Unanticipated impacts of spatial variance of biodiversity on plant productivity

Experiments on biodiversity have shown that productivity is often a decelerating monotonic function of biodiversity. A property of nonlinear functions, known as Jensen's inequality, predicts negative effects of the variance of predictor variables on the mean of response variables. One implication of this relationship is that an increase in spatial variability of biodiversity can cause dramatic decreases in the mean productivity of the system. Here I quantify these effects by conducting a meta‐analysis of experimental data on biodiversity–productivity relationships in grasslands and using the empirically derived estimates of parameters to simulate various scenarios of levels of spatial variance and mean values of biodiversity. Jensen's inequality was estimated independently using Monte Carlo simulations and quadratic approximations. The median values of Jensen's inequality estimated with the first method ranged from 3.2 to 26.7%, whilst values obtained with the second method ranged from 5.0 to 45.0%. Meta‐analyses conducted separately for each combination of simulated values of mean and spatial variance of biodiversity indicated that effect sizes were significantly larger than zero in all cases. Because patterns of biodiversity are becoming increasingly variable under intense anthropogenic pressure, the impact of loss of biodiversity on productivity may be larger than current estimates indicate.     

Testing the differential predation hypothesis for the invasion of rusty crayfish in a stream community: laboratory and field experiments

1. We tested the hypothesis that the non‐native rusty crayfish (Orconectes rusticus) is less vulnerable to predators than two native species (O. propinquus and O. obscurus) it is replacing in streams of the upper Susquehanna River catchment (New York, U.S.A.). 2. We used laboratory experiments to compare species‐specific predation rates by smallmouth bass (Micropterus dolomieu) on crayfish of equal size and field tethering experiments to compare relative predation rates between native O. propinquus and non‐native O. rusticus by the suite of crayfish predators in our system. We predicted that crayfish size would affect predation rate but that predation rates would be equal among species when size was controlled. 3. We also tested for two potential artefacts of tethering. We tethered crayfish in cages to test whether the ability to escape from tethers is size specific, and we tested whether tethering alters differential predation among crayfish species by the smallmouth bass. 4. In the laboratory, smallmouth bass predation on rusty crayfish was lower than on either of the native species. In the field, predation risk for tethered crayfish was inversely related to size but did not differ among species when size was taken into account. Because rusty crayfish in the field experiment were slightly larger than the native species, as in nature, mortality was overall lower for the rusty crayfish. 5. In cages, smaller crayfish were more probably to escape from tethers than larger ones, an artefact that may partially confound results from our tethering experiments. Unexpectedly, tethering nearly eliminated predation by smallmouth bass. This artefact prevented us from testing for an interaction of tethering with differential predation and means that the results of field tethering experiments do not include any contribution from smallmouth bass predation. 6. Our experiments highlight the importance of explicitly considering potential artefacts that could confound results. 7. Our results indicate that differential predation contributes to the rusty crayfish's invasion of a stream community. In our study system, predation rates on rusty crayfish are lower than for native species mostly because of selection by predators for smaller crayfish; species‐specific characteristics such as behaviour that further reduce predation may also contribute, especially where smallmouth bass predation is important.     

Between‐lake variation in the trophic ecology of an invasive crayfish

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Taylor's law and body size in exploited marine ecosystems

Taylor's law (TL), which states that variance in population density is related to mean density via a power law, and density‐mass allometry, which states that mean density is related to body mass via a power law, are two of the most widely observed patterns in ecology. Combining these two laws predicts that the variance in density is related to body mass via a power law (variance‐mass allometry). Marine size spectra are known to exhibit density‐mass allometry, but variance‐mass allometry has not been investigated. We show that variance and body mass in unexploited size spectrum models are related by a power law, and that this leads to TL with an exponent slightly <2. These simulated relationships are disrupted less by balanced harvesting, in which fishing effort is spread across a wide range of body sizes, than by size‐at‐entry fishing, in which only fish above a certain size may legally be caught.     

An invasive species may be better than none: invasive signal and native noble crayfish have similar community effects

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Nonconsumptive predator effects modify crayfish‐induced bioturbation as mediated by limb loss: Field and mesocosm experiments

1. We addressed the implications of limb loss and regeneration for multispecies interactions and their impacts on ecosystem engineering in freshwater stream environments.
2. We included regenerative and nonregenerative crayfish as well as fish predators in a 2 × 2 factorial design to assess the effects on water turbidity of interactions between crayfish ecosystem engineers differing in regenerative status and their fish predators.
3. We demonstrated that crayfish limb loss and predation risks lead to more turbidity in field and mesocosm conditions. Moreover, ongoing regeneration of crayfish increased turbidity, while fish presence seemed to hinder crayfish turbidity‐inducing behaviors (such as tail‐flipping and burrowing) in the mesocosm experiment.
4. We confirmed that greater numbers of crayfish produce a greater amount of turbidity in situ in streams.
5. Although mechanical burrowing crayfish capacities may depend on crayfish burrowing classification (primary, secondary, or tertiary), our work emphasizes the implication for turbidity levels of crayfish autotomy in freshwater streams.

     

Estimating the effects of non‐native species on nutrient recycling using species‐specific and general allometric models

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A Note on Variance Bounds for an Inverse Binomial Estimator

BEST (1974) found the variance of the minimum variance unbiased estimator of the Bernoulli parameter with an inverse sample. Noting its intricacy MIKULSKI and SMITH (1976) found bounds on this variance. SATHE (1977) developed closer bounds on it. In this paper still closer upper bound on the variance is achieved using Jensen's inequality.     

Effect of phytoplankton size diversity on primary productivity in the North Pacific: trait distributions under environmental variability

While most biodiversity and ecosystem functioning (BEF) studies have found positive effects of species richness on productivity, it remain unclear whether similar patterns hold for marine phytoplankton with high local richness. We use the continuous trait‐based modelling approach, which assumes infinite richness and represents diversity in terms of the variance of the size distribution, to investigate the effects of phytoplankton size diversity on productivity in a three‐dimensional ocean circulation model driven by realistic physics forcing. We find a slightly negative effect of size diversity on primary production, which we attribute to several factors including functional trait‐environment interactions, flexible stoichiometry and the saturation of productivity at low diversity levels. The benefits of trait optimisation, whereby narrow size distributions enhance productivity under relatively stable conditions, tend to dominate over those of adaptive capacity, whereby greater diversity enhances the ability of the community to respond to environmental variability.     

Effects of sample size on estimates of population growth rates calculated with matrix models

Background

Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (λ) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of λ–Jensen''s Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of λ due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of λ.

Methodology/Principal Findings

Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating λ for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of λ with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography.

Conclusions/Significance

We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities.     

Bony pelvic canal size and shape in relation to body proportionality in humans

Obstetric selection acts on the female pelvic canal to accommodate the human neonate and contributes to pelvic sexual dimorphism. There is a complex relationship between selection for obstetric sufficiency and for overall body size in humans. The relationship between selective pressures may differ among populations of different body sizes and proportions, as pelvic canal dimensions vary among populations. Size and shape of the pelvic canal in relation to body size and shape were examined using nine skeletal samples (total female n = 57; male n = 84) from diverse geographical regions. Pelvic, vertebral, and lower limb bone measurements were collected. Principal component analyses demonstrate pelvic canal size and shape differences among the samples. Male multivariate variance in pelvic shape is greater than female variance for North and South Africans. High‐latitude samples have larger and broader bodies, and pelvic canals of larger size and, among females, relatively broader medio‐lateral dimensions relative to low‐latitude samples, which tend to display relatively expanded inlet antero‐posterior (A‐P) and posterior canal dimensions. Differences in canal shape exist among samples that are not associated with latitude or body size, suggesting independence of some canal shape characteristics from body size and shape. The South Africans are distinctive with very narrow bodies and small pelvic inlets relative to an elongated lower canal in A‐P and posterior lengths. Variation in pelvic canal geometry among populations is consistent with a high degree of evolvability in the human pelvis. Am J Phys Anthropol 151:88–101, 2013. © 2013 Wiley Periodicals, Inc.     

Body size distributions in North American freshwater fish: large‐scale factors

Aim To document continental‐ and regional‐scale variation in the size distributions of freshwater fish and examine some energetic, evolutionary and biogeographic explanations for these patterns. Location North America. Methods Regional species lists, coupled with habitat and body size information, were used to document the spatial patterns. Results At the continental scale, riverine specialist fishes show a unimodal, right‐skewed, body size distribution whereas habitat generalist and lacustrine specialist species exhibit bimodal size distributions, with only a slight preponderance of small‐mode species. Most large‐mode species are migratory. Resident species, unlike migratory ones, show a latitudinal increase in mean size, but the size increase across all species is steeper because the importance of large migratory species increases with latitude. Size distributions change from right‐ to left‐skewed with increasing latitude. Maximum body size does not change with increasing family richness but minimum size declines and skewness increases, consistent with diversification of small species. Skewness does not vary with mean family body size. Main conclusions Post‐glacial recolonization by large, habitat generalist, migratory species is the main determinant of latitudinal size distribution trends. There is little support for the energetic hypothesis, but the data are consistent with a negative Cope's rule.     

Leaf size of woody dicots predicts ecosystem primary productivity

A key challenge in ecology is to understand the relationships between organismal traits and ecosystem processes. Here, with a novel dataset of leaf length and width for 10 480 woody dicots in China and 2374 in North America, we show that the variation in community mean leaf size is highly correlated with the variation in climate and ecosystem primary productivity, independent of plant life form. These relationships likely reflect how natural selection modifies leaf size across varying climates in conjunction with how climate influences canopy total leaf area. We find that the leaf size?primary productivity functions based on the Chinese dataset can predict productivity in North America and vice‐versa. In addition to advancing understanding of the relationship between a climate‐driven trait and ecosystem functioning, our findings suggest that leaf size can also be a promising tool in palaeoecology for scaling from fossil leaves to palaeo‐primary productivity of woody ecosystems.     

Increased body size along urbanization gradients at both community and intraspecific level in macro‐moths

Urbanization involves a cocktail of human‐induced rapid environmental changes and is forecasted to gain further importance. Urban‐heat‐island effects result in increased metabolic costs expected to drive shifts towards smaller body sizes. However, urban environments are also characterized by strong habitat fragmentation, often selecting for dispersal phenotypes. Here, we investigate to what extent, and at which spatial scale(s), urbanization drives body size shifts in macro‐moths—an insect group characterized by positive size‐dispersal links—at both the community and intraspecific level. Using light and bait trapping as part of a replicated, spatially nested sampling design, we show that despite the observed urban warming of their woodland habitat, macro‐moth communities display considerable increases in community‐weighted mean body size because of stronger filtering against small species along urbanization gradients. Urbanization drives intraspecific shifts towards increased body size too, at least for a third of species analysed. These results indicate that urbanization drives shifts towards larger, and hence, more mobile species and individuals in order to mitigate low connectivity of ecological resources in urban settings. Macro‐moths are a key group within terrestrial ecosystems, and since body size is central to species interactions, such urbanization‐driven phenotypic change may impact urban ecosystem functioning, especially in terms of nocturnal pollination and food web dynamics. Although we show that urbanization's size‐biased filtering happens simultaneously and coherently at both the inter‐ and intraspecific level, we demonstrate that the impact at the community level is most pronounced at the 800 m radius scale, whereas species‐specific size increases happen at local and landscape scales (50–3,200 m radius), depending on the species. Hence, measures—such as creating and improving urban green infrastructure—to mitigate the effects of urbanization on body size will have to be implemented at multiple spatial scales in order to be most effective.     

The fiddler crab,Minuca pugnax,follows Bergmann's rule

Bergmann's rule predicts that organisms at higher latitudes are larger than ones at lower latitudes. Here, we examine the body size pattern of the Atlantic marsh fiddler crab, Minuca pugnax (formerly Uca pugnax), from salt marshes on the east coast of the United States across 12 degrees of latitude. We found that M. pugnax followed Bergmann's rule and that, on average, crab carapace width increased by 0.5 mm per degree of latitude. Minuca pugnax body size also followed the temperature–size rule with body size inversely related to mean water temperature. Because an organism's size influences its impact on an ecosystem, and M. pugnax is an ecosystem engineer that affects marsh functioning, the larger crabs at higher latitudes may have greater per‐capita impacts on salt marshes than the smaller crabs at lower latitudes.     

Sexual size dimorphism and Rensch's rule in Canidae

The size variation between males and females of a species is a phenomenon known as sexual size dimorphism (SSD). The observed patterns of variation in SSD among species has led to the formulation of Rensch's rule, which establishes that, in species showing a male size bias, SSD increases with an increase in the body size of the species. However, for species in which there is a female size bias, the SSD would decrease when the body size of the species increases. In the present study, we examined the variation in body size and SSD of 33 species of canids from estimates of body mass and body length. We studied its relationship with life‐history characteristics and tested Rensch's rule using phylogenetic generalized least squares and phylogenetic reduced major axis regressions, respectively. We observed the existence of correlation between body mass and body length, although the SSDs from these estimators are uncorrelated. SSD did not show the pattern predicted by Rensch's rule. SSD also did not show any correlation with life‐history traits. It is likely that the low SSD observed in canids is related to the monogamy observed in the family, which is a rare situation in mammals.     

Body size explains interspecific variation in size–latitude relationships in geographically widespread beetle species

1. In most birds and mammals, larger individuals of the same species tend to be found at higher latitudes, but in insects, body size–latitude relationships are highly variable. 2. Recent studies have shown that larger‐bodied insect species are more likely to decrease in size when reared at increased temperature, compared with smaller‐sized species. These findings have led to the prediction that a positive relationship between body size and latitude should be more prevalent in larger‐bodied insect species. 3. This study measured the body size of > 4000 beetle specimens (12 species) collected throughout North America. Some beetle species increased in size with latitude, while others decreased. Importantly, mean species body size explained c. 30% of the interspecific variation in the size–latitude response. 4. As predicted, larger‐bodied beetle species were more likely to show a positive relationship between body size and latitude (Bergmann's rule), and smaller‐bodied species were more likely to show a negative body size–latitude relationship (inverse Bergmann's rule). 5. These body size–latitude patterns suggest that size‐specific responses to temperature may underlie global latitudinal distributions of body size in Coleoptera, as well as other insects.     

Habitat structure and body size distributions: cross‐ecosystem comparison for taxa with determinate and indeterminate growth

Habitat structure across multiple spatial and temporal scales has been proposed as a key driver of body size distributions for associated communities. Thus, understanding the relationship between habitat and body size is fundamental to developing predictions regarding the influence of habitat change on animal communities. Much of the work assessing the relationship between habitat structure and body size distributions has focused on terrestrial taxa with determinate growth, and has primarily analysed discontinuities (gaps) in the distribution of species mean sizes (species size relationships or SSRs). The suitability of this approach for taxa with indeterminate growth has yet to be determined. We provide a cross‐ecosystem comparison of bird (determinate growth) and fish (indeterminate growth) body mass distributions using four independent data sets. We evaluate three size distribution indices: SSRs, species size–density relationships (SSDRs) and individual size–density relationships (ISDRs), and two types of analysis: looking for either discontinuities or abundance patterns and multi‐modality in the distributions. To assess the respective suitability of these three indices and two analytical approaches for understanding habitat–size relationships in different ecosystems, we compare their ability to differentiate bird or fish communities found within contrasting habitat conditions. All three indices of body size distribution are useful for examining the relationship between cross‐scale patterns of habitat structure and size for species with determinate growth, such as birds. In contrast, for species with indeterminate growth such as fish, the relationship between habitat structure and body size may be masked when using mean summary metrics, and thus individual‐level data (ISDRs) are more useful. Furthermore, ISDRs, which have traditionally been used to study aquatic systems, present a potentially useful common currency for comparing body size distributions across terrestrial and aquatic ecosystems.     

Understanding bias in geographic range size estimates

Aim Estimates of geographic range size derived from natural history museum specimens are probably biased for many species. We aim to determine how bias in these estimates relates to range size. Location We conducted computer simulations based on herbarium specimen records from localities ranging from the southern United States to northern Argentina. Methods We used theory on the sampling distribution of the mean and variance to develop working hypotheses about how range size, defined as area of occupancy (AOO), was related to the inter‐specific distribution of: (1) mean collection effort per area across the range of a species (MC); (2) variance in collection effort per area across the range of a species (VC); and (3) proportional bias in AOO estimates (PBias: the difference between the expected value of the estimate of AOO and true AOO, divided by true AOO). We tested predictions from these hypotheses using computer simulations based on a dataset of more than 29,000 herbarium specimen records documenting occurrences of 377 plant species in the tribe Bignonieae (Bignoniaceae). Results The working hypotheses predicted that the mean of the inter‐specific distribution of MC, VC and PBias were independent of AOO, but that the respective variance and skewness decreased with increasing AOO. Computer simulations supported all but one prediction: the variance of the inter‐specific distribution of VC did not decrease with increasing AOO. Main conclusions Our results suggest that, despite an invariant mean, the dispersion and symmetry of the inter‐specific distribution of PBias decreases as AOO increases. As AOO increased, range size was less severely underestimated for a large proportion of simulated species. However, as AOO increased, range size estimates having extremely low bias were less common.     

Multi‐faceted impacts of native and invasive alien decapod species on freshwater biodiversity and ecosystem functioning

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