The size–grain hypothesis: do macroarthropods see a fractal world?

Abstract.  1. In the size–grain hypothesis (a) long legs allow walking organisms to step over gaps and pores in substrate but prohibit them from entering those gaps; (b) the world is more rugose for small organisms; and (c) the relative cost of long legs increases as organisms grow smaller. The hypothesis predicts a positive allometry of leg length ( = mass ^b where b > 0.33 of isometry), a pattern that robustly holds for ants.
2. Toward testing for leg length allometries in other taxa, arthropods were extracted from the Panama leaf litter and measured. Three common taxa (spiders, diplopods, Coleoptera) yielded b s that exceeded 0.33 while three others (Acarina, Pseudoscorpiones, and Collembola) did not. The exponent b tended to increase ( P = 0.06, n = 7) with an arthropod taxon's average body mass.
3. Since leg length in cursorial organisms tends toward isometry in very small and very large taxa (i.e. mammals) this suggests that the size–grain hypothesis may best apply at a transition zone of intermediate body mass: the macroarthropods.
4. Body length was a robust predictor of mass in all groups despite variation in shape.     

The interspecific range size–body size relationship in Australian frogs

Aim There is substantial residual scatter about the positive range size–body size relationship in Australian frogs. We test whether species’ life history and abundance can account for this residual scatter. Location Australia. Methods Multiple regressions were performed using both cross‐species and independent contrasts analyses to determine whether clutch size, egg size and species abundance account for variation in range size over and above the effects of body size. Results In both cross‐species and independents contrasts models with body size, clutch size and egg size as predictors, partial r² values revealed that only egg size was significantly and uniquely related to range size. Contrary to expectation, neither body size nor clutch size could account for significant variation in range size. Incorporating species abundance as a predictor in further multiple regression analysis demonstrated that while abundance accounted for a significant proportion of range size variation, the contribution of egg size was reduced but still significant. Notably, non‐significant relationships persisted between range size and both body size and clutch size. Conclusions The weak positive correlation between body size and range size in Australian frogs disappears after accounting for species abundance and egg size. Our findings demonstrate that species with both high local abundance and small eggs occupy comparatively wider geographical ranges than species with low abundance and large eggs.     

Metabolic scaling in insects supports the predictions of the WBE model

The functional association between body size and metabolic rate (BS-MR) is one of the most intriguing issues in ecological physiology. An average scaling exponent of 3/4 is broadly observed across animal and plant taxa. The numerical value of 3/4 is theoretically predicted under the optimized version of West, Brown, and Enquist's vascular resource supply network model. Insects, however, have recently been proposed to express a numerically different scaling exponent and thus application of the WBE network model to insects has been rejected. Here, we re-analyze whether such variation is indeed supported by a global deviation across all insect taxa at the order and family levels to assess if specific taxa influence insect metabolic scaling. We show that a previous reported deviation is largely due to the effect of a single insect family (Termitidae). We conclude that the BS-MR relationship in insects broadly supports the core predictions of the WBE model. We suggest that the deviation observed within the termites warrants further investigation and may be due to either difficulty in accurately measuring termite metabolism and/or particularities of their life history. Future work on allometric scaling should assess the nature of variation around the central tendencies in scaling exponents in order to test if this variation is consistent with core assumptions and predictions of the WBE model that stem by relaxing its secondary optimizing assumptions that lead to the 3/4 exponent.     

The origin of allometric scaling laws in biology

The empirical rules relating metabolic rate and body size are described in terms of (i) a scaling exponent, which refers to the ratio of the fractional change in metabolic rate to a change in body size, (ii) a proportionality constant, which describes the rate of energy expenditure in an organism of unit mass. This article integrates the chemiosmotic theory of energy transduction with the methods of quantum statistics to propose a molecular mechanism which, in sharp contrast to competing models, explains both the variation in scaling exponents and the taxon-specific differences in proportionality constants. The new model is universal in the sense that it applies to unicellular organisms, plants and animals.     

代谢异速生长理论及其在微生物生态学领域的应用

新陈代谢是生物的基本生理过程,影响生物在不同环境中参与物质循环和能量转化的过程.代谢速率作为生物体重要的生命过程指标,几乎影响所有的生物活性速率,且在很多研究中均表现出异速生长现象.所谓代谢异速是指生物体代谢速率与其个体大小(或质量)之间存在的幂函数关系.代谢异速生长理论的提出,从机制模型角度解释了代谢异速关系这一普遍存在的生命现象.该理论利用分形几何学及流体动力学等原理,从生物能量学角度阐释了异速生长规律的机理,证实了3/4权度指数的存在;但同时有研究表明,权度指数因环境因素等影响处于2/3-1范围之间而非定值.随着研究工作的深入,代谢异速生长理论研究从起初的宏观动植物领域拓展到了微生物领域,在研究微生物的代谢异速生长理论时,可将微生物的可操作分类单元(Operational taxonomic unit,OTU)或具有特定功能的功能群视为一个微生物个体,基于其遗传多样性和功能多样性特征进行表征,以便于将微生物群落多样性与其生态功能性联系起来,使该理论在微生物生态学领域得到有效的补充和完善.尽管细菌具有独特的生物学特性,但与宏观生物系统中观测到的现象表现出明显的一致性.有研究表明,3个农田土壤细菌基于遗传多样性的OTU数的平均周转率分别为0.71、0.80和0.84,介于2/3与1之间,可能与生物代谢异速指数有一定关联,为微生物代谢异速指数的研究提出了一个参考解决方案.鉴于微生物个体特征和生物学特性,在分析代谢速率与个体大小关系中,从微生物单位个体的定义、个体大小表征到计量单位的统一,仍需更多的理论支持.分析了代谢异速生长理论在微生物与生态系统功能关系研究中的可能应用,延伸了该理论的应用范围,并对尚待加强的研究问题进行了评述和展望.     

Allometry between leg and body length of insects: lack of support for the size–grain hypothesis

• 1 The size–grain hypothesis ( Kaspari & Weiser, 1999 ) states that (1) as organisms decrease in size, they perceive their environment as being more rugose; (2) long legs allow organisms to step over obstacles but hinder them from entering small gaps; and (3) as the size of an organism decreases, the benefits of long legs begin to be outweighed by the costs of construction. Natural selection should therefore favour proportionally longer legs in larger organisms, thereby leading to a positive allometry between leg and body length (scaling exponent b > 1).
• 2 Here we compare the scaling exponent of leg‐to‐body length relationships among insects that walk, walk and fly, and predominantly fly. We measured the lengths of the hind tibia, hind femur, and body length of each species.
• 3 The taxa varied considerably in the scaling exponent b. In seven out of ten groups (Formicidae, Isoptera, Carabidae, Pentatomidae, Apidae, Lepidoptera, Odonata adult), b was significantly greater than one. However, there was no gradual decrease in b from walking to walking/flying to flying insects.
• 4 The results of the present study provide no support for the size–grain hypothesis. We propose that leg length is not only affected by the rugosity of the environment, but also by (1) functional adaptations, (2) phylogeny, (3) lifestyle, (4) the type of insect development (hemimetabolism or holometabolism), and (5) constraints of gas exchange.

     

Beyond the '3/4-power law': variation in the intra- and interspecific scaling of metabolic rate in animals

In this review I show that the '3/4-power scaling law' of metabolic rate is not universal, either within or among animal species. Significant variation in the scaling of metabolic rate with body mass is described mainly for animals, but also for unicells and plants. Much of this variation, which can be related to taxonomic, physiological, and/or environmental differences, is not adequately explained by existing theoretical models, which are also reviewed. As a result, synthetic explanatory schemes based on multiple boundary constraints and on the scaling of multiple energy-using processes are advocated. It is also stressed that a complete understanding of metabolic scaling will require the identification of both proximate (functional) and ultimate (evolutionary) causes. Four major types of intraspecific metabolic scaling with body mass are recognized [based on the power function R=aMb, where R is respiration (metabolic) rate, a is a constant, M is body mass, and b is the scaling exponent]: Type I: linear, negatively allometric (b<1); Type II: linear, isometric (b=1); Type III: nonlinear, ontogenetic shift from isometric (b=1), or nearly isometric, to negatively allometric (b<1); and Type IV: nonlinear, ontogenetic shift from positively allometric (b>1) to one or two later phases of negative allometry (b<1). Ontogenetic changes in the metabolic intensity of four component processes (i.e. growth, reproduction, locomotion, and heat production) appear to be important in these different patterns of metabolic scaling. These changes may, in turn, be shaped by age (size)-specific patterns of mortality. In addition, major differences in interspecific metabolic scaling are described, especially with respect to mode of temperature regulation, body-size range, and activity level. A 'metabolic-level boundaries hypothesis' focusing on two major constraints (surface-area limits on resource/waste exchange processes and mass/volume limits on power production) can explain much, but not all of this variation. My analysis indicates that further empirical and theoretical work is needed to understand fully the physiological and ecological bases for the considerable variation in metabolic scaling that is observed both within and among species. Recommended approaches for doing this are discussed. I conclude that the scaling of metabolism is not the simple result of a physical law, but rather appears to be the more complex result of diverse adaptations evolved in the context of both physico-chemical and ecological constraints.     

Body size and microclimate use in Neotropical granivorous ants

The stability of tropical microclimates has left microclimate use by tropical species little unexplored. At La Selva Costa Rica, I related foraging activity at seed baits to humidity in two forests types. I recorded 38 and 35 ant species at seed baits in closed and open canopy forest. The microclimate 5 cm above the forest floor in the younger, Open Forest was warmer, drier, more variable, and more sensitive to current weather than in the older Closed Forest. Ant species within both forests foraged at different Vapor Pressure Deficits (kPa), a measure of the drying power of the air. VPD use was not confounded with diel activity patterns. Body size explained 46% of the variance in mean VPD use among ant species. Small ant species tended to forage in moist microclimates; large species tended to be microclimate generalists. Larger species were also more active in the drier Open Forest. Foraging activity by these assemblages varies 4-fold, and peaks close to the mean VPD for each habitat. The behavior of these assemblages suggest that 1) small ant species at La Selva potentially compete with the entire range of ant body sizes, whereas large ants forage when and where small ants are inactive; and 2) seeds dispersed to the forest floor at dawn will be consumed or further dispersed by a larger suite of ants species than those falling in the heat of the tropical afternoon.     

Allometric scaling of foraging rate with trail dimensions in leaf-cutting ants

Leaf-cutting ants (Atta spp.) create physical pathways to support the transport of resources on which colony growth and reproduction depend. We determined the scaling relationship between the rate of resource acquisition and the size of the trail system and foraging workforce for 18 colonies of Atta colombica and Atta cephalotes. We examined conventional power-law scaling patterns, but did so in a multivariate analysis that reveals the simultaneous effects of forager number, trail length and trail width. Foraging rate (number of resource-laden ants returning to the nest per unit time) scaled at the 0.93 power of worker numbers, the -1.02 power of total trail length and the 0.65 power of trail width. These scaling exponents indicate that individual performance declines only slightly as more foragers are recruited to the workforce, but that trail length imposes a severe penalty on the foraging rate. A model of mass traffic flow predicts the allometric patterns for workforce and trail length, although the effect of trail width is unexpected and points to the importance of the little-known mechanisms that regulate a colony's investment in trail clearance. These results provide a point of comparison for the role that resource flows may play in allometric scaling patterns in other transport-dependent entities, such as human cities.     

The size-grain hypothesis: a phylogenetic and field test

Abstract.  1. The size-grain hypothesis predicts that environmental rugosity results in positive allometric scaling of leg length on body length because of changes in locomotion costs.
2. The scaling of leg length and body length in ants was re-examined using phylogenetic independent contrast methods, and the allometric relationship found by Kaspari and Weiser ( Functional Ecology , 13 , 530–538, 1999) was supported.
3. The size-grain hypothesis was tested further by comparing the body sizes of ants from areas of contrasting habitat complexity in two different savanna habitats. No support for the size-grain hypothesis was found. Small body size classes were no more speciose in the rugose than in the more planar environment, and small ants were more abundant in the planar environment.     

Cryptic individual scaling relationships and the evolution of morphological scaling

Morphological scaling relationships between organ and body size—also known as allometries—describe the shape of a species, and the evolution of such scaling relationships is central to the generation of morphological diversity. Despite extensive modeling and empirical tests, however, the modes of selection that generate changes in scaling remain largely unknown. Here, we mathematically model the evolution of the group‐level scaling as an emergent property of individual‐level variation in the developmental mechanisms that regulate trait and body size. We show that these mechanisms generate a “cryptic individual scaling relationship” unique to each genotype in a population, which determines body and trait size expressed by each individual, depending on developmental nutrition. We find that populations may have identical population‐level allometries but very different underlying patterns of cryptic individual scaling relationships. Consequently, two populations with apparently the same morphological scaling relationship may respond very differently to the same form of selection. By focusing on the developmental mechanisms that regulate trait size and the patterns of cryptic individual scaling relationships they produce, our approach reveals the forms of selection that should be most effective in altering morphological scaling, and directs researcher attention on the actual, hitherto overlooked, targets of selection.     

Lifespan in male ants linked to mating syndrome

Male ants have long been thought to leave the nest, swarm, mate and die in quick succession (male aggregation syndrome). However, the ancestors of the ants likely used female calling, where females advertise with pheromones for longer lived and presumably free living males. In this study, male lifespan was compared in four species from a Panama rain forest. Males of two species with aggregation syndrome (Atta colombica and Azteca sp.) lived only days after collection at a light trap, and their lifespan failed to increase when supplied sugar water ad libitum. In contrast, two species with female calling syndrome (Ectatomma ruidum and Paraponera clavata) lived up to 116 days when fed. These results link male lifespan to mating systems, and provide a framework to examine variation in how ant colonies invest in males.     

Transcriptional and chromatin-based partitioning mechanisms uncouple protein scaling from cell size

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On the context‐dependent scaling of consumer feeding rates

The stability of consumer–resource systems can depend on the form of feeding interactions (i.e. functional responses). Size‐based models predict interactions – and thus stability – based on consumer–resource size ratios. However, little is known about how interaction contexts (e.g. simple or complex habitats) might alter scaling relationships. Addressing this, we experimentally measured interactions between a large size range of aquatic predators (4–6400 mg over 1347 feeding trials) and an invasive prey that transitions among habitats: from the water column (3D interactions) to simple and complex benthic substrates (2D interactions). Simple and complex substrates mediated successive reductions in capture rates – particularly around the unimodal optimum – and promoted prey population stability in model simulations. Many real consumer–resource systems transition between 2D and 3D interactions, and along complexity gradients. Thus, Context‐Dependent Scaling (CDS) of feeding interactions could represent an unrecognised aspect of food webs, and quantifying the extent of CDS might enhance predictive ecology.     

Body size and fecundity in the waterstrider Aquarius remigis: a test of Darwin's fecundity advantage hypothesis

The general female bias in body size of animals is usually attributed to fecundity selection. While many studies have demonstrated a positive relationship between body size and fecundity, the most common interpretation of fecundity selection is that larger females have larger abdomens and can hold more eggs, yet the relationship between abdomen size and fecundity has rarely been examined. For the waterstrider, Aquarius remigis, we find a significant relationship between body size and fecundity and demonstrate that the target of fecundity selection is abdomen size. Thus, larger females have higher fecundities because they have larger abdomens and not because of their total size per se. The rate at which fecundity increases with increasing abdomen size exceeds that which would be expected due to a simple volume constraint and suggests that other factors, such as increased ability to obtain resources, may contribute to the increase in fecundity with body size. Selection intensities estimated from our data indicate that fecundity selection could be a significant selective force on both total and abdomen lengths. Previous studies have found that abdomen size increased faster than body size and thus, larger females had relatively larger abdomens. The relationship of abdomen length and thorax length in A. remigis is hypoallometric and indicates that larger females have relatively smaller abdomens. We hypothesize that this may reflect conservation of abdomen size in females developing under poor conditions. Finally, while egg size is not directly related to body size, we find a trade-off between egg size and number when female abdomen length is held constant, suggesting that selection on egg size may influence abdomen length only indirectly through its effects on fecundity.