Fitness and Optimal Body Size in Zooplankton Population

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We determined if data on strepsirhine body and home range sizes support an optimal body size (OBS) model of 100 g, as predicted from studies of energetics in terrestrial mammals. We also tested the following predictions of the OBS model: 1) relationships between body and home range sizes will change slope and sign above and below the OBS threshold of 100 g and 2) best-fit lines for OBS regression models (above and below the 100-g threshold) will intersect at ca. 100 g (range of 80–250 g). We collected data on body mass, home range size, and vertical ranging behavior for 37 strepsirhines from the literature. Linear regression analyses and phylogenetic independent contrasts methods revealed that body size is a significant determinant of both 2-dimensional (ha) and 3-dimensional (km3) home range sizes only in taxa weighing >100 g. There were consistent changes in the sign of the slopes above and below the OBS threshold. The intersections of the best-fit lines were within the OBS range for the body size to 3-dimensional home range comparisons. Thus, the data provide some support for the OBS model in strepsirhines. However, no regression model was statistically significant for the taxa below the OBS threshold, which may reflect small sample sizes. Also, no slope differed significantly between taxa above and below the OBS. Significant correlations between body and home range sizes for the complete data sets refute the √-shaped constraint space predicted via the OBS model.

ABSTRACTAim Optimal body size theories predict that large clades have a single, optimal, body size that serves as an evolutionary attractor, with the full body size spectrum of a clade resulting from interspecific competition. Because interspecific competition is believed to be reduced on islands, such theories predict that insular animals should be closer to the optimal size than mainland animals. We test the resulting prediction that insular clade members should therefore have narrower body size ranges than their mainland relatives.Location World‐wide.Methods We used body sizes and a phylogenetic tree of 4004 mammal species, including more than 200 species that went extinct since the last ice age. We tested, in a phylogenetically explicit framework, whether insular taxa converge on an optimal size and whether insular clades have narrow size ranges.Results We found no support for any of the predictions of the optimal size theory. No specific size serves as an evolutionary attractor. We did find consistent evidence that large (> 10 kg) mammals grow smaller on islands. Smaller species, however, show no consistent tendency to either dwarf or grow larger on islands. Size ranges of insular taxa are not narrower than expected by chance given the number of species in their clades, nor are they narrower than the size ranges of their mainland sister clades – despite insular clade members showing strong phylogenetic clustering.Main conclusions The concept of a single optimal body size is not supported by the data that were thought most likely to show it. We reject the notion that inclusive clades evolve towards a body‐plan‐specific optimum.

It is hypothesized that the body size of a bumblebee will be that size which maximizes its average net rate of energy intake while collecting nectar. A mathematical model is developed with the result that the net rate of energy intake of a nectar-collecting bumblebee is expressed as a function of the body size of the bumblebee. From this model the body size which maximizes the net rate of energy intake (i.e., optimal body size) is found (as the solution of an implicit equation). In this situation the advantage of large size is that larger bumblebees fly faster and hence take less flight time than smaller bumblebees. The disadvantage of larger size is greater energetic costs.The parameters of the model are estimated using data obtained from the foraging behavior of bumblebees on monkshood (Aconitum columbianum). The optimal body size is then calculated for workers of Bombus appositus which obtained almost all their nectar from monkshood. The observed and expected (i.e., optimal) body size are found to be close and not significantly different.The model also predicts that, from the bumblebee's point of view, there should be a positive correlation between the size of the bumblebee and the average amount of nectar obtained per flower. Evidence of this correlation is presented and the possible significance of the correlation from the plant's point of view is discussed. A possible extension of the model to general relationships between predator body size, prey size and prey density is discussed.

Kozlowski and Weiner (1997) challenged the idea that interspecific allometries reflect unitary functional relationships between parameters that are shared by all of the species within a set. They suggested that these allometries might also be produced as a by-product of underlying intraspecific processes. In the course of their argument, Kozlowski and Weiner developed a model for the optimal adult body size and found a striking result, which is that optimizing body size produces a distribution of sizes within a taxon that is skewed to the right, even when examined on a logarithmic scale. In this note, we point out that while this result was based on a limited range of parameters, it is actually a very general outcome of optimizing body size in their model. Kozlowski and Weiner’s (1997) new model is based on the assumptions that assimilation and respiration are allometric functions of body size, aw and hw , respectively; that the production rate, P(w), is the difference between assimilation and respiration, that is, ; b b P(w) 5 aw 2 hw that the mortality rate, m(w), can be described by ; and that the optimal adult body size can l m(wx) 5 2gw be found as a solution of

Cope's rule--the generalization that animal taxa tend to evolve toward larger body size--suggests that there are widespread net selective advantages to being large. Size-abundance relationships within bird and desert rodent guilds show that larger species usually do control more energy locally, and thus maintain larger populations than expected for their body size, implying that larger individuals are relatively better at obtaining and using local resources. But we report here results that show that this is not generally the case among mammal species. Within dietary groups containing only small species, larger species usually do better, but within those that contain the largest mammals, small species tend to control more energy. This suggests that in mammals there is an optimum body size for energy acquisition at about 1 kg. Thus, net adaptive advantages of large individuals for resource control cannot be used as a general explanation for evolutionary size increase in mammals, although other proposed explanations for Cope's rule are unaffected. Instead, these results suggest a partial explanation for another widespread ecotypic pattern, the 'island rule': that on islands, small mammal species evolve to larger size and large species to smaller size. If on an island a species' usual competitors and predators are absent, it should often tend to evolve toward the optimum body size, and the adaptive advantages of doing so would be greatest for populations starting at body-size extremes.

For the past twenty years, it has been recognized that body size is convergent among solitary species of Anolis lizards endemic to different island banks of the Lesser Antilles. Community ecologists have assumed that this "solitary size" is an optimal size, yet the basis behind such optimality has not been shown. Our goal in this study was to explore the existence of an energetic basis of an optimal body size in these lizards. A computer model is presented that incorporates quantitative descriptions of lizard metabolism, locomotion, digestion, and visual acuity, and simulates foraging in a sit—and—wait predator. Quantitative estimates of daily foraging energetics are presented, which are then used together with estimates of resting metabolism to simulate growth. An optimal growth strategy is incorporated to determine adult body sizes that maximize lifetime reproductive output. Such optimal body sizes were determined for different prey densities and activity levels, predator life expectancies, and field metabolic rates. Predicted optimal body sizes are close to the observed body sizes of Lesser Antillean anoles, and are relatively insensitive to both levels of prey activity and up to fourfold differences in prey density, while life expectancy and rates of field metabolism may influence predictions. The insensitivity of predicted optimal body size to prey density lends support to the assumption that the solitary size observed among anoles throughout the Lesser Antilles is an optimal body size. Additional findings were made regarding home—range sizes, growth patterns, and visual constraints to foraging performance.

1. Females of solitary, nest‐constructing bees determine both sex (haplo‐diploidy) as well as body size (by amount of provision) of each single offspring.2. According to the Optimal Allocation Theory, females should allocate resources in portions that maximise fitness returns. A key fitness component in bees is body size that is determined solely by the provisions supplied by the mother.3. The optimal progeny body size relies on different factors in both sexes. In females, provision efficiency is crucial for reproductive success. In males, however, fitness depends primarily on mating success.4. Provision efficiency of Osmia bicornis L. females depends on the capacity to stow pollen (scopa) and their ability to carry the packed loads. Scopa capacity increases isometrically with body size whereas indices of flight performance (EPI, free lift) decrease. These complementary effects substantially contribute to the adjustment of optimal body size in daughters.5. The impact of body mass on fitness of males is determined by the mating system. Owing to the opportunistic polygyny in O. bicornis, there was no detectable correlation between body size and male mating success. Consequently, mother bees distribute their provisions to many, but small sons to increase the number of descendant competitors in the race for matings. Optimal body size in sons is a trade‐off between a large male advantage in rare scrambles over receptive females and small‐size‐related disadvantages in viability.

Winter is energetically challenging for small herbivores because of greater energy requirements for thermogenesis at a time when little energy is available. We formulated a model predicting optimal wintering body size, accounting for the scaling of both energy expenditure and assimilation to body size, and the trade-off between survival benefits of a large size and avoiding survival costs of foraging. The model predicts that if the energy cost of maintaining a given body mass differs between environments, animals should be smaller in the more demanding environments, and there should be a negative correlation between body mass and daily energy expenditure (DEE) across environments. In contrast, if animals adjust their energy intake according to variation in survival costs of foraging, there should be a positive correlation between body mass and DEE. Decreasing temperature always increases equilibrium DEE, but optimal body mass may either increase or decrease in colder climates depending on the exact effects of temperature on mass-specific survival and energy demands. Measuring DEE with doubly labeled water on wintering Microtus agrestis at four field sites, we found that DEE was highest at the sites where voles were smallest despite a positive correlation between DEE and body mass within sites. This suggests that variation in wintering body mass between sites was due to variation in food quality/availability and not adjustments in foraging activity to varying risks of predation.

Hutchinson and MacArthur (1959) argued that the number of available habitats and thus the number of species should decrease with body size. May (1978) presented an estimate of species number as a function of body length for all terrestrial animals, and he interpreted his data to be more or less in accord with the prediction of Hutchinson and MacArthur (1959; see also Morse et al. 1985). However, recent analysis showed that the smallest organisms are not the most diverse and that global body size distributions among species are humped and right-skewed even on a logscale (Brown and Nicoletto 1991, Blackburn and Gaston 1994a, Barlow 1994; Fig. 1). If a variety of factors acts in a multiplicative way then a lognormal distribution would be expected (May 1975). Thus, the central issue is, why body size distributions deviate from a lognormal shape and show a considerable right-skew (for a review see Blackburn and Gaston 1994b). Based on an energetic definition of fitness, Brown et al. (1993) developed a model which predicts not only the right-skewed shape of the frequency distribution but also an optimal body size. This model simplifies the physiological processes of reproduction and uses scaling functions derived for mammals. It was successful in predicting the optimal body size of mammals and the body size shifts of mammals on islands. However, predictions for other taxa remain obscure because it is unclear whether the scaling functions are valid for other taxa. Another approach to predict a right-skew of body size distributions applies size-biased extinction and speciation rates (Dial and Marzluff 1988, Maurer et al. 1992). There is a complex and scattered literature on speciation rates in correlation to body size (e.g. Bush 1993, Fenchel 1993) with the general conclusion that speciation rates decrease with body size. Thus, the higher speciation rates of small animal species can generate a right-skewed pattern. Maurer et al. (1992), however, conclude that a right-skewed distribution needs size-biased speciation and extinction rates. Until now the relationship between extinction risk and body size is equivocal. In general, population persistence is more likely when fluctuations in numbers are small and the recovery from low numbers is fast. Lawton (1995) notes that these factors can be correlated with body size but not necessarily in ways that act consistently to either promote or reduce the risk of extinction. Pimm et al. (1988) argued that large-bodied organisms are at greater disadvantage in a stochastic environment due to their small growth rates and thus long recovery times from population crashes. This generates a positive relationship between extinction risk and body size (see also Brown and Maurer 1986, Lawton 1989, Blackburn et al. 1990, Gaston and Blackburn 1995). However, Cook and Hanski (1995) found an opposite pattern in shrews. They argued that smallbodied species are more sensitive to environmental fluctuations than large-bodied species (see also Tracy and George 1992). Thus, small-bodied species fluctuate more likely to extinction. Furthermore, in a stable environment large organisms are favoured because they may achieve dominance over resources (Dial and Marzluff 1988). The above discussion shows that the relationship between body size and species' vulnerability to extinction is poorly understood and a unifying approach is badly needed. Using a simulation model we explore how extinction risk of populations in a stochastic environment may depend on body size. We distinguish between two different types of environmental perturbations: fluctuations (frequent, weak perturbations) and catastrophes (rare, strong perturbations). We hypothesize that species respond to environmental fluctuations along different timescales and with different sensitivities, both assumed to be correlated with body size. Catastrophes, however, are special strong perturbations that cause sudden major declines of the population size of all species independent of their biological characteristics and thus independent of body size. We will show that these different types of perturbations translate into a relationship of extinction risk versus body size, which is U-shaped with a skew depending on the actual environmental perturbations and the biological traits of the species. Therefore, even under the assumption of a

Optimal Body Size and Resource Density

Telomere dynamics could underlie life-history trade-offs among growth, size and longevity, but our ability to quantify such processes in natural, unmanipulated populations is limited. We investigated how 4years of artificial selection for either larger or smaller tarsus length, a proxy for body size, affected early-life telomere length (TL) and several components of fitness in two insular populations of wild house sparrows over a study period of 11years. The artificial selection was expected to shift the populations away from their optimal body size and increase the phenotypic variance in body size. Artificial selection for larger individuals caused TL to decrease, but there was little evidence that TL increased when selecting for smaller individuals. There was a negative correlation between nestling TL and tarsus length under both selection regimes. Males had longer telomeres than females and there was a negative effect of harsh weather on TL. We then investigated whether changes in TL might underpin fitness effects due to the deviation from the optimal body size. Mortality analyses indicated disruptive selection on TL because both short and long early-life telomeres tended to be associated with the lowest mortality rates. In addition, there was a tendency for a negative association between TL and annual reproductive success, but only in the population where body size was increased experimentally. Our results suggest that natural selection for optimal body size in the wild may be associated with changes in TL during growth, which is known to be linked to longevity in some bird species.

Within many animal taxa there is a trend for the species of larger body size to eat food of lower caloric value. For example, most large extant lizards are herbivorous. Reasonable arguments based on energetic considerations are often invoked to explain this trend, yet, while these factors set limits to feasible body size, they do not in themselves mathematically produce optimum body sizes. A simple optimization model is developed here which considers food search, capture, and eating rates and the metabolic cost of these activities for animals of different sizes. The optimization criterion is defined as the net calorie gain a consumer accrues per day. This model does produce an optimum intermediate body size which increases with food quality--not the reverse. This discrepancy is accounted for, however, because the model also predicts that body size should be even more sensitive to increases in food abundance. In nature, many poor quality foods are also relatively abundant foods, hence the consumers eating them may maximize their daily energetic profit by evolving a relatively large body size. Optimum consumer body size also decreases with increases in consumer metabolic rate and "prey" speed.

Previous articleNext article No AccessNotes and CommentsDarwinian Fitness and Reproductive Power: Reply to KozlowskiJames H. Brown, Mark L. Taper, and Pablo A. MarquetJames H. Brown Search for more articles by this author , Mark L. Taper Search for more articles by this author , and Pablo A. Marquet Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The American Naturalist Volume 147, Number 6Jun., 1996 Published for The American Society of Naturalists Article DOIhttps://doi.org/10.1086/285895 Views: 9Total views on this site Citations: 22Citations are reported from Crossref Copyright 1996 The University of ChicagoPDF download Crossref reports the following articles citing this article:Craig R. McClain, James P. Barry, Thomas J. 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Several hypotheses have been put forward to explain the evolution of extreme sexual size dimorphism (SSD). Among them, the gravity hypothesis (GH) explains that extreme SSD has evolved in spiders because smaller males have a mating or survival advantage by climbing faster. However, few studies have supported this hypothesis thus far. Using a wide span of spider body sizes, we show that there is an optimal body size (7.4 mm) for climbing and that extreme SSD evolves only in spiders that: (1) live in high-habitat patches and (2) in which females are larger than the optimal size. We report that the evidence for the GH across studies depends on whether the body size of individuals expands beyond the optimal climbing size. We also present an ad hoc biomechanical model that shows how the higher stride frequency of small animals predicts an optimal body size for climbing.