UNDESIRABLE CONSEQUENCES OF NEGLECTING NONLINEARITY: RESPONSE TO COMMENTS BY LIEFTING ET AL. (2013) ON ROCHA & KLACZKO (2012)

In response to our previous study, Liefting et al. argue, in defense of their work on latitudinal variation of developmental‐rate reaction norms (RNs), that (1) developmental rate (the reciprocal of development time: rate = time^?1) is a more biologically relevant variable than development time; (2) the linear RN model is a valid approximation; and (3) three experimental points suffice to estimate RN parameters. Here, we reply to their comments. First, we give evidence that the complexity of actual development challenges the appealing simplicity of developmental rate. Using the same analysis as Liefting et al. to test their hypothesis with development time, instead of rate, reveals a pattern that is the opposite of their conclusion. Second, we show that a quadratic model is consistent with the whole development‐time RNs and explains this contradiction. Third, with the quadratic model, we introduce two parameters to study plasticity: the RN shape (the quadratic coefficient) and RN local plasticity (the derivative of the RN function). The first showed a statistically significant correlation with latitude; and the second showed a continuous variation pattern where all localized patterns can be found (positive, negative, or nonsignificant correlations with latitude) but certainly cannot be generalized.     

The genetics of phenotypic plasticity. V. Evolution of reaction norm shape

We present a general quantitative genetic model for the evolution of reaction norms. This model goes beyond previous models by simultaneously permitting any shaped reaction norm and allowing for the imposition of genetic constraints. Earlier models are shown to be special cases of our general model; we discuss in detail models involving just two macroenvironments, linear reaction norms, and quadratic reaction norms. The model predicts that, for the case of a temporally varying environment, a population will converge on (1) the genotype with the maximum mean geometric fitness over all environments, (2) a linear reaction norm whose slope is proportional to the covariance between the environment of development and the environment of selection, and (3) a linear reaction norm even if nonlinear reaction norms are possible. An examination of experimental studies finds some limited support for these predictions. We discuss the limitations of our model and the need for more realistic gametic models and additional data on the genetic and developmental bases of plasticity.     

Thermal plasticity of growth and development varies adaptively among alternative developmental pathways

Polyphenism, the expression of discrete alternative phenotypes, is often a consequence of a developmental switch. Physiological changes induced by a developmental switch potentially affect reaction norms, but the evolution and existence of alternative reaction norms remains poorly understood. Here, we demonstrate that, in the butterfly Pieris napi (Lepidoptera: Pieridae), thermal reaction norms of several life history traits vary adaptively among switch‐induced alternative developmental pathways of diapause and direct development. The switch was affected both by photoperiod and temperature, ambient temperature during late development having the potential to override earlier photoperiodic cues. Directly developing larvae had higher development and growth rates than diapausing ones across the studied thermal gradient. Reaction norm shapes also differed between the alternative developmental pathways, indicating pathway‐specific selection on thermal sensitivity. Relative mass increments decreased linearly with increasing temperature and were higher under direct development than diapause. Contrary to predictions, population phenology did not explain trait variation or thermal sensitivity, but our experimental design probably lacks power for finding subtle phenology effects. We demonstrate adaptive differentiation in thermal reaction norms among alternative phenotypes, and suggest that the consequences of an environmentally dependent developmental switch primarily drive the evolution of alternative thermal reaction norms in P. napi.     

Reaction norms for metamorphic traits in natterjack toads to larval density and pond duration

The evolution of environmentally-induced changes in phenotype or reaction norm implies both the existence at some time of genetic variation within a population for that plasticity measured by the presence of genotype x environment interaction (G x E), and that phenotypic variation affects fitness. Otherwise, the genetic structure of polygenic traits may restrict the evolution of the reaction norm by the lack of independent evolution of a given trait in different environments or by genetic trade-offs with other traits that affect fitness. In this paper, we analyze the existence of G x E in metamorphic traits to two environmental factors, larval density and pond duration in a factorial experiment with Bufo calamita tadpoles in semi-natural conditions and in the laboratory. Results showed no plastic temporal response in metamorphosis to pond durability at low larval density. The rank of genotypes did not change across different hydroperiods, implying a high genetic correlation that may constrain the evolution of the reaction norm. At high larval density a significant G x E interaction was found, suggesting the potential for the evolution of the reaction norm. A sibship (#1) attained the presumed “optimal” reaction norm by accelerating developmental rate in short duration ponds and delaying it in longer ponds. This could be translated in fitness by an increment in metamorphic survival and size at metamorphosis in short and long ponds respectively with respect to non-plastic sibships. However, genetic variability for plasticity suggests that optimal reaction norm for developmental rates may be variable and hard to achieve in the heterogeneous pond environment. Mass at metamorphosis was not plastic across different pond durations but decreased at high larval density. Significant adaptive plasticity for growth rates appeared in environments that differed drastically in level of crowding conditions, both in the field and in the laboratory. The fact that survival of juveniles metamorphosed at high density ponds was a monotonic function of metamorphic size, implies that response to selection may occur in this population of natterjacks and that genetic variability in plasticity may be a reliable mechanism maintaining adaptive genetic variation in growth rates in the highly variable pond environment.     

Individual variation in thermal plasticity and its impact on mass-scaling

Physiological processes vary widely across individuals and can influence how individuals respond to environmental change. Repeatability in how metabolic rate changes across temperatures (i.e. metabolic thermal plasticity) can influence mass-scaling exponents in different thermal environments. Moreover, repeatable plastic responses are necessary for reaction norms to respond to selective forces which is important for populations living in fluctuating environments. Nonetheless, only a small number of studies have explicitly quantified repeatability in metabolic plasticity, and fewer have explored how it can impact mass-scaling. We repeatedly measured standard metabolic rate of n = 42 delicate skinks Lampropholis delicata at six temperatures over the course of four months (N_{[observations]} = 4952). Using hierarchical statistical techniques, we accounted for multi-level variation and measurement error in our data in order to obtain more precise estimates of reaction norm repeatability and mass-scaling exponents at different acute temperatures. Our results show that individual differences in metabolic thermal plasticity were somewhat consistent over time (R_slope = 0.25, 95% CI = 2.48 × 10⁻⁸ – 0.67), however estimates were associated with a large degree of error. After accounting for measurement error, which decreased steadily with temperature, we show that among individual variance remained consistent across all temperatures. Congruently, temperature specific repeatability of average metabolic rate was stable across temperatures. Cross-temperature correlations were positive but were not uniform across the reaction norm. After taking into account multiple sources of variation, our estimates for mass-scaling did not change with temperature and were in line with published values for snakes and lizards. This implies that repeatable plastic responses may promote thermal stability of scaling exponents. Our work contributes to understanding how energy expenditure scales with abiotic and biotic factors and the capacity for reaction norms to respond to selection.     

The ontogenetic complexity of developmental constraints

Developmental constraint is a theoretically important construct bridging ontogenetic and evolutionary studies. We propose a new operationalization of this notion that exploits the unusually rich measurement structure of landmark data. We represent landmark configurations by their partial warps, a basis for morphospace that represents a set of localized features of form. A finding of developmental constraint arises from the interplay between age-varying means and age-specific variances in these subspaces of morphospace. Examination of variances and means in 16 ventral skull landmarks in the cotton rat S. fulviventer at ages 1, 10, 20, and 30 days yielded three types of developmental constraint: canalization (constraint to relatively constant form age by age); chreods (reduction of variance orthogonal to the mean trajectory over ages); and opposition (reduction of age-specific variance along the mean trajectory over ages). While canalization and chreodic constraints have been noted previously, the oppositional type of constraint appears novel. Only one of our characters, relative length and orientation of the incisive foramen, appears to be canalized. Although skull growth becomes increasingly integrated through ontogeny, our characters display a remarkable spatiotemporal complexity in patterns of variance reduction. The specific assortment of constraints observed may be related to the precociality of Sigmodon. We suggest that Waddington's diagrammatic presentation of the “epigenetic landscape” may be misleading in quantitative studies of developmental regulation.     

Uptake and utilization of14C-glycine by embryos ofSebastes melanops

Synopsis The ability of embryos of the viviparous scorpaenidSebastes melanops to take up nutrients from an exogenous substrate was demonstrated by incubating embryos at various stages of development (18–30 days after fertilization) in¹⁴C-labeled glycine for 24 h. Uptake was highest for embryos at the latest stages (28–30 days) and increased at a linear rate during the incubation period. Nutrient uptake was not time dependent in embryos at the early stages (18–22 days). Nutrient utilization byS. melanops embryos was measured by the oxidation of¹⁴C-labeled glycine to¹⁴CO₂. The amount of respired¹⁴CO₂ by the oldest embryos increased significantly at a linear rate over the 24 h incubation period. There was no evidence of nutrient utilization by the youngest embryos. The developmental changes we observed in the uptake and utilization of exogenous glycine are supported by our previous findings that the oldest embryos have fully developed mouths and guts, and require additional nutrition from intraovarian sources at this stage of development.     

np2QTL: networking phenotypic plasticity quantitative trait loci across heterogeneous environments

Despite its critical importance to our understanding of plant growth and adaptation, the question of how environment‐induced plastic response is affected genetically remains elusive. Previous studies have shown that the reaction norm of an organism across environmental index obeys the allometrical scaling law of part‐whole relationships. The implementation of this phenomenon into functional mapping can characterize how quantitative trait loci (QTLs) modulate the phenotypic plasticity of complex traits to heterogeneous environments. Here, we assemble functional mapping and allometry theory through Lokta?Volterra ordinary differential equations (LVODE) into an R‐based computing platform, np²QTL, aimed to map and visualize phenotypic plasticity QTLs. Based on LVODE parameters, np²QTL constructs a bidirectional, signed and weighted network of QTL?QTL epistasis, whose emergent properties reflect the ecological mechanisms for genotype?environment interactions over any range of environmental change. The utility of np²QTL was validated by comprehending the genetic architecture of phenotypic plasticity via the reanalysis of published plant height data involving 3502 recombinant inbred lines of maize planted in multiple discrete environments. np²QTL also provides a tool for constructing a predictive model of phenotypic responses in extreme environments relative to the median environment.     

The development of the macronucleus in the ciliated protozoan Stylonychia mytilus

Ciliated protozoa are characterized by generative micronuclei and vegetative polyploid macronuclei. Micronuclei of Stylonychia mytilus contain 1 600 times as much DNA per haploid genome as E. coli. Most of this DNA is shown to be repetitive. The development of the macronucleus involves, as demonstrated by cytology, only 1/3 of the chromosomes which in a first replication phase are polytenized in probably 5 replication steps and appear as giant chromosomes. At this developmental stage considerable amounts of repetitive DNA are still present in the chromosomes. During the subsequent disintegration phase more than 90% of the DNA are eliminated from the macronucleus anlage. The remainder is further replicated five times and composes the final macronucleus. Since this DNA reassociates with a reaction rate almost identical to an ideal second order reaction its kinetic complexity can be determined by comparison with the kinetic complexity of E. coli DNA. Macronuclear DNA reassociates with a kinetic complexity of 26 times the kinetic complexity of E. coli DNA (corrected for GC content) which indicates that macronuclear DNA sequences exist at a ploidy level of 4 096 C. We assume that macronuclear DNA may be present only once per haploid genome. In this case it represents only 1.6% of the DNA in micronuclei or 10% of the DNA in the giant chromosome stage.     

THE EVOLUTION OF PHENOTYPIC PLASTICITY IN LIFE-HISTORY TRAITS: PREDICTIONS OF REACTION NORMS FOR AGE AND SIZE AT MATURITY

We used life-history theory to predict reaction norms for age and size at maturation. We assumed that fecundity increases with size and that juvenile mortality rates of offspring decrease as ages-at-maturity of parents increase, then calculated the reaction norm by varying growth rate and calculating an optimal age at maturity for each growth rate. The reaction norm for maturation should take one of at least four shapes that depend on specific relations between changes in growth rates and changes in adult mortality rates, juvenile mortality rates, or both. Most organisms should mature neither at a fixed size nor at a fixed age, but along an age-size trajectory. The model makes possible a clear distinction between the genetic and phenotypic components of variation. The evolved response to selection is reflected in the shape and position of the reaction norm. The phenotypic response of a single organism to rapid or slow growth is defined by the location of its maturation event as a point on the reaction norm. A quantitative test with data from 19 populations and species of fish showed that predictions were in good agreement with observations (r = 0.93, P < 0.0001). The predictions of the model also agreed qualitatively with observed phenotypic variation in age and size at maturity in humans, platyfish, fruit flies, and red deer. This preliminary success suggests that experiments designed to test the predictions directly will be worthwhile.     

Life history plasticity in the satyrine butterfly Lasiommata petropolitana: investigating an adaptive reaction norm

This study addresses the general hypothesis that insects living in seasonal environments should shorten development times at progressively later dates in the growth season, and that insects living outside equatorial areas should use daylength as a cue to determine the date. Diapause strategies and reaction norms relating the duration of larval development to daylength was investigated in a French population of the butterfly, Lasiommata petropolitana. The results are compared with those of an earlier study of the species in Sweden. Because of the diapausing strategy and phenology of the population, it was expected that an adaptive reaction norm relating larval time to daylength should have a positive slope, i.e. relatively shorter daylengths induce faster growth and development. This prediction was supported, and the reaction norm was qualitatively similar to the one found in Swedish populations. In the French population it was, however, shifted to a range of shorter photoperiods which corresponds to the regime of shorter daylengths in southern Europe. Shorter larval development times and high growth rates were associated with a reduction in pupal size, suggesting a trade off between time and size at pupation. There was no evidence of a trade off between growth rate and starvation endurance. The results suggests that the daylength-dependent decision of what growth trajectory an individual larva will follow, is not made continuously but rather at one or a few occasions during larval development. It is clear that larvae of L. petropolitana make developmental decisions in relation to the daylength they experience during larval growth. The result is a reaction norm that agrees closely to what is predicted by some life history models, suggesting that it is an adaptation for optimising life history traits in a seasonal environment.     

MEASURING SELECTION ON REACTION NORMS: AN EXPLORATION OF THE EUROSTA-SOLIDAGO SYSTEM

The sensitivity of genotypic expression to the environment can be depicted as the reaction norm, which is defined as the array of phenotypes produced by a single genotype over a range of environments. We studied selection on reaction norms of the gall-inducing insect Eurosta solidaginis (Diptera; Tephritidae), which attacks tall goldenrod Solidago altissima (Compositae). Gall size was treated as a component of insect phenotype and attributes of the host plant as environmental influences on gall development. Genetic differences in the response of gall size to plant lag time (the number of days before a plant responds to the gall maker) were examined. Reaction norms for full-sib families of flies were quantified as linear functions; the elevation of the function denoted gall size produced by the family averaged across all plants, and the function's slope denoted family sensitivity to lag time. Expected fitness of each family was regressed over reaction norm elevation and slope to yield selection gradients on these reaction norm parameters. Directional selection on gall size averaged across environments is four times stronger than selection on sensitivity. Yet, genetic variation for sensitivity contributes more than twice as much to gall phenotypic variance as family mean gall size. Our results suggest that selection on environmental sensitivity will be weak for populations restricted to a narrow segment of an environmental gradient, but strong for broadly distributed species.     

Reaction norms and the genetic basis of phenotypic plasticity in the wing pattern of the butterfly Bicyclus anynana

The genetic basis of the dry-wet season polyphenism of wing pattern in response to temperature shown by Bicyclus anynana was studied, using a split-family design over four temperatures. Reaction norms crossed, but were only linear in the three highest temperatures, and only when larval development time was used as the environmental axis. Significant full-sib additive variances (V_A) and heritabilities (h²) for plasticity were found using slopes of reaction norms in a bootstrap procedure. Heritabilities were lower in intermediate temperatures, mainly due to differences in the residual variances (V_R). There was no clear trend in V_A across temperatures, contrary to the expectation that V_A would have been depleted by natural selection at the extreme temperatures and not depleted at the intermediate temperatures which occur less frequently in the field. Unpredictability in the onset of the following season at intermediate temperatures might lead to selection for diverse flresponses resulting in relatively high V_Rs. Theoretical models linking reaction norms to genetic parameters in separate environments were difficult to apply in this study, particularly because they are based on the assumption that V_Rs are constant. However the reaction norm approach combined with quantitative genetics provided a valuable insight into the evolution of the observed polyphenism.     

Life cycles,plasticity and palaeoecology in temnospondyl amphibians

In the largest early tetrapod clade, the temnospondyls, ontogenies were diverse and quite distinct from the life cycles of extant amphibians. Three well‐studied clades exemplify the diversity of these long‐extinct ontogenies, here analysed with respect to their bearing on developmental plasticity, reaction norms and evolution. Sclerocephalus readily adjusted by means of developmental evolution to different lake environments. In addition, plasticity (reaction norm) played a significant role, apparent both morphologically and by altered developmental traits. Size increase and extension of the ontogenetic trajectory gave larger predators, a phenomenon also found in the dissorophoid Micromelerpeton. Whereas Sclerocephalus was throughout preying on the same fishes, Micromelerpeton was able to fit into different trophic levels. In the branchiosaurid Apateon, a biphasic life cycle was established, with metamorphosis producing a terrestrial morph in some species; truncation of the ontogenetic trajectory gave a sexually mature larva as an alternative morph (neoteny). Plasticity was high in the larval morphs, permitting neotenes to live as filter feeders or small carnivores. Fine‐tuning of development permitted Apateon populations to adjust to specific lake properties and readily change from a filter‐feeding to carnivorous mode of life. In the nonmetamorphosing Triassic Gerrothorax, morphology was extremely conserved, but histology reveals much plasticity at the microscopical level, correlating with fluctuating salinity and water energy. In responding to environmental fluctuations by enhanced plasticity, the studied temnospondyls managed to populate lakes inhabitable to other tetrapods and fishes.     

The relationship between habitat permanence and larval development in California spadefoot toads: field and laboratory comparisons of developmental plasticity

We evaluated differences in larval habitats and life history of three species of spadefoot toads, then compared their life histories in a common garden study. Our field work defined the selective regime encountered by each species. Our Great Basin spadefoot (Spea intermontana) bred asynchronously in permanent streams and springs where there was no risk of larval mortality due to drying. The water chemistry remained fairly stable throughout the larval period. The western spadefoot toad, Sp. hammondii, bred fairly synchronously following heavy spring rains in temporary pools that remained filled an average of 81 d. Fifteen % of the breeding pools dried completely on or before the day the first larvae metamorphosed. The desert spadefoot toad, Scaphiopus couchii, bred synchronously after heavy summer showers in very short duration pools; 62% of the breeding pools dried completely on or before the day the first larvae metamorphosed. The concentration of ammonium nitrogen and CaCO₃ increased markedly as the Sp. hammondii and S. couchii pools dried. S. couchii attained metamorphosis at a much earlier age and smaller size than the other two species. S. couchii also showed little variation in the age at metamorphosis but considerable variation in the size at metamorphosis, while the other two species varied in both age and size. The results identify some variables that could serve as cues of pool drying and demonstrate an association between breeding pool duration, breeding synchrony, development rate, and larval development. Our laboratory study yields information about the genetic basis of the differences in development and controlled comparisons of phenotypic plasticity. We manipulated food supply to study the plastic response of age and size at metamorphosis and hence construct the reaction norm for these variables as a function of growth rate. The growth rates ranged from below to above those observed in natural populations. As in the field, in the lab S. couchii attained metamorphosis at an earlier age and smaller size than the other two species. All three species had a similarly shaped reaction norm for size(y‐axis) and age (x‐axis) at metamorphosis, which was a concave upward curve. A consequence of this shape is that age at metamorphosis changes more readily at low levels of food availability and size at metamorphosis changes more readily at high levels of food availability. If we restrict our observations to just those growth rates that are seen in nature, then S. couchii has almost no variation in the age at metamorphosis but considerable variation in size at metamorphosis, while the other two species vary in both age and size at metamorphosis. All three species increased in size at metamorphosis with increased food levels. Our comparative reaction norm approach thus demonstrates that S. couchii has adapted to ephemeral environments by shifting its growth rate reaction norm so that age at metamorphosis is uniformly fast and is not associated with growth rate. The realized variation is concentrated in size rather than age at metamorphosis.     

A simple and novel method for radiometric analysis of glucose utilization by adrenal chromaffin cells

Glucose utilization by cells and tissues can be followed by measuring the release of [³H]H₂O from added -[5-³H]glucose, and we have developed a method whereby the whole reaction and assay can be performed in a single scintillation vial. The basic principle behind our new assay is that the released tritiated hydrogen ion in water can be quantitatively exchanged with the hydroxyl proton of simple alcohols such as isoamyl alcohol. The radiolabeled alcohol can then be extracted into an organic solvent to which 2,5-diphenyloxazole and p-bis[2-(5-phenyloxazoyl)]benzene have been previously added. Using this new assay we studied isolated chromaffin cells and found them to utilize glucose at a linear rate for at least 30 min. The assay was precise and reproducible enough to allow detailed analysis of various inhibitors of glycolysis and of oxidative phosphorylation. The new method is simple and rapid, can be done in open test tubes, requires no complex equipment, and is intrinsically highly accurate.     

Determination of charge,stoichiometry and reaction constants fromI–V curve studies on a K+ transporter inNitella

Summary InNitella cells with low pump activity, the electrical characteristics of membrane transport are mainly determined by K⁺ transport. Current-voltage curves were measured at outside K⁺ concentrations ranging from 0.1 to 100 mol m^–3. Above 1 mol m^–3, current saturated at positive and at very negative potentials. It was found that theseI–V curves could be fitted by a Class 1, case 1 reaction kinetic model, which is a cyclic reaction scheme with one pair of rate constants sensitive to membrane potential (Class I) and neutral transporter (or electrically charged substrate-transporter complex, case I). The analysis revealed the relative rate constants of a 3-state model. From the linear dependence of the rate constant of substrate binding (k ₃₂) on [K⁺] _a the stoichiometry of 1 K⁺/cycle was obtained. The complex transporter substrate is very unstable (very high value ofK ₂₃) resulting in a very low density of this state and in what can be called Mitchellian behavior; namely, the driving forces resulting from the electrical and from the concentration gradient can hardly be distinguished.     

Testing the rate isomorphy hypothesis using five statistical methods

Abstract Organisms are said to be in developmental rate isomorphy when the proportions of developmental stage durations are unaffected by temperature. Comprehensive stage‐specific developmental data were generated on the cabbage beetle, Colaphellus bowringi Baly (Coleoptera: Chrysomelidae), at eight temperatures ranging from 16°C to 30°C (in 2°C increments) and five analytical methods were used to test the rate isomorphy hypothesis, including: (i) direct comparison of lower developmental thresholds with standard errors based on the traditional linear equation describing developmental rate as the linear function of temperature; (ii) analysis of covariance to compare the lower developmental thresholds of different stages based on the Ikemoto‐Takai linear equation; (iii) testing the significance of the slope item in the regression line of versus temperature, where p is the ratio of the developmental duration of a particular developmental stage to the entire pre‐imaginal developmental duration for one insect or mite species; (iv) analysis of variance to test for significant differences between the ratios of developmental stage durations to that of pre‐imaginal development; and (v) checking whether there is an element less than a given level of significance in the p‐value matrix of rotating regression line. The results revealed no significant difference among the lower developmental thresholds or among the aforementioned ratios, and thus convincingly confirmed the rate isomorphy hypothesis.