the past decade, hundreds of studies have examined the abilities of whole organisms to modify their physiology and behaviour in response to environmental temperature changes; despite this, virtually nothing is known about the ability of sex cells to adjust to different temperature conditions. In fact, a recent meta‐analysis based on studies of 309 species and 112 physiological and ecological traits found no studies examining the influence of temperature on gamete function. Because sex cells play a critical role in the adaptation and persistence of species, this represents a severe oversight in physiological studies of thermal adaptation. Our study examines whether sex cells can respond phenotypically to variation in the thermal environment that is experienced by the whole‐organism. Specifically, we studied the thermal dependence of sperm swimming and the critical thermal limits of sperm cells in males of the poeciliid fish, Gambusia holbrooki. This species is well known for its ability to modify physiological function and maintains burst and sustained swimming performance and mating ability across a wide range of thermal conditions. In contrast, we found that sperm cells from male G. holbrooki did not adjust their physiological function as predicted by adaptive models. After acclimation of adult males to cool or warm temperatures, we found that the critical thermal limits of sperm function remained unchanged, as did the effect of temperature on sperm swimming performance. However, warm‐acclimated fish had sperm with higher swimming speeds across all temperatures. The absence of phenotypic changes in the critical thermal limits of sperm or thermal dependence of sperm swimming performance is surprising given that whole‐organism traits in G. holbrooki generally show improved performance after exposure to novel environments. As such an inability to thermally adjust gamete function may be widespread among other organisms, we urge biologists to investigate the generality of this result.     

Thermal optimality of net ecosystem exchange of carbon dioxide and underlying mechanisms

? It is well established that individual organisms can acclimate and adapt to temperature to optimize their functioning. However, thermal optimization of ecosystems, as an assemblage of organisms, has not been examined at broad spatial and temporal scales. ? Here, we compiled data from 169 globally distributed sites of eddy covariance and quantified the temperature response functions of net ecosystem exchange (NEE), an ecosystem-level property, to determine whether NEE shows thermal optimality and to explore the underlying mechanisms. ? We found that the temperature response of NEE followed a peak curve, with the optimum temperature (corresponding to the maximum magnitude of NEE) being positively correlated with annual mean temperature over years and across sites. Shifts of the optimum temperature of NEE were mostly a result of temperature acclimation of gross primary productivity (upward shift of optimum temperature) rather than changes in the temperature sensitivity of ecosystem respiration. ? Ecosystem-level thermal optimality is a newly revealed ecosystem property, presumably reflecting associated evolutionary adaptation of organisms within ecosystems, and has the potential to significantly regulate ecosystem-climate change feedbacks. The thermal optimality of NEE has implications for understanding fundamental properties of ecosystems in changing environments and benchmarking global models.     

The combined effects of reactant kinetics and enzyme stability explain the temperature dependence of metabolic rates

A mechanistic understanding of the response of metabolic rate to temperature is essential for understanding thermal ecology and metabolic adaptation. Although the Arrhenius equation has been used to describe the effects of temperature on reaction rates and metabolic traits, it does not adequately describe two aspects of the thermal performance curve (TPC) for metabolic rate—that metabolic rate is a unimodal function of temperature often with maximal values in the biologically relevant temperature range and that activation energies are temperature dependent. We show that the temperature dependence of metabolic rate in ectotherms is well described by an enzyme‐assisted Arrhenius (EAAR) model that accounts for the temperature‐dependent contribution of enzymes to decreasing the activation energy required for reactions to occur. The model is mechanistically derived using the thermodynamic rules that govern protein stability. We contrast our model with other unimodal functions that also can be used to describe the temperature dependence of metabolic rate to show how the EAAR model provides an important advance over previous work. We fit the EAAR model to metabolic rate data for a variety of taxa to demonstrate the model's utility in describing metabolic rate TPCs while revealing significant differences in thermodynamic properties across species and acclimation temperatures. Our model advances our ability to understand the metabolic and ecological consequences of increases in the mean and variance of temperature associated with global climate change. In addition, the model suggests avenues by which organisms can acclimate and adapt to changing thermal environments. Furthermore, the parameters in the EAAR model generate links between organismal level performance and underlying molecular processes that can be tested for in future work.     

Quantitative genetics of continuous reaction norms: thermal sensitivity of caterpillar growth rates

A continuous reaction norm or performance curve represents a phenotypic trait of an individual or genotype in which the trait value may vary with some continuous environmental variable. We explore patterns of genetic variation in thermal performance curves of short-term caterpillar growth rate in a population of Pieris rapae. We compare multivariate methods, which treat performance at each test temperature as a distinct trait, with function-valued methods that treat a performance curve as a continuous function. Mean growth rate increased with increasing temperatures from 8 to 35 degrees C, was highest at 35 degrees C, and declined at 40 degrees C. There was substantial and significant variation among full-sib families in their thermal performance curves. Estimates of broad-sense genetic variances and covariances showed that genetic variance in growth rate increased more than 30-fold from low (8-11 degrees C) to high (35-40 degrees C) temperatures, even after differences in mean growth rate across temperatures were removed. Growth rate at 35 and 40 degrees C was negatively correlated genetically, suggesting a genetic trade-off in growth rate at these temperatures; this trade-off may represent either a generalist-specialist trade-off and/or variation in the optimal temperature for growth. The estimated genetic variance-covariance function (G function), the function-valued analog of the variance-covariance matrix (G matrix), was quite bumpy compared with the estimated G matrix; and results of principal component analyses of the G function were difficult to interpret. The use of orthogonal polynomials as the basis functions in current function-valued estimation methods may generate artifacts when the true G function has prominent local features, such as strong negative covariances at nearby temperatures (e.g. at 35 and 40 degrees C); this may be a particular issue for thermal performance curves and other highly nonlinear reaction norms.     

Variation in growth and developmental responses to supraoptimal temperatures near latitudinal range limits of gypsy moth Lymantria dispar (L.), an expanding invasive species

Variation in thermal performance within and between populations provides the potential for adaptive responses to increasing temperatures associated with climate change. Organisms experiencing temperatures above their optimum on a thermal performance curve exhibit rapid declines in function and these supraoptimal temperatures can be a critical physiological component of range limits. The gypsy moth, Lymantria dispar (L.) (Lepidoptera: Erebidae), is one of the best‐documented biological invasions and factors driving its spatial spread are of significant ecological and economic interest. The present study examines gypsy moth sourced from different latitudes across its North American range for sensitivity to high temperature in constant temperature growth chamber experiments. Supraoptimal temperatures result in higher mortality in northern populations compared with populations from the southern range extent (West Virginia and coastal plain of Virginia, U.S.A.). Sublethal effects of high temperature on traits associated with fitness, such as smaller pupal mass, are apparent in northern and West Virginia populations. Overall, the results indicate that populations near the southern limits of the range are less sensitive to high temperatures than northern populations from the established range. However, southern populations are lower performing overall, based on pupal mass and development time, relative to northern populations. This suggests that there may be a trade‐off associated with decreased heat sensitivity in gypsy moth. Understanding how species adapt to thermal limits and possible fitness trade‐offs of heat tolerance represents an important step toward predicting climatically driven changes in species ranges, which is a particularly critical consideration in conservation and invasion ecology.     

Modelling the ontogeny of ectotherms exhibiting indeterminate growth

Numerous growth functions exist to describe the ontogeny of animals. Such functions (e.g., von Bertalanffy's equation, thermal-unit growth coefficient) are currently applied to ectotherms even though they fail to provide analytical expressions that adapt to a wide range of fluctuating temperatures. The underlying mechanisms responsible for the ontogeny of ectotherms exhibiting indeterminate growth have not yet been summarised in terms of a simple but meaningful mathematical equation. Here, a growth function is developed, with parameters having physical or biological interpretation that accommodates indeterminate growth under fluctuating temperatures assuming the latter vary seasonally. The equation is derived as a special case of von Bertalanffy's equation providing realistic growth trajectories throughout the ontogeny of several groups of ectotherms (R²>0.90). The results suggest that the effect of temperature on growth trajectory supersedes that of reproduction in an environment with fluctuating temperature. Furthermore, values of the allometric weight exponent (0<b<0.75) indicate that the rules of body surface and body weight do not apply under certain circumstances. Finally, the growth function circumvents problems associated with models based on thermodynamic and chemical kinetic principles (e.g., inability to predict growth of organisms in which ontogeny exceeds 3 months) and on rule of thermal summation (e.g., reliable only in a certain range of temperature). The growth function can handle a wide range of temperature fluctuations, encompass life stages and apply to key organisms in ecology, fisheries and agriculture.     

Local divergence of thermal reaction norms among amphibian populations is affected by pond temperature variation

Although temperature variation is known to cause large‐scale adaptive divergence, its potential role as a selective factor over microgeographic scales is less well‐understood. Here, we investigated how variation in breeding pond temperature affects divergence in multiple physiological (thermal performance curve and critical thermal maximum [CT_max]) and life‐history (thermal developmental reaction norms) traits in a network of Rana arvalis populations. The results supported adaptive responses to face two main constraints limiting the evolution of thermal adaptation. First, we found support for the faster–slower model, indicating an adaptive response to compensate for the thermodynamic constraint of low temperatures in colder environments. Second, we found evidence for the generalist–specialist trade‐off with populations from colder and less thermally variable environments exhibiting a specialist phenotype performing at higher rates but over a narrower range of temperatures. By contrast, the local optimal temperature for locomotor performance and CT_max did not match either mean or maximum pond temperatures. These results highlight the complexity of the adaptive multiple‐trait thermal responses in natural populations, and the role of local thermal variation as a selective force driving diversity in life‐history and physiological traits in the presence of gene flow.     

Modelling temperature,photoperiod and vernalization responses of Brunonia australis (Goodeniaceae) and Calandrinia sp. (Portulacaceae) to predict flowering time

Background and Aims

Crop models for herbaceous ornamental species typically include functions for temperature and photoperiod responses, but very few incorporate vernalization, which is a requirement of many traditional crops. This study investigated the development of floriculture crop models, which describe temperature responses, plus photoperiod or vernalization requirements, using Australian native ephemerals Brunonia australis and Calandrinia sp.

Methods

A novel approach involved the use of a field crop modelling tool, DEVEL2. This optimization program estimates the parameters of selected functions within the development rate models using an iterative process that minimizes sum of squares residual between estimated and observed days for the phenological event. Parameter profiling and jack-knifing are included in DEVEL2 to remove bias from parameter estimates and introduce rigour into the parameter selection process.

Key Results

Development rate of B. australis from planting to first visible floral bud (VFB) was predicted using a multiplicative approach with a curvilinear function to describe temperature responses and a broken linear function to explain photoperiod responses. A similar model was used to describe the development rate of Calandrinia sp., except the photoperiod function was replaced with an exponential vernalization function, which explained a facultative cold requirement and included a coefficient for determining the vernalization ceiling temperature. Temperature was the main environmental factor influencing development rate for VFB to anthesis of both species and was predicted using a linear model.

Conclusions

The phenology models for B. australis and Calandrinia sp. described development rate from planting to VFB and from VFB to anthesis in response to temperature and photoperiod or vernalization and may assist modelling efforts of other herbaceous ornamental plants. In addition to crop management, the vernalization function could be used to identify plant communities most at risk from predicted increases in temperature due to global warming.     

Upper thermal limits of aquatic macroinvertebrates: Comparing critical thermal maxima with 96-LT50 values

Water temperature is an important abiotic driver of aquatic ecosystems. It influences many aspects of an organism's existence including its metabolic, growth and feeding rates; fecundity; emergence; behaviour and ultimately survival. This study determined the upper thermal limits of a range of aquatic macroinvertebrates from rivers in the south-western Cape, South Africa, using two methods: the critical thermal method (CTM) and the LT₅₀ method, which is equivalent to the incipient lethal temperature (ILT) technique. The relationship between the two methods was examined with the intention of establishing if the simpler CTM could be used for future testing of thermal sensitivity thereby allowing for extrapolation of longer duration thermal stress. Of the ten species examined, Aphanicerca capensis, Paramelita nigroculus, Chimarra ambulans, Castanophlebia sp. and Afronurus barnardi were all thermally sensitive and had distinct thermal endpoints making them excellent test organisms. There was a significant positive linear relationship between the estimated incipient lethal upper temperature (ILUT) and critical thermal maximum (CTmax), which facilitates future experimental work based on CTM. Future evaluation of hourly in situ stream temperatures to identify periods of exceedance of these 96 h LT₅₀s, in addition to experimental 10 day LT₅₀s, will enable comparison of laboratory data with field conditions, and ultimately the derivation of target water temperature thresholds for management purposes.     

Thermal ecology and physiology of an elongate and semi-fossorial arthropod,the bark centipede

Organismal performance is strongly linked to temperature because of the fundamental thermal dependence of chemical reaction rates. However, the relationship between the environment and body temperature can be altered by morphology and ecology. In particular, body size and body shape can impact thermal inertia, as high surface area to volume ratios will possess low thermal mass. Habitat type can also influence thermal physiology by altering the opportunity for thermoregulation. We studied the thermal ecology and physiology of an elongate invertebrate, the bark centipede (Scolopocryptops sexspinosus). We characterized field body temperature and environmental temperature distributions, measured thermal tolerance limits, and constructed thermal performance curves for a population in southern Georgia. We found evidence that bark centipedes behaviorally thermoregulate, despite living in sheltered microhabitats, and that performance was maintained over a broad range of temperatures (over 20 °C). However, both the thermal optimum for performance and upper thermal tolerance were much higher than mean body temperature in the field. Together, these results suggest that centipedes can thermoregulate and maintain performance over a broad range of temperatures but are sensitive to extreme temperatures. More broadly, our results suggest that wide performance breadth could be an adaptation to thermal heterogeneity in space and time for a species with low thermal inertia.     

The costs of phenotypic adaptation to repeatedly fluctuating temperatures in a soil arthropod

Costs of phenotypic adaptation to changing environments have often been studied in morphological structures. Such structures typically are irreversible for at least some stage in the organism's life. In this study we investigated whether recurrent and reversible adaptation to changes in the thermal environment incurs a cost in terms of some key life-history traits in the collembolan Orchesella cincta. We exposed juvenile O. cincta to two treatments differing in the frequency of temperature fluctuation but with equal total temperature sums. In the high frequency treatment temperature fluctuated daily between 10 and 20 °C, while in the low frequency treatment temperature fluctuated on a weekly schedule. During the treatments we measured juvenile growth rate and juvenile mortality, and after six weeks the animals were transferred to constant 15 °C and adult starvation resistance was assessed. We found no significant differences between the treatments in juvenile growth rate or juvenile survival. Also, adults that had grown up under high frequency temperature fluctuations did not suffer from reduced starvation resistance compared to animals growing under low frequency temperature fluctuations. This finding supports the hypothesis that selection minimizes the production costs of inducible phenotypes and suggests that the development of optimal phenotypes and evolution of temperature reaction norms are not constrained by such costs.