Search

Research on mathematical cognition, learning, and instruction (MCLI) often takes cognition as its point of departure and considers instruction at a later point in the research cycle. In this article, we call for psychologists who study MCLI to reflect on the "status quo" of their research practices and to consider making instruction an earlier and more central aspect of their work. We encourage scholars of MCLI (a) to consider the needs of educators and schools when selecting research questions and developing interventions; (b) to compose research teams that are diverse in the personal, disciplinary, and occupational backgrounds of team members; (c) to make efforts to broaden participation in research and to conduct research in authentic settings; and (d) to communicate research in ways that are accessible to practitioners and to the general public. We argue that a more central consideration of instruction will lead to shifts that make research on MCLI more theoretically valuable, more actionable for educators, and more relevant to pressing societal challenges., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Policy instruments that integrate the actions of multiple farmers are of growing interest for improving landscape scale environmental sustainability of agriculture. We conducted in-depth, semi-structured interviews with farmers in south-east England and applied thematic analysis to the responses to perform a qualitative investigation into the combined role of economic, social, and cultural barriers to cooperative environmental management, and identify possible solutions for these barriers. Interviewees recognised environmental benefits of cooperative management, but this was a low priority compared to other management activities, being seen as complex and time-consuming, with uncertainty over direct benefits to participants. External coordination could address this by overseeing information sharing on cooperation benefits and minimising the logistical burden for participants, but given farmer mistrust of outside intervention, these projects will be more successful when collaborating farmers feel they are in control. The efforts of both pioneering farmers able to initiate projects with their peers, and respected facilitators who embody local knowledge and experience, will be vital for balancing coordination and collaboration. Finding the optimal balance between these different elements will vary with local circumstances: policy should have the flexibility to accommodate this. Farmers were wary of connecting with others possessing different farming ideals and thus having to compromise on their management approach. Some respondents sought to bridge these gaps by focusing on aspects of farming identities they shared with their peers, raising the possibility that support targeting these individuals will help develop relationships that foster lasting cultural change for farmer cooperative environmental management., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Integrating diverse perspectives in psychological science can enhance innovation in research and allow research teams to better study diverse populations of individuals through an authentic lens. Despite recent efforts to better address issues of race and ethnicity in research samples, the field of psychology broadly-and the area of mathematics cognition specifically-has largely failed to support scientists from diverse racial and ethnic backgrounds. In this essay, we consider the unique contributions that scholars of color can make to psychological research in mathematics cognition. Next, we reveal common challenges faced by scholars of color and challenges to recruiting and maintaining scholars of color in our community with a focus on Black scholars. Finally, we propose actions for diversifying the "pipeline" of promising scholars., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction x/y, children are often taught to use partitioning: Break the whole into y parts and shade in x parts. Past research has shown that partitioning on number lines supports children's fraction magnitude knowledge more than partitioning on area models. However, partitioning may not take full advantage of children's prior knowledge or the structure of the number line. We tested an alternative fraction number line lesson that leveraged children's preexisting whole number knowledge using a domain-general learning tool: analogy. In a preregistered online experiment, second and third graders (N = 84, M = 8.83 years) were randomly assigned to an analogy lesson (e.g., if I know how big 3 is on a 0-4 line, I know how big ¾ is on a 0-1 line), a partitioning lesson on number lines, or a control lesson using square area models. Results showed that the analogy lesson was more effective for promoting fraction magnitude understanding than the control lesson, and it was at least as effective as the partitioning lesson. The analogy group, but not the partitioning group, significantly outperformed the control group with large-denominator fractions at retention (i.e., 1-week delayed posttest) and on transfer tests (i.e., fraction comparison). We also replicated past findings that fraction partitioning lessons are more effective on number lines than on area models, and this advantage was partially sustained after a 1-week delay. Overall, these findings highlight the power of domain-general analogy to support mathematical development. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Visual displays, such as icon arrays and risk ladders, are often used to communicate numerical health information. Number lines improve reasoning with rational numbers but are seldom used in health contexts. College students solved ratio problems related to COVID-19 (e.g., number of deaths and number of cases) in one of four randomly assigned conditions: icon arrays, risk ladders, number lines, or no accompanying visual display. As predicted, number lines facilitated performance on these problems-the number line condition outperformed the other visual display conditions, which did not perform any better than the no visual display condition. In addition, higher performance on the health-related ratio problems was associated with higher COVID-19 worry for oneself and others, higher perceptions of COVID-19 severity, and higher endorsement of intentions to engage in preventive health behaviors, even when controlling for baseline math skills. These findings have important implications for effectively presenting health statistics. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

It has long been known that people have the ability to estimate numerical quantities without counting. A standard account is that people develop a sense of the size of symbolic numbers by learning to map symbolic numbers (e.g., 6) to their corresponding numerosities (e.g. :::) and concomitant approximate magnitude system (ANS) representations. However, we here demonstrate that adults are capable of extracting fractional numerical quantities from non-symbolic visual ratios (i.e., labeling a ratio of two circle areas with the appropriate symbolic fraction). Not only were adult participants able to perform this task, but they were remarkably accurate: linear regressions on median estimates yielded slopes near 1, and accounted for 97% of the variability. Participants also performed at least as well on line-estimation and ratio-estimation tasks using non-numeric circular stimuli as they did in earlier experiments using non-symbolic numerosities, which are frequently considered to be numeric stimuli. We discuss results as consistent with accounts suggesting that non-symbolic ratios have the potential to act as a reliable and stable ground for symbolic number, even when composed of non-numeric stimuli., (© 2022. The Psychonomic Society, Inc.)

Understanding of the equal sign is associated with early algebraic competence in the elementary grades and equation-solving success in middle school. Thus, it is important to find ways to build foundational understanding of the equal sign as a relational symbol. Past work promoted a conception of the equal sign as meaning "the same as". However, recent work highlights another dimension of relational understanding-a substitutive conception, which emphasizes the idea that an expression can be substituted for another equivalent one. This work suggests a substitutive conception may support algebra performance above and beyond a sameness conception alone. In this paper, we share a subset of results from an online intervention designed to foster a relational understanding of the equal sign among fourth and fifth graders ( n  = 146). We compare lessons focused on a sameness conception alone and a dual sameness and substitutive conception to each other, and we compare both to a control condition. The lessons influenced students' likelihood of producing and endorsing sameness and substitutive definitions of the equal sign. However, the impact of the lessons on students' approaches to missing value equations was less clear. We discuss possible interpretations, and we argue that further research is needed to explore the roles of sameness and substitutive views of the equal sign in supporting structural approaches to algebraic equation solving., (© FIZ Karlsruhe 2022.)

Clarke and Beck suggest that the ratio processing system (RPS) may be a component of the approximate number system (ANS), which they suggest represents rational numbers. We argue that available evidence is inconsistent with their account and advocate for a two-systems view. This implies that there may be many access points for numerical cognition - and that privileging the ANS may be a mistake.

At the onset of the coronavirus disease (COVID-19) global pandemic, our interdisciplinary team hypothesized that a mathematical misconception-whole number bias (WNB)-contributed to beliefs that COVID-19 was less fatal than the flu. We created a brief online educational intervention for adults, leveraging evidence-based cognitive science research, to promote accurate understanding of rational numbers related to COVID-19. Participants from a Qualtrics panel (N = 1,297; 75% White) were randomly assigned to an intervention or control condition, solved health-related math problems, and subsequently completed 10 days of daily diaries in which health cognitions and affect were assessed. Participants who engaged with the intervention, relative to those in the control condition, were more accurate and less likely to explicitly mention WNB errors in their strategy reports as they solved COVID-19-related math problems. Math anxiety was positively associated with risk perceptions, worry, and negative affect immediately after the intervention and across the daily diaries. These results extend the benefits of worked examples in a practically relevant domain. Ameliorating WNB errors could not only help people think more accurately about COVID-19 statistics expressed as rational numbers, but also about novel future health crises, or any other context that involves information expressed as rational numbers. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Insects coordinate the opening and closing of spiracles with convective ventilatory movements to produce considerable intraspecific and interspecific variation in gas exchange patterns. But fundamental questions remain regarding how these movements are coordinated and modulated by central and peripheral respiratory chemoreceptors, and where these chemoreceptors are located and how they function. Recent findings have revealed regions of the CNS that generate coordinated respiratory motor activity, while peripheral neurons sensitive to respiratory gases have been identified in Drosophila. Importantly, plasticity in structure and function of neural elements of respiratory control indicate the need for caution when generalizing the mechanistic basis for breathing in insects, and an adaptive explanation for breathing pattern variability., (Copyright © 2021 Elsevier Inc. All rights reserved.)

Humans perceptually extract quantity information from our environments, be it from simple stimuli in isolation, or from relational magnitudes formed by taking ratios of pairs of simple stimuli. Some have proposed that these two types of magnitude are processed by a common system, whereas others have proposed separate systems. To test these competing possibilities, the present study examined the developmental trajectories of simple and relational magnitude discrimination and relations among these abilities for preschoolers (n = 42), 2nd-graders (n = 31), 5th-graders (n = 29), and adults (n = 32). Participants completed simple magnitude and ratio discrimination tasks in four different nonsymbolic formats, using dots, lines, circles, and irregular blobs. All age cohorts accurately discriminated both simple and ratio magnitudes. Discriminability differed by format such that performance was highest with line and lowest with dot stimuli. Moreover, developmental trajectories calculated for each format were similar across simple and ratio discriminations. Although some characteristics were similar for both types of discrimination, ratio acuity in a given format was more closely related with ratio acuities in alternate formats than to within-format simple magnitude acuity. Results demonstrate that ratio magnitude processing shares several similarities to simple magnitude processing, but is also substantially different., (© 2020 John Wiley & Sons Ltd.)

Previously, we showed that the evolution of high acuity vision in fishes was directly associated with their unique pH-sensitive hemoglobins that allow O 2 to be delivered to the retina at PO 2 s more than ten-fold that of arterial blood (Damsgaard et al., 2019). Here, we show strong evidence that vacuolar-type H + -ATPase and plasma-accessible carbonic anhydrase in the vascular structure supplying the retina act together to acidify the red blood cell leading to O 2 secretion. In vivo data indicate that this pathway primarily affects the oxygenation of the inner retina involved in signal processing and transduction, and that the evolution of this pathway was tightly associated with the morphological expansion of the inner retina. We conclude that this mechanism for retinal oxygenation played a vital role in the adaptive evolution of vision in teleost fishes., Competing Interests: CD, HL, TH, GK, JT, AF, CS, MT, PM, CB No competing interests declared, (© 2020, Damsgaard et al.)

A fundamental question about fractions is whether they are grounded in an abstract nonsymbolic magnitude code similar to that postulated for whole numbers. Mounting evidence suggests that symbolic fractions could be grounded in mechanisms for perceiving nonsymbolic ratio magnitudes. However, systematic examination of such mechanisms in children has been lacking. We asked second- and fifth-grade children (prior to and after formal instructions with fractions, respectively) to compare pairs of symbolic fractions, nonsymbolic ratios, and mixed symbolic-nonsymbolic pairs. This paradigm allowed us to test three key questions: (a) whether children show an analog magnitude code for rational numbers, (b) whether that code is compatible with mental representations of symbolic fractions, and (c) how formal education with fractions affects the symbolic-nonsymbolic relation. We examined distance effects as a marker of analog ratio magnitude processing and notation effects as a marker of converting across numerical codes. Second and fifth graders' reaction times and error rates showed classic distance and notation effects. Nonsymbolic ratios were processed most efficiently, with mixed and symbolic notations being relatively slower. Children with more formal instruction in symbolic fractions had a significant advantage in comparing symbolic fractions but had a smaller advantage for nonsymbolic ratio stimuli. Supplemental analyses showed that second graders relied on numerator distance more than holistic distance and that fifth graders relied on holistic fraction magnitude distance more than numerator distance. These results suggest that children have a nonsymbolic ratio magnitude code and that symbolic fractions can be translated into that magnitude code., (Copyright © 2020 Elsevier Inc. All rights reserved.)

Understanding and using symbolic fractions in mathematics is critical for access to advanced STEM concepts. However, children and adults consistently struggle with fractions. Here, we take a novel perspective on symbolic fractions, considering them within the framework of relational structures in cognitive psychology, such as those studied in analogy research. We tested the hypothesis that relational reasoning ability is important for reasoning about fractions by examining the relation between scores on a domain-general test of relational reasoning (TORR Jr.) and a test of fraction knowledge consisting of various types of fraction problems in 194 second grade and 145 fifth grade students. We found that relational reasoning was a significant predictor of fractions knowledge, even when controlling for non-verbal IQ and fractions magnitude processing for both grades. The effects of relational reasoning also remained significant when controlling for overall mathematics knowledge and skill for second graders but was attenuated for fifth graders. These findings suggest that this important subdomain of mathematical cognition is integrally tied to relational reasoning and opens the possibility that instruction targeting relational reasoning may prove to be a viable avenue for improving children's fractions skills.

Algebraic competence is a major determinant of college access and career prospects, and equal sign knowledge is taken to be foundational to algebra knowledge. However, few studies have documented a causal effect of early equal sign knowledge on later algebra skill. This study assessed whether second-grade students' equal sign knowledge prospectively predicts their fourth-grade algebra knowledge, when controlling for demographic and individual difference factors. Children (N = 177; M age  = 7.61) were assessed on a battery of tests in Grade 2 and on algebraic knowledge in Grade 4. Second-grade equal sign knowledge was a powerful predictor of these algebraic skills. Findings are discussed in terms of the importance of foregrounding equal sign knowledge to promote effective pedagogy and educational equity., (© 2018 Society for Research in Child Development.)

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and connections to symbolic numbers remains in its infancy. The current research aims to further explore these similarities by investigating whether the magnitudes of nonsymbolic ratios are associated with space just as symbolic numbers are. In two experiments, we found that responses were faster on the left for smaller nonsymbolic ratio magnitudes and faster on the right for larger nonsymbolic ratio magnitudes. These results further elucidate the nature of nonsymbolic ratio processing, extending the literature of spatial-numerical associations to nonsymbolic relative magnitudes. We discuss potential implications of these findings for theories of human magnitude processing in general and how this general processing relates to numerical processing., (© 2019 Cognitive Science Society, Inc.)

The Approximate Number System (ANS) allows individuals to assess nonsymbolic numerical magnitudes (e.g., the number of apples on a tree) without counting. Several prominent theories posit that human understanding of symbolic numbers is based - at least in part - on mapping number symbols (e.g., 14) to their ANS-processed nonsymbolic analogs. Number-line estimation - where participants place numerical values on a bounded number-line - has become a key task used in research on this mapping. However, some research suggests that such number-line estimation tasks are actually proportion judgment tasks, as number-line estimation requires people to estimate the magnitude of the to-be-placed value, relative to set upper and lower endpoints, and thus do not so directly reflect magnitude representations. Here, we extend this work, assessing performance on nonsymbolic tasks that should more directly interface with the ANS. We compared adults' ( n = 31) performance when placing nonsymbolic numerosities (dot arrays) on number-lines to their performance with the same stimuli on two other tasks: Free estimation tasks where participants simply estimate the cardinality of dot arrays, and ratio estimation tasks where participants estimate the ratio instantiated by a pair of arrays. We found that performance on these tasks was quite different, with number-line and ratio estimation tasks failing to the show classic psychophysical error patterns of scalar variability seen in the free estimation task. We conclude the constraints of tasks using stimuli that access the ANS lead to considerably different mapping performance and that these differences must be accounted for when evaluating theories of numerical cognition. Additionally, participants showed typical underestimation patterns in the free estimation task, but were quite accurate on the ratio task. We discuss potential implications of these findings for theories regarding the mapping between ANS magnitudes and symbolic numbers.

The overwhelming majority of efforts to cultivate early mathematical thinking rely primarily on counting and associated natural number concepts. Unfortunately, natural numbers and discretized thinking do not align well with a large swath of the mathematical concepts we wish for children to learn. This misalignment presents an important impediment to teaching and learning. We suggest that one way to circumvent these pitfalls is to leverage students' non-numerical experiences that can provide intuitive access to foundational mathematical concepts. Specifically, we advocate for explicitly leveraging a) students' perceptually based intuitions about quantity and b) students' reasoning about change and variation, and we address the affordances offered by this approach. We argue that it can support ways of thinking that may at times align better with to-be-learned mathematical ideas, and thus may serve as a productive alternative for particular mathematical concepts when compared to number. We illustrate this argument using the domain of ratio, and we do so from the distinct disciplinary lenses we employ respectively as a cognitive psychologist and as a mathematics education researcher. Finally, we discuss the potential for productive synthesis given the substantial differences in our preferred methods and general epistemologies.

The three target articles presented in this special issue converged on an emerging theme: the importance of spatial proportional reasoning. They suggest that the ability to map between symbolic fractions (like 1/5) and nonsymbolic, spatial representations of their sizes or magnitudes may be especially important for building robust fractions knowledge. In this commentary, we first reflect upon where these findings stand in a larger theoretical context, largely borrowed from mathematics education research. Next, we emphasize parallels between this work and emerging work suggesting that nonsymbolic proportional reasoning may provide an intuitive foundation for understanding fraction magnitudes. Finally, we end by exploring some open questions that suggest specific future directions in this burgeoning area.

Although many researchers theorize that primitive numerosity processing abilities may lay the foundation for whole number concepts, other classes of numbers, like fractions, are sometimes assumed to be inaccessible to primitive architectures. This research presents evidence that the automatic processing of nonsymbolic magnitudes affects processing of symbolic fractions. Participants completed modified Stroop tasks in which they selected the larger of two symbolic fractions while the ratios of the fonts in which the fractions were printed and the overall sizes of the compared fractions were manipulated as irrelevant dimensions. Participants were slower and less accurate when nonsymbolic dimensions of printed fractions were incongruent with the symbolic comparison decision. Results indicated a robust basic sensitivity to nonsymbolic ratios that exceeds prior conceptions about the accessibility of fraction values. Results also indicated a congruity effect for overall fraction size, contrary to findings of prior research. These findings have implications for extending theory about the nature of human number sense and mathematical cognition more generally., (Copyright © 2016 Cognitive Science Society, Inc.)

The present study describes and validates a novel yet simple system for simultaneous in vivo measurements of rates of aquatic CO 2 production ( Ṁ CO 2 ) and oxygen consumption ( Ṁ O 2 ), thus allowing the calculation of respiratory exchange ratios (RER). Diffusion of CO 2 from the aquatic phase into a gas phase, across a hollow fibre membrane, enabled aquatic Ṁ CO 2  measurements with a high-precision infrared gas CO 2 analyser. Ṁ O 2  was measured with a P O 2  optode using a stop-flow approach. Injections of known amounts of CO 2 into the apparatus yielded accurate and highly reproducible measurements of CO 2 content ( R 2 =0.997, P <0.001). The viability of in vivo measurements was demonstrated on aquatic dragonfly nymphs (Aeshnidae; wet mass 2.17 mg-1.46 g, n =15) and the apparatus produced precise Ṁ CO 2  ( R 2 =0.967, P <0.001) and Ṁ O 2  ( R 2 =0.957, P <0.001) measurements; average RER was 0.73±0.06. The described system is scalable, offering great potential for the study of a wide range of aquatic species, including fish., (© 2017. Published by The Company of Biologists Ltd.)

Leibovich et al.'s theory neither accounts for the deep connections between whole numbers and other classes of number nor provides a potential mechanism for mapping continuous magnitudes to symbolic numbers. We argue that focusing on non-symbolic ratio processing abilities can furnish a more expansive account of numerical cognition that remedies these shortcomings.

What basic capacities lay the foundation for advanced numerical cognition? Are there basic nonsymbolic abilities that support the understanding of advanced numerical concepts, such as fractions? To date, most theories have posited that previously identified core numerical systems, such as the approximate number system (ANS), are ill-suited for learning fraction concepts. However, recent research in developmental psychology and neuroscience has revealed a ratio-processing system (RPS) that is sensitive to magnitudes of nonsymbolic ratios and may be ideally suited for supporting fraction concepts. We provide evidence for this hypothesis by showing that individual differences in RPS acuity predict performance on four measures of mathematical competence, including a university entrance exam in algebra. We suggest that the nonsymbolic RPS may support symbolic fraction understanding much as the ANS supports whole-number concepts. Thus, even abstract mathematical concepts, such as fractions, may be grounded not only in higher-order logic and language, but also in basic nonsymbolic processing abilities., (© The Author(s) 2015.)

Objective: The present retrospective study was performed to assess the anatomical features of the pedicle in isthmic spondylolisthesis and to correlate this with degree of slip., Methods: Twenty-six patients with isthmic spondylolytic spondylolisthesis were studied. Relevant patient variables, length, width, height of the L5 pedicle, and the product of height and angle between pedicle and vertebral midline were measured. The length of the posterior compartment of the pedicle was calculated as the product of the pedicle length and angle., Results: With measurements comparable to those reported in previous publications, the L5 pedicle was found to be longer, and the height and width of the body shorter, than published values for patients without spondylolysis. The difference between the length of the posterior compartment of the pedicle and height of body is significantly proportional to the degree of slip and may reflect an adaptive response for stabilizing the vertebral body with posterior elements., Conclusions: The pedicle anatomy was found to be altered in patients with L5 S1 spondylolytic spondylolisthesis. These anatomical changes have implications for surgeons performing fusion operations in terms of length of screw, landmarks used and entry approach., (© 2015 Chinese Orthopaedic Association and Wiley Publishing Asia Pty Ltd.)

This study presents evidence that humans have intuitive, perceptually based access to the abstract fraction magnitudes instantiated by nonsymbolic ratio stimuli. Moreover, it shows these perceptually accessed magnitudes can be easily compared with symbolically represented fractions. In cross-format comparisons, participants picked the larger of two ratios. Ratios were presented either symbolically as fractions or nonsymbolically as paired dot arrays or as paired circles. Response patterns were consistent with participants comparing specific analog fractional magnitudes independently of the particular formats in which they were presented. These results pose a challenge to accounts that argue human cognitive architecture is ill-suited for processing fractions. Instead, it seems that humans can process nonsymbolic ratio magnitudes via perceptual routes and without recourse to conscious symbolic algorithms, analogous to the processing of whole number magnitudes. These findings have important implications for theories regarding the nature of human number sense - they imply that fractions may in some sense be natural numbers, too., (Copyright © 2015 Elsevier Inc. All rights reserved.)

The rate of change in resting metabolic rate (RMR) as a result of a temperature increase of 10 °C is termed the temperature coefficient (Q10), which is often used to predict how an organism's total MR will change with temperature. However, this method neglects a potentially key component of MR; changes in activity level (and thus activity MR; AMR) with temperature may significantly alter the relationship between MR and temperature. The present study seeks to describe how thermal effects on total MR estimated from RMR-temperature measurements can be misleading when the contribution of activity to total MR is neglected. A simple conceptual framework illustrates that since the relationship between activity levels and temperature can be different to the relationship between RMR and temperature, a consistent relationship between RMR and total MR cannot be assumed. Thus the thermal effect on total MR can be considerably different to the thermal effect on RMR. Simultaneously measured MR and activity from three ectotherm species with differing behavioural and physiological ecologies were used to empirically examine how changes in temperature drive changes in RMR, activity level, AMR and the Q10 of MR. These species exhibited varied activity- and MR-temperature relationships, underlining the difficulty in predicting thermal influences on activity levels and total MR. These data support a model showing that thermal effects on total MR will deviate from predictions based solely on RMR; this deviation will depend upon the difference in Q10 between AMR and RMR, and the relative contribution of AMR to total MR. To develop mechanistic, predictive models for species' metabolic responses to temperature changes, empirical information about the relationships between activity levels, MR and temperature, such as reported here, is required. This will supersede predictions based on RMR alone.

The function and mechanism underlying discontinuous gas exchange in terrestrial arthropods continues to be debated. Three adaptive hypotheses have been proposed to explain the evolutionary origin or maintenance of discontinuous gas exchange cycles (DGCs), which may have evolved to reduce respiratory water loss, facilitate gas exchange in high CO2 and low O2 micro-environments, or to ameliorate potential damage as a result of oversupply of O2. None of these hypotheses have unequivocal support, and several non-adaptive hypotheses have also been proposed. In the present study, we reared cockroaches Nauphoeta cinerea in selected levels of O2 throughout development, and examined how this affected growth rate, tracheal morphology and patterns of gas exchange. O2 level in the rearing environment caused significant changes in tracheal morphology and the exhibition of DGCs, but the direction of these effects was inconsistent with all three adaptive hypotheses: water loss was not associated with DGC length, cockroaches grew fastest in hyperoxia, and DGCs exhibited by cockroaches reared in normoxia were shorter than those exhibited by cockroaches reared in hypoxia or hyperoxia.

The sacred lotus Nelumbo nucifera (Gaertn.) possesses a complex system of gas canals that channel pressurized air from its leaves, down through its petioles and rhizomes, before venting this air back to the atmosphere through large stomata found in the centre of every lotus leaf. These central plate stomata (CPS) lie over a gas canal junction that connects with two-thirds of the gas canals within the leaf blade and with the larger of two discrete pairs of gas canals within the petiole that join with those in the rhizome. It is hypothesized that the lotus actively regulates the pressure, direction and rate of airflow within its gas canals by opening and closing these stomata. Impression casting the CPS reveal that they are open in the morning, close at midday and reopen in the afternoon. The periodic closure of the CPS during the day coincides with a temporary reversal in airflow direction within the petiolar gas canals. Experiments show that the conductance of the CPS decreases in response to increasing light level. This behaviour ventilates the rhizome and possibly directs benthic CO2 towards photosynthesis in the leaves. These results demonstrate a novel function for stomata: the active regulation of convective airflow., (© 2013 John Wiley & Sons Ltd.)

It has been suggested that differences in performance on number-line estimation tasks are indicative of fundamental differences in people's underlying representations of numerical magnitude. However, we were able to induce logarithmic-looking performance in adults for magnitude ranges over which they can typically perform linearly by manipulating their familiarity with the symbolic number formats that we used for the stimuli. This serves as an existence proof that individuals' performances on number-line estimation tasks do not necessarily reflect the functional form of their underlying numerical magnitude representations. Rather, performance differences may result from symbolic difficulties (i.e., number-to-symbol mappings), independently of the underlying functional form. We demonstrated that number-line estimates that are well fit by logarithmic functions need not be produced by logarithmic functions. These findings led us to question the validity of considering logarithmic-looking performance on number-line estimation tasks as being indicative that magnitudes are being represented logarithmically, particularly when symbolic understanding is in question.

Resting metabolic rates can vary greatly between individuals of the same species. These differences are generally repeatable and show moderate-to-high heritability, suggesting that they could be a target for natural selection. The present study therefore aimed to determine if inter-individual differences in resting metabolic rates (RMR) in garden skinks Lampropholis delicata were associated with inter-individual differences in a suite of physiological and behavioural variables: aerobic capacity, burst sprinting speed and thermal preference. Whole-animal measures of aerobic capacity and RMR were significantly positively correlated, but mass-independent measures were not. Burst sprinting speed and thermal preference were also not correlated with RMR.

The regulation of insect respiratory gas exchange has long been an area of interest. In particular, the reason why insects from at least five orders exhibit patterns of gas exchange that include regular periods of spiracular closure has been the source of much controversy. Three adaptive hypotheses propose that these discontinuous gas-exchange cycles (DGCs) evolved to either limit water loss across respiratory surfaces, facilitate gas exchange in underground environments or to limit oxidative damage. It is possible that DGCs evolved independently multiple times and for different reasons, but for DGCs to be a plausible target for natural selection, they must be heritable and confer a fitness benefit. In a previous study of cockroaches Nauphoeta cinerea, we demonstrated that DGCs are repeatable and extend survival under food and water restriction. Here, we show for the first time that DGCs are heritable, suggesting that they are a plausible target for natural selection., (© 2013 The Authors. Journal of Evolutionary Biology © 2013 European Society For Evolutionary Biology.)

Many insects at rest breathe discontinuously, alternating between brief bouts of gas exchange and extended periods of breath-holding. The association between discontinuous gas exchange cycles (DGCs) and inactivity has long been recognised, leading to speculation that DGCs lie at one end of a continuum of gas exchange patterns, from continuous to discontinuous, linked to metabolic rate (MR). However, the neural hypothesis posits that it is the downregulation of brain activity and a change in the neural control of gas exchange, rather than low MR per se, which is responsible for the emergence of DGCs during inactivity. To test this, Nauphoeta cinerea cockroaches had their brains inactivated by applying a Peltier-chilled cold probe to the head. Once brain temperature fell to 8°C, cockroaches switched from a continuous to a discontinuous breathing pattern. Re-warming the brain abolished the DGC and re-established a continuous breathing pattern. Chilling the brain did not significantly reduce the cockroaches' MR and there was no association between the gas exchange pattern displayed by the insect and its MR. This demonstrates that DGCs can arise due to a decrease in brain activity and a change in the underlying regulation of gas exchange, and are not necessarily a simple consequence of low respiratory demand.

Insects and spiders rely on gas-filled airways for respiration in air. However, some diving species take a tiny air-store bubble from the surface that acts as a primary O(2) source and also as a physical gill to obtain dissolved O(2) from the water. After a long history of modelling, recent work with O(2)-sensitive optodes has tested the models and extended our understanding of physical gill function. Models predict that compressible gas gills can extend dives up to more than eightfold, but this is never reached, because the animals surface long before the bubble is exhausted. Incompressible gas gills are theoretically permanent. However, neither compressible nor incompressible gas gills can support even resting metabolic rate unless the animal is very small, has a low metabolic rate or ventilates the bubble's surface, because the volume of gas required to produce an adequate surface area is too large to permit diving. Diving-bell spiders appear to be the only large aquatic arthropods that can have gas gill surface areas large enough to supply resting metabolic demands in stagnant, oxygenated water, because they suspend a large bubble in a submerged web.

Metabolic rate varies significantly between individuals, and these differences persist even when the wide range of biotic and abiotic factors that influence metabolism are accounted for. It is important to understand the life history implications of variation in metabolic rate, but they remain poorly characterised despite a growing body of work examining relationships between metabolism and a range of traits. In the present study we used laboratory-bred families (one sire to three dams) of Nauphoeta cinerea (Olivier) (speckled cockroaches) to examine the relationship between standard metabolic rate (SMR) and reproductive performance (number of offspring and gestation duration). We show that SMR is negatively associated with female gestation duration. Age at mating is negatively associated with gestation duration for females, and mass is negatively associated with the average gestation duration of the females a male was mated with. In addition to the results in the current literature, the results from the present study suggest that the association between metabolism and life history is more complex than simple relationships between metabolism and various fitness traits. Future work should consider longitudinal, ontogenetic as well as selective and quantitative genetic breeding approaches to fully examine the associations between metabolism and fitness.

The discontinuous gas exchange cycle (DGC) is a three-phase breathing pattern displayed by many insects at rest. The pattern consists of an extended breath-hold period (closed phase), followed by a sequence of rapid gas exchange pulses (flutter phase), and then a period in which respiratory gases move freely between insect and environment (open phase). This study measured CO(2) emission in resting locusts Locusta migratoria throughout ontogeny, in normoxia (21 kPa P(O2)), hypoxia (7 kPa P(O2)) and hyperoxia (40 kPa P(O2)), to determine whether body mass and ambient O(2) affect DGC phase duration. In normoxia, mean CO(2) production rate scales with body mass (M(b); g) according to the allometric power equation , closed phase duration (C; min) scales with body mass according to the equation C=8.0M(b)(0.38±0.29), closed+flutter period (C+F; min) scales with body mass according to the equation C+F=26.6M (0.20±0.25)(b) and open phase duration (O; min) scales with body mass according to the equation O=13.3M(b) (0.23±0.18). Hypoxia results in a shorter C phase and longer O phase across all life stages, whereas hyperoxia elicits shorter C, C+F and O phases across all life stages. The tendency for larger locusts to exhibit longer C and C+F phases might arise if the positive allometric scaling of locust tracheal volume prolongs the time taken to reach the minimum O(2) and maximum CO(2) set-points that determine the duration of these respective periods, whereas an increasingly protracted O phase could reflect the additional time required for larger locusts to expel CO(2) through a relatively longer tracheal pathway. Observed changes in phase duration under hypoxia possibly serve to maximise O(2) uptake from the environment, whereas the response of the DGC to hyperoxia is difficult to explain, but could be affected by elevated levels of reactive oxygen species.

Flying insects achieve the highest mass-specific aerobic metabolic rates of all animals. However, few studies attempt to maximise the metabolic cost of flight and so many estimates could be sub-maximal, especially where insects have been tethered. To address this issue, oxygen consumption was measured during tethered flight in adult locusts Locusta migratoria, some of which had a weight attached to each wing (totalling 30-45% of body mass). Mass-specific metabolic rate increased from 28±2 μmol O(2) g(-1) h(-1) at rest to 896±101 μmol O(2)g(-1) h(-1) during flight in weighted locusts, and to 1032±69 μmol O(2) g(-1) h(-1) in unweighted locusts. Maximum metabolic rate of locusts during tethered flight (m(O(2)); μmol O(2) h(-1)) increased with body mass (M(b); g) according to the allometric equation m(O(2))=994M(b)(0.75±0.19), whereas published metabolic rates of moths and orchid bees during hovering free flight (h(O(2))) are approximately 2.8-fold higher, h(O(2))=2767M(b)(0.72±0.08). The modest flight metabolic rate of locusts is unlikely to be an artefact of individuals failing to exert themselves, because mean maximum lift was not significantly different from that required to support body mass (95±8%), mean wingbeat frequency was 23.7±0.6 Hz, and mean stroke amplitude was 105±5 deg in the forewing and 96±5 deg in the hindwing - all of which are close to free-flight values. Instead, the low cost of flight could reflect the relatively small size and relatively modest anatomical power density of the locust flight motor, which is a likely evolutionary trade-off between flight muscle maintenance costs and aerial performance.

Weibel and Taylor's theory of symmorphosis predicts that the structural components of the respiratory system are quantitatively adjusted to satisfy, but not exceed, an animal's maximum requirement for oxygen. We tested this in the respiratory system of the adult migratory locust Locusta migratoria by comparing the aerobic capacity of hopping and flight muscle with the morphology of the oxygen cascade. Maximum oxygen uptake by flight muscle during tethered flight is 967±76 μmol h(-1) g(-1) (body mass specific, ±95% confidence interval CI), whereas the hopping muscles consume a maximum of 158±8 μmol h(-1) g(-1) during jumping. The 6.1-fold difference in aerobic capacity between the two muscles is matched by a 6.4-fold difference in tracheole lumen volume, which is 3.5×10(8)±1.2×10(8) μm(3) g(-1) in flight muscle and 5.5×10(7)±1.8×10(7) μm(3) g(-1) in the hopping muscles, a 6.4-fold difference in tracheole inner cuticle surface area, which is 3.2×10(9)±1.1×10(9) μm(2) g(-1) in flight muscle and 5.0×10(8)±1.7×10(8) μm(2) g(-1) in the hopping muscles, and a 6.8-fold difference in tracheole radial diffusing capacity, which is 113±47 μmol kPa(-1) h(-1) g(-1) in flight muscle and 16.7±6.5 μmol kPa(-1) h(-1) g(-1) in the hopping muscles. However, there is little congruence between the 6.1-fold difference in aerobic capacity and the 19.8-fold difference in mitochondrial volume, which is 3.2×10(10)±3.9×10(9) μm(3) g(-1) in flight muscle and only 1.6×10(9)±1.4×10(8) μm(3) g(-1) in the hopping muscles. Therefore, symmorphosis is upheld in the design of the tracheal system, but not in relation to the amount of mitochondria, which might be due to other factors operating at the molecular level.

While O(2)-binding hemoglobin-like proteins are present in many insects, prominent amounts of hemoglobin have only been found in a few species. Backswimmers of the genera Anisops and Buenoa (Notonectidae) have high concentrations of hemoglobin in the large tracheal cells of the abdomen. Oxygen from the hemoglobin is delivered to a gas bubble and controls the buoyant density, which enables the bugs to maintain their position without swimming and to remain stationary in the mid-water zone where they hunt for prey. We have obtained the cDNA sequences of three Anisops deanei hemoglobin chains by RT-PCR and RACE techniques. The deduced amino acid sequences show an unusual insertion of a single amino acid in the conserved helix E, but this does not affect protein stability or ligand binding kinetics. Recombinant A. deanei hemoglobin has an oxygen affinity of P(50) = 2.4 kPa (18 torr) and reveals the presence of a dimeric fraction or two different conformations. The absorption spectra demonstrate that the Anisops hemoglobin is a typical pentacoordinate globin. Phylogenetic analyses show that the backswimmer hemoglobins evolved within Heteroptera and most likely originated from an intracellular hemoglobin with divergent function., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

The discontinuous gas exchange cycle (DGC) is a breathing pattern displayed by many insects, characterized by periodic breath-holding and intermittently low tracheal O(2) levels. It has been hypothesized that the adaptive value of DGCs is to reduce oxidative damage, with low tracheal O(2) partial pressures (PO(2) ≈ 2-5 kPa) occurring to reduce the production of oxygen free radicals. If this is so, insects displaying DGCs should continue to actively defend a low tracheal PO(2) even when breathing higher than atmospheric levels of oxygen (hyperoxia). This behaviour has been observed in moth pupae exposed to ambient PO(2) up to 50 kPa. To test this observation in adult insects, we implanted fibre-optic oxygen optodes within the tracheal systems of adult migratory locusts Locusta migratoria exposed to normoxia, hypoxia and hyperoxia. In normoxic and hypoxic atmospheres, the minimum tracheal PO(2) that occurred during DGCs varied between 3.4 and 1.2 kPa. In hyperoxia up to 40.5 kPa, the minimum tracheal PO(2) achieved during a DGC exceeded 30 kPa, increasing with ambient levels. These results are consistent with a respiratory control mechanism that functions to satisfy O(2) requirements by maintaining PO(2) above a critical level, not defend against high levels of O(2).

Insects are at high risk of desiccation because of their small size, high surface-area-to-volume ratio, and air-filled tracheal system that ramifies throughout their bodies to transport O(2) and CO(2) to and from respiring cells. Although the tracheal system offers a high-conductance pathway for the movement of respiratory gases, it has the unintended consequence of allowing respiratory transpiration to the atmosphere. When resting, many species exchange respiratory gases discontinuously, and an early hypothesis for the origin of these discontinuous gas exchange cycles (DGCs) is that they serve to reduce respiratory water loss. In this study, we test this "hygric" hypothesis by comparing rates of CO(2) exchange and water loss among flower beetles Protaetia cretica (Cetoniinae, Scarabaeidae) breathing either continuously or discontinuously. We show that, consistent with the expectations of the hygric hypothesis, rates of total water loss are higher during continuous gas exchange than during discontinuous gas exchange and that the ratio of respiratory water loss to CO(2) exchange is lower during discontinuous gas exchange. This conclusion is in agreement with other studies of beetles and cockroaches that also support the hygric hypothesis. However, this result does not exclude other adaptive hypotheses supported by work on ants and moth pupae. This ambiguity may arise because there are multiple independent evolutionary origins of DGCs and no single adaptive function underlying their genesis. Alternatively, the observed reduction in water loss during DGCs may be a side effect of a nonadaptive gas exchange pattern that is elicited during periods of inactivity.

Metabolic rate and respiratory gas exchange patterns vary significantly both between and within species, even after a number of biotic and abiotic factors are taken into account. This suggests that such variation is of evolutionary importance, but the life history implications of this variation remain relatively poorly characterized. In the present study, we examine the effect of metabolic variation on starvation and desiccation resistance in the speckled cockroach Nauphoeta cinerea. We also compare the starvation and desiccation resistance of individuals that exchange respiratory gases continuously with those that breathe discontinuously. We show that metabolic rate has no effect on survival during food and water restriction, but cockroaches exhibiting discontinuous gas exchange cycles (DGCs) live longer than those that do not and those provisioned with water lived longer than those that were not. This finding represents the first demonstration that DGCs confer a fitness benefit, and supports the oldest hypothesis for the evolution of DGCs (which suggests that DGCs arose or are maintained to reduce respiratory water loss) as we also reveal reduced water loss (both respiratory and total) in cockroaches exhibiting discontinuous gas exchange., (© 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.)

Aquatic backswimmers (Anisops spp.) collect oxygen from the atmosphere in order to breathe underwater, carrying it within a bubble of air on the ventral surface of their body and bound within haemoglobin-filled cells inside their abdomen. These oxygen stores are interconnected via the abdominal spiracles and the tracheal system. Fibre optic oxygen probes were used to measure PO(2) changes within the air bubbles of submerged backswimmers (Anisops deanei) and these measurements were transformed into in vivo haemoglobin-oxygen equilibrium curves (OECs) using a biotonometric approach. The haemoglobin displayed a triphasic, highly sigmoid OEC with a P(50) of 3.90 kPa. Comparisons made with a previous in vitro analysis of Anisops haemoglobin demonstrate that while the apparent cooperativity and oxygen affinity are considerably higher in vivo, both measurements share unusual Hb-O(2) binding characteristics. The affinity and cooperativity of the backswimmers' haemoglobin appears adaptive as it lengthens dives and promotes neutral buoyancy. While there are limitations associated with biotonometry, the in vivo OEC accurately represents the loading and unloading of biologically available oxygen within the backswimmers' haemoglobin cells. Potential errors associated with determining the OEC are small, as evaluated with sensitivity analyses in numerical models., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

The reasons why metabolic rate (B) scales allometrically with body mass (M) remain hotly debated. The field is dominated by correlational analyses of the relationship between B and M; these struggle to disentangle competing explanations because both B and M are confounded with ontogeny, life history, and ecology. Here, we overcome these problems by using an experimental approach to test among competing metabolic theories. We examined the scaling of B in size-manipulated and intact colonies of a bryozoan and show that B scales with M(0.5). To explain this, we apply a general model based on the dynamic energy budget theory for metabolic organization that predicts B on the basis of energy allocation to assimilation, maintenance, growth, and maturation. Uniquely, this model predicts the absolute value of B, emphasizes that there is no single scaling exponent of B, and demonstrates that a single model can explain the variation in B seen in nature.

The hemimetabolous migratory locust Locusta migratoria progresses through five instars to the adult, increasing in size from 0.02 to 0.95 g, a 45-fold change. Hopping locomotion occurs at all life stages and is supported by aerobic metabolism and provision of oxygen through the tracheal system. This allometric study investigates the effect of body mass (Mb) on oxygen consumption rate (MO2, μmol h(-1)) to establish resting metabolic rate (MRO2), maximum metabolic rate during hopping (MMO2) and maximum metabolic rate of the hopping muscles (MMO2,hop) in first instar, third instar, fifth instar and adult locusts. Oxygen consumption rates increased throughout development according to the allometric equations MRO2=30.1Mb(0.83±0.02), MMO2=155Mb(1.01±0.02), MMO2,hop=120Mb(1.07±0.02) and, if adults are excluded, MMO2,juv=136Mb(0.97±0.02) and MMO2,juv,hop=103Mb(1.02±0.02). Increasing body mass by 20-45% with attached weights did not increase mass-specific MMO2 significantly at any life stage, although mean mass-specific hopping MO2 was slightly higher (ca. 8%) when juvenile data were pooled. The allometric exponents for all measures of metabolic rate are much greater than 0.75, and therefore do not support West, Brown and Enquist’s optimised fractal network model, which predicts that metabolism scales with a 3⁄4-power exponent owing to limitations in the rate at which resources can be transported within the body.

Taylor and Weibel's theory of symmorphosis predicts that structures of the respiratory system are matched to maximum functional requirements with minimal excess capacity. We tested this hypothesis in the respiratory system of the migratory locust, Locusta migratoria, by comparing the aerobic capacity of the jumping muscles with the morphology of the oxygen cascade in the hopping legs using an intraspecific allometric analysis of different body mass (M(b)) at selected juvenile life stages. The maximum oxygen consumption rate of the hopping muscle during jumping exercise scales as M(b)(1.02±0.02), which parallels the scaling of mitochondrial volume in the hopping muscle, M(b)(1.02±0.08), and the total surface area of inner mitochondrial membrane, M(b)(0.99±0.10). Likewise, at the oxygen supply end of the insect respiratory system, there is congruence between the aerobic capacity of the hopping muscle and the total volume of tracheoles in the hopping muscle, M(b)(0.99±0.16), the total inner surface area of the tracheoles, M(b)(0.99±0.16), and the anatomical radial diffusing capacity of the tracheoles, M(b)(0.99±0.18). Therefore, the principles of symmorphosis are upheld at each step of the oxygen cascade in the respiratory system of the migratory locust.

Ventilatory control of internal CO(2) plays an important role in regulating extracellular acid-base balance in terrestrial animals. While this phenomenon is well understood among vertebrates, the role that respiration plays in the acid-base balance of insects is in need of much further study. To measure changes in insect haemolymph pH, we implanted micro pH optodes into the haemocoel of cockroaches (Nauphoeta cinerea). They were then exposed to normoxic, hypoxic, hyperoxic and hypercapnic atmospheres while their haemolymph pH, VCO(2) and abdominal ventilation frequency were measured simultaneously. Intratracheal O(2) levels were also measured in separate experiments. It was found that cockroaches breathing continuously control their ventilation to defend a haemolymph pH of 7.3, except under conditions where hypoxia (<10% O(2)) induces hyperventilation, or where ambient hypercapnia is in excess of haemolymph (>1% CO(2)). In contrast, intratracheal O(2) levels fluctuated widely, but on average remained above 15% in normoxic (21% O(2)) atmospheres. Decapitation caused the cockroaches to display discontinuous gas exchange cycles (DGCs). The alternating periods of ventilation and apnoea during DGCs caused haemolymph pH to fluctuate by 0.11 units. Exposure to hypoxia caused haemolymph pH to increase and initiated brief bouts of spiracular opening prior to the active ventilation phase. The spontaneous occurrence of DGCs in decapitated cockroaches indicates that central pattern generators in the thoracic and abdominal ganglia generate the periodic gas exchange pattern in the absence of control from the cephalic ganglion. This pattern continues to maintain gas exchange, but with less precision.