A novel alternative to F-tests for ecological studies

Differences or similarities in the variance of fitness traits are crucial in several biological disciplines, e.g. ecological, toxicological, developmental and evolutionary studies. For example the variance of traits can be utilized as a biomarker of differences in environmental conditions. In the absence of environmental variability, the differences of the variance of a trait can be interpreted as differences of the genetic background. Several tests and transformations are utilized when testing differences between variances. There is, however, a biological tendency for the variance to scale proportionally to the square of the mean (scaling effect) which can considerably bias the results of the tests. We propose a novel method which allows for a more precise correction of the scaling effect and proper comparisons among treatment groups and between investigations. This is relevant for all data sets of distributions with different means and suggests the reanalysis of comparisons among treatment groups. This correction will provide a more reliable method when using bioindicators.     

Stochastic multiplicative population growth predicts and interprets Taylor's power law of fluctuation scaling

Taylor''s law (TL) asserts that the variance of the density (individuals per area or volume) of a set of comparable populations is a power-law function of the mean density of those populations. Despite the empirical confirmation of TL in hundreds of species, there is little consensus about why TL is so widely observed and how its estimated parameters should be interpreted. Here, we report that the Lewontin–Cohen (henceforth LC) model of stochastic population dynamics, which has been widely discussed and applied, leads to a spatial TL in the limit of large time and provides an explicit, exact interpretation of its parameters. The exponent of TL exceeds 2 if and only if the LC model is supercritical (growing on average), equals 2 if and only if the LC model is deterministic, and is less than 2 if and only if the LC model is subcritical (declining on average). TL and the LC model describe the spatial variability and the temporal dynamics of populations of trees on long-term plots censused over 75 years at the Black Rock Forest, Cornwall, NY, USA.     

Ordinary least squares regression is indicated for studies of allometry

When it comes to fitting simple allometric slopes through measurement data, evolutionary biologists have been torn between regression methods. On the one hand, there is the ordinary least squares (OLS) regression, which is commonly used across many disciplines of biology to fit lines through data, but which has a reputation for underestimating slopes when measurement error is present. On the other hand, there is the reduced major axis (RMA) regression, which is often recommended as a substitute for OLS regression in studies of allometry, but which has several weaknesses of its own. Here, we review statistical theory as it applies to evolutionary biology and studies of allometry. We point out that the concerns that arise from measurement error for OLS regression are small and straightforward to deal with, whereas RMA has several key properties that make it unfit for use in the field of allometry. The recommended approach for researchers interested in allometry is to use OLS regression on measurements taken with low (but realistically achievable) measurement error. If measurement error is unavoidable and relatively large, it is preferable to correct for slope attenuation rather than to turn to RMA regression, or to take the expected amount of attenuation into account when interpreting the data.     

Spatial distribution and settlement strategies in willow ptarmigan

In heterogeneous landscapes individuals select among several habitat patches. The fitness rewards of these choices are assumed to play an important role in the distribution of individuals across landscapes. Individuals can either use environmental cues to directly assess the quality of breeding sites, or rely on social cues to guide the settlement decision. We estimated the density of adult birds and per capita reproductive success of willow ptarmigan over 5–15 years in 42 survey areas, nested within 5 spatially separated populations in south-central Norway. Our aims were to (1) examine spatial and temporal patterns of variation in densities of adult birds (i.e., the breeding densities) and reproductive success (juveniles/pair) measured in autumn and (2) evaluate which habitat distribution model best described the distribution of willow ptarmigan across heterogeneous mountain landscapes. Variation in density of adult birds was primarily attributable to variation between survey areas which could arise from spatial heterogeneity in adult survival or as a consequence of spacing behavior of juveniles during the settlement stage. In contrast, reproductive success was more variable between years and did not vary consistently between survey areas once year effects were accounted for. The lack of any relationship between the density of adult birds and reproductive success supported the predictions of an ideal free distribution (IFD), implying that within years, the mean reproductive success was approximately equal across survey areas. However, analysis based on Taylor's power law (i.e., the relationship between logarithms of spatial variance and mean density of adult birds) suggested that aggregation was stronger than expected under IFD. This implies that the relative change in density of adult birds was larger in areas with high mean densities than in areas with low densities. The exact mechanisms causing this statistical pattern are unclear, but based on the breeding biology of willow ptarmigan we suggest that yearlings are attracted to areas of high densities during the settlement period in spring. Our study was conducted during a period of low overall density and we suggest that this pattern might be particular to such situations. This implies that the presence of conspecifics might represent a cue signaling high adult survival and thus high habitat quality.     

Surveillance of the chikungunya vector Aedes albopictus (Skuse) in Emilia‐Romagna (northern Italy): organizational and technical aspects of a large scale monitoring system

The chikungunya virus outbreak that occurred in 2007 in northern Italy (Emilia‐Romagna region) prompted the development of a large scale monitoring system of the population density of Aedes albopictus (Skuse, 1894), comparable at the provincial and municipal levels. In 2007, egg density data presented an aggregated distribution (VMR >1) and Taylor's power law was applied to calculate the minimum number of ovitraps needed to obtain the prefixed precision levels: D=0.2 in the areas where the chikungunya epidemic occurred and D=0.3 in all the other urban areas >600 ha. The estimated minimum ovitrap number was then used to set up a monitoring network at the regional scale in season 2008 (May‐October). In 242 municipalities 2,741 ovitraps were activated and the 2008 sampled data showed a similar aggregated distribution as in 2007. The adequacy of the monitoring design was evaluated by recalculating the Taylor's coefficients and the minimum ovitrap number for each urban area >600 ha using the 2008 egg density data. The comparison between the two estimates showed that the minimum ovitrap number calculated in 2007 was underestimated by 2.7% in weeks 22–41 but was overestimated by 29.4% if referring to the period of highest population density (weeks 27–37). The low cost of the proposed monitoring system, based on the use of fortnightly checked ovitraps, could make it economically sustainable even in a non‐epidemic season.     

Effect of Quadrat and Core Sizes on Determining the Spatial Pattern of Criconemella sphaerocephalus

An unmanaged pasture was sampled on four occasions (A, B, C, D) with five different quadrat sizes for Criconemella sphaerocephalus by removing a constant soil core volume of 75 cm³ (A) and 300 cm³ (C) from increasing quadrat areas of 0.5-8 m², and removing soil core volumes of increasing size - 75-1,200 cm³ (B) and 300-4,800 cm³ (D) - proportionally with an increase in quadrat area (0.5-8 m²). Frequency counts of C. sphaerocephalus were fitted to six probability distributions. The index of aggregation (b) for Taylor''s power law and Morisita''s index of dispersion were also calculated where appropriate. Twelve of nineteen of the sampling combinations were best described by negative binomial distribution (P = 0.05). Criconemella sphaerocephalus appeared more highly aggregated when sampled with constant soil core volumes (A and C) than from increasing soil core volumes (B and D) based on Taylor''s index of aggregation (b). Morisita''s index of dispersion indicated aggregation at the smallest quadrat area (0.5 m²) for all sampling occasions (A, B, C, D).     

A unified model explains commonness and rarity on coral reefs

Abundance patterns in ecological communities have important implications for biodiversity maintenance and ecosystem functioning. However, ecological theory has been largely unsuccessful at capturing multiple macroecological abundance patterns simultaneously. Here, we propose a parsimonious model that unifies widespread ecological relationships involving local aggregation, species‐abundance distributions, and species associations, and we test this model against the metacommunity structure of reef‐building corals and coral reef fishes across the western and central Pacific. For both corals and fishes, the unified model simultaneously captures extremely well local species‐abundance distributions, interspecific variation in the strength of spatial aggregation, patterns of community similarity, species accumulation, and regional species richness, performing far better than alternative models also examined here and in previous work on coral reefs. Our approach contributes to the development of synthetic theory for large‐scale patterns of community structure in nature, and to addressing ongoing challenges in biodiversity conservation at macroecological scales.     

Effects of environmental synchrony and density-dependent dispersal on temporal and spatial slopes of Taylor's law

Taylor's law (TL) is an empirical rule that describes an approximate relationship between the variance and mean of population density: log₁₀(variance) ≈ log₁₀(a) + b × log₁₀(mean). Population synchrony is another prevailing feature observed in empirical populations. This study investigated the effects of environmental synchrony and density-dependent dispersal on the temporal (b_T) and spatial (b_S) slopes of TL, using an empirical dataset of gray-sided vole populations and simulation analyses based on the second-order autoregressive (AR) model. Eighty-five empirical populations satisfied the temporal and spatial TLs with b_T = 1.943 (±SE 0.143) and b_S = 1.579 (±SE 0.136). The pairwise synchrony of population was 0.377 ± 0.199 (mean ± SD). Most simulated populations that obeyed the AR model satisfied the form of the temporal and spatial TLs without being affected by the environmental synchrony and density-dependent dispersal; however, those simulated slopes were too steep. The incorporation of environmental synchrony resulted in reduced simulated slopes, but those slopes, too, were still unrealistically steep. By incorporating density-dependent dispersal, simulated slopes decreased and fell within a realistic range. However, the simulated populations without environmental synchrony did not exhibit an adequate degree of density synchrony. In simulations that included both environmental synchrony and density-dependent dispersal, 92.7% of the simulated datasets provided realistic values for b_T, b_S and population synchrony. Because the two slopes were more sensitive to the variation of density-dependent dispersal than that of environmental synchrony, density-dependent dispersal may be the key to the determination of b_T and b_S.     

Covariation between mean vole density and variability drives the numerical response of storks to vole prey

Hušek et al. (Popul Ecol 55:363–375, 2013 ) showed that the numerical response of storks to vole prey was stronger in regions where variability in vole density was higher. This finding is, at first sight, in contradiction with the predictions of life-history theory in stochastic environments. Since the stork productivity-vole density relationship is concave, theory predicts a negative association between the temporal variability in vole density and stork productivity. Here, we illustrate this negative effect of vole variability on stork productivity with a simple mathematical model relating expected stork productivity to vole dynamics. When comparing model simulations to the observed mean density and variability of thirteen Czech and Polish vole populations, we find that the observed positive effect of vole variability on stork numerical response is most likely due to an unusual positive correlation between mean and variability of vole density.     

Comparative power law analysis for the spatial heterogeneity scaling of the hot‐spring microbiomes

Spatial heterogeneity is a fundamental property of any natural ecosystems, including hot spring and human microbiomes. Two important scales that spatial heterogeneity exhibits are population and community scales, and Taylor's power law (PL) and its extensions (PLEs) offer ideal quantitative models to assess population‐ and community‐level heterogeneities. Here we analyse 165 hot spring microbiome samples at the global scale that cover a wide range of temperatures (7.5–99°C) and pH levels (3.3–9). We explore a question of fundamental importance for measuring the spatial heterogeneity of the hot‐spring microbiome and further discuss their ecological implications: How do critical environmental factors such as temperature and pH influence the scaling of community spatial heterogeneity? We are particularly interested in the existence of a universal scaling model that is independent of environmental gradients. By applying PL and PLEs, we were able to obtain such scaling parameters of the hot spring at both community and population levels, which are temperature‐ and pH‐invariant. These findings suggest that while the hot‐spring microbiomes located at different regions may have different environmental conditions, they share a fundamental heterogeneity scaling parameter, analogically similar to the gravitational acceleration on Earth, which may vary slightly depending on altitude and latitude, but is invariant overall. In contrast, similar to the physics of the Moon and Earth, which have different gravitational accelerations, the hot spring and human microbiomes can have different scaling parameters as demonstrated in this study.     

Predictable changes in aboveground allometry of trees along gradients of temperature,aridity and competition

Aim Trees are often observed to get shorter and more narrowly crowned in dry regions and at high elevations. We explore how this pattern is driven by two opposing factors: competition for light makes it advantageous to extend branches to their biomechanical limit, whereas under cold or arid conditions it is advantageous to have shorter branches, thereby reducing the length of the hydraulic transport system and embolism risk. Using data from 700,000 trees of 26 species, we quantify how environmental conditions influence the scaling of height and crown diameter (CD) with stem diameter (d.b.h.). We compare our predictions with those of metabolic scaling theory (MST), which suggests that allometry is invariant of environment. Location 48,000 inventory plots that systematically sample mainland Spain, a region in which climate varies strongly. Methods We fit d.b.h.–height and d.b.h.–CD functions using Bayesian methods, allowing comparison of within‐ and across‐species trends in allometry along gradients of temperature, precipitation, drought and competition for light (i.e. the basal area of taller trees). Results The competitive environment had a strong influence on aboveground allometry, but all trees were far shorter than predicted by biomechanical models, suggesting that factors other than biomechanics are important. Species that dominate in arid and cold habitats were much shorter (for a given diameter) than those from benign conditions; but within‐species heights did not vary strongly across climatic gradients. Main conclusions Our results do not support the MST prediction that d.b.h.–height and d.b.h.–CD allometries are invariant, or that biomechanical constraints determine height allometry. Rather, we highlight the role of hydraulic limitations in this region. The fact that intra‐specific adjustment in d.b.h.–CD – height allometry along environmental gradients was far weaker than across‐species changes may indicate genetic constraints on allometry which might contribute to niche differentiation among species.     

幂指数异速生长机制模型综述

 个体大小对生物的各种生理属性有重要意义, 描述个体大小和生理属性关系的规律叫做异速生长。生物的异速生长通常以幂函数的形 式表示, 在众多的异速生长关系中, Kleiber定律所描述的新陈代谢率和个体大小的3/4幂指数关系最为重要和基本, 解释此有充分数据支持的 定律的机理也最具挑战性。围绕该著名的3/4幂指数异速生长关系, 该文回顾历史上主要的有关模型假说, 并重点介绍1990年代中期以来, 由 West等提出的分形分配网络模型和由其它研究人员建立的代表性模型: 最少载体网络模型、多因理论、最小总熵理论、构造理论、细胞优化生 长理论和能量消耗理论。     

Power laws and plant trait variation in spatio-temporally heterogeneous environments

A challenge

Variation is ubiquitous in nature across all spatial and temporal scales and underlies prominent ecological and evolutionary theories. Although understanding the causes and consequences of trait variation is a central goal of trait-based ecology, the scaling of trait variance across space and time (variance scaling) is unresolved.

A solution

We argue that characterizing trait variance across spatio-temporal scales using a combination of prominent power laws can elucidate the role of environmental variability in trait variation and potential mechanisms driving trait patterns. In particular, the species–time–area relationship and Taylor's power law help to establish a generalizable framework for developing and testing variance scaling theory. Finally, we outline priority research questions and tractable systems for answering them. Successional forests, long-term forest monitoring networks and censuses of short-lived taxa are ideal for coupling high-resolution environmental data with measurements of trait variance across scales to test the models proposed here.

Main conclusions

Characterizing the behaviour of variance across spatio-temporal scales is feasible and a prerequisite for developing a predictive theory of trait-based ecology.     

How fast is fast? Eco‐evolutionary dynamics and rates of change in populations and phenotypes

It is increasingly recognized that evolution may occur in ecological time. It is not clear, however, how fast evolution – or phenotypic change more generally – may be in comparison with the associated ecology, or whether systems with fast ecological dynamics generally have relatively fast rates of phenotypic change. We developed a new dataset on standardized rates of change in population size and phenotypic traits for a wide range of species and taxonomic groups. We show that rates of change in phenotypes are generally no more than 2/3, and on average about 1/4, the concurrent rates of change in population size. There was no relationship between rates of population change and rates of phenotypic change across systems. We also found that the variance of both phenotypic and ecological rates increased with the mean across studies following a power law with an exponent of two, while temporal variation in phenotypic rates was lower than in ecological rates. Our results are consistent with the view that ecology and evolution may occur at similar time scales, but clarify that only rarely do populations change as fast in traits as they do in abundance.     

植物种群自疏过程中构件生物量与密度的关系

不论是在对植物种群自疏规律还是在对能量守衡法则的研究中,个体大小(M)大多针对植物地上部分生物量,地下部分和构件生物量及其动态十分重要又多被忽视。以1年生植物荞麦为材料研究了自疏种群地下部分生物量、包括地下部分的个体总生物量以及各构件生物量与密度的关系。结果表明:平均地上生物量和个体总生物量与密度的异速关系指数(γabove-ground和γindividual)分别为-1.293和-1.253,与-4/3无显著性差异(P>0.05),为-4/3自疏法则提供了有力证据;平均根生物量-密度异速指数γroot(-1.128)与-1无显著性差异(P>0.05),与最终产量恒定法则一致;平均茎生物量-密度异速指数γstem(-1.263)接近-4/3(P>0.05),平均叶生物量-密度异速指数γleaf(-1.524)接近-3/2(P>0.05),分别符合-4/3自疏法则与-3/2自疏法则;而繁殖生物量与密度的异速关系指数γreproductive(-2.005)显著小于-3/2、-4/3或-1(P<0.001)。因此,不存在一个对植物不同构件普适的生物量-密度之间的关系。光合产物在地上和地下构件的生物量分配格局以及构件生物量与地上生物量之间特异的异速生长关系导致不同构件具有不同的自疏指数。无论对于地上生物量还是个体总生物量,荞麦种群能量均守衡,而对于地下生物量,荞麦种群能量不守衡。     

The phenotypic variance gradient – a novel concept

Evolutionary ecologists commonly use reaction norms, which show the range of phenotypes produced by a set of genotypes exposed to different environments, to quantify the degree of phenotypic variance and the magnitude of plasticity of morphometric and life‐history traits. Significant differences among the values of the slopes of the reaction norms are interpreted as significant differences in phenotypic plasticity, whereas significant differences among phenotypic variances (variance or coefficient of variation) are interpreted as differences in the degree of developmental instability or canalization. We highlight some potential problems with this approach to quantifying phenotypic variance and suggest a novel and more informative way to plot reaction norms: namely “a plot of log (variance) on the y‐axis versus log (mean) on the x‐axis, with a reference line added”. This approach gives an immediate impression of how the degree of phenotypic variance varies across an environmental gradient, taking into account the consequences of the scaling effect of the variance with the mean. The evolutionary implications of the variation in the degree of phenotypic variance, which we call a “phenotypic variance gradient”, are discussed together with its potential interactions with variation in the degree of phenotypic plasticity and canalization.     

Size matters for lice on birds: Coevolutionary allometry of host and parasite body size

Body size is one of the most fundamental characteristics of all organisms. It influences physiology, morphology, behavior, and even interspecific interactions such as those between parasites and their hosts. Host body size influences the magnitude and variability of parasite size according to Harrison's rule (HR: positive relationship between host and parasite body sizes) and Poulin's Increasing Variance Hypothesis (PIVH: positive relationship between host body size and the variability of parasite body size). We analyzed parasite–host body size allometry for 581 species of avian lice (～15% of known diversity) and their hosts. We applied phylogenetic generalized least squares (PGLS) methods to account for phylogenetic nonindependence controlling for host and parasite phylogenies separately and variance heterogeneity. We tested HR and PIVH for the major families of avian lice (Ricinidae, Menoponidae, Philopteridae), and for distinct ecological guilds within Philopteridae. Our data indicate that most families and guilds of avian lice follow both HR and PIVH; however, ricinids did not follow PIVH and the “body lice” guild of philopterid lice did not follow HR or PIVH. We discuss mathematical and ecological factors that may be responsible for these patterns, and we discuss the potential pervasiveness of these relationships among all parasites on Earth.     

Income distribution trends and future food demand

This paper surveys the theoretical literature on the relationship between income distribution and food demand, and identifies main gaps of current food modelling techniques that affect the accuracy of food demand projections. At the heart of the relationship between income distribution and food demand is Engel''s law. Engel''s law establishes that as income increases, households'' demand for food increases less than proportionally. A consequence of this law is that the particular shape of the distribution of income across individuals and countries affects the rate of growth of food demand. Our review of the literature suggests that existing models of food demand fail to incorporate the required Engel flexibility when (i) aggregating different food budget shares among households; and (ii) changing budget shares as income grows. We perform simple simulations to predict growth in food demand under alternative income distribution scenarios taking into account nonlinearity of food demand. Results suggest that (i) distributional effects are to be expected from changes in between-countries inequality, rather than within-country inequality; and (ii) simulations of an optimistic and a pessimistic scenario of income inequality suggest that world food demand in 2050 would be 2.7 per cent higher and 5.4 per cent lower than distributional-neutral growth, respectively.     

Scaling law in sizes of protein sequence families: from super-families to orphan genes

It has been observed that the size of protein sequence families is unevenly distributed, with few super families with a large number of members and many "orphan" proteins that do not belong to any family. Here it is shown that the distribution of sizes of protein families in different databases and classifications (Protomap, Prodom, Cog) follows a power-law behavior with similar scaling exponents, which is characteristic of self-organizing systems. Since large databases are used in this study, a more detailed analysis of the data than in previous studies was possible. Hence, it is shown that the size distribution is governed by two exponents, different for the super families and the orphan proteins. A simple model of protein evolution is proposed, in which proteins are dynamically generated and clustered into families. The model yields a scaling behavior very similar to the distribution observed in the actual sequence databases, including the two distinct regimes for the large and small families, and thus suggests that the existence of "super families" of proteins and "orphan" proteins are two manifestations of the same evolutionary process.