Stability and lawlikeness

There appear to be no biological regularities that have the properties traditionally associated with laws, such as an unlimited scope or holding in all or many possible background conditions. Mitchell, Lange, and others have therefore suggested redefining laws to redeem the lawlike status of biological regularities. These authors suggest that biological regularities are lawlike because they are pragmatically or paradigmatically similar to laws or stable regularities. I will review these re-definitions by arguing both that there are difficulties in applying their accounts to biology and difficulties in the accounts themselves, which suggests that the accounts are not adequate to redeem the lawlike status of biological regularities. Finally, I will suggest a new account of laws that also shows how non-laws might function in some of the roles of laws.     

Causal and Mechanistic Explanations in Ecology

How are scientific explanations possible in ecology, given that there do not appear to be many-if any-ecological laws? To answer this question, I present and defend an account of scientific causal explanation in which ecological generalizations are explanatory if they are invariant rather than lawlike. An invariant generalization continues to hold or be valid under a special change-called an intervention-that changes the value of its variables. According to this account, causes are difference-makers that can be intervened upon to manipulate or control their effects. I apply the account to ecological generalizations to show that invariance under interventions as a criterion of explanatory relevance provides interesting interpretations for the explanatory status of many ecological generalizations. Thus, I argue that there could be causal explanations in ecology by generalizations that are not, in a strict sense, laws. I also address the issue of mechanistic explanations in ecology by arguing that invariance and modularity constitute such explanations.     

The fractal nature of nature: power laws,ecological complexity and biodiversity

Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes. Power laws describe empirical scaling relationships that are emergent quantitative features of biodiversity. These features are patterns of structure or dynamics that are self-similar or fractal-like over many orders of magnitude. Power laws allow extrapolation and prediction over a wide range of scales. Some appear to be universal, occurring in virtually all taxa of organisms and types of environments. They offer clues to underlying mechanisms that powerfully constrain biodiversity. We describe recent progress and future prospects for understanding the mechanisms that generate these power laws, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science.     

Sober and Elgin on laws of biology: a critique

In this short discussion note, I discuss whether any of the generalizations made in biology should be construed as laws. Specifically, I examine a strategy offered by Elliot Sober (1997) and supported by Mehmet Elgin (2006) to reformulate certain biological generalizations so as to eliminate their contingency, thereby allowing them to count as laws. I argue that this strategy entails a conception of laws that is unacceptable on two counts: (1) Sober and Elgin’s approach allows the possibility of formulating laws describing any biological phenomenon whatsoever; and (2) on Sober and Elgin’s view, any interesting contrast between so-called laws and obviously accidental generalizations collapses. I conclude by offering suggestions to refine their view in order to avoid these theoretical problems.     

Causal Regularities in the Biological World of Contingent Distributions

Former discussions of biological generalizations have focused on the question of whether there are universal laws of biology. These discussions typically analyzed generalizations out of their investigative and explanatory contexts and concluded that whatever biological generalizations are, they are not universal laws. The aim of this paper is to explain what biological generalizations are by shifting attention towards the contexts in which they are drawn. I argue that within the context of any particular biological explanation or investigation, biologists employ two types of generations. One type identifies causal regularities exhibited by particular kinds of biological entities. The other type identifies how these entities are distributed in the biological world.     

Testing the allometric scaling laws

Allometric scaling laws have received increasing attention due to the recent theoretical advancements. However, existing evidence suggests that the scaling relationships may vary a lot without much consistency, which poses a challenge to the applicability of general theories. In this report, I demonstrate that much of the discrepancy may be an artefact caused by the limited use of methods for estimating the parameters in the allometric scaling equations. I suggest alternative procedures that can be utilized to avoid biased interpretations. The comments are largely applicable to any research that involves parameterization of equations.     

Genetic mapping of allometric scaling laws

Many biological processes, from cellular metabolism to population dynamics, are characterized by particular allometric scaling relationships between rate and size (power laws). A statistical model for mapping specific quantitative trait loci (QTLs) that are responsible for allometric scaling laws has been developed. We present an improved model for allometric mapping of QTLs based on a more general allometry equation. This improved model includes two steps: (1) use model II regression analysis to estimate the parameters underlying universal allometric scaling laws, and (2) substitute the estimated allometric parameters in the mixture-based mapping model to obtain the estimation of QTL position and effects. This model has been validated by a real example for a mouse F2 progeny, in which two QTLs were detected on different chromosomes that determine the allometric relationship between growth rate and body weight.     

Biological power laws and Darwin's principle

Assuming that the repertoire of responses by living systems to perturbation gives a measure of their Darwinian fitness in a rapidly fluctuating environment, those that fulfill allometries (power laws) are described by means of catastrophes, whose variables and parameters are smooth functions of biological attributes. Using empirical allometries from a given system as input, a method is proposed to construct its associated catastrophe, allowing specific predictions on its susceptibility to perturbation and related properties, based on general results from catastrophe theory. The method is discussed within the macroecological context, and an example is provided by applying it to ecological systems that satisfy the self-thinning rule.     

Size and shape interspecific divergence patterns partly reflect phylogeny in an Onthophagus species‐complex (Coleoptera: Scarabaeidae)

Polyphenism has been suggested as an accelerator for morphological evolution and speciation. In the dung beetles of the genus Onthophagus, horn expression is polyphenic: large males develop horns whereas smaller males express greatly reduced or no horns. Horn static allometries seem to diverge rapidly amongst extant taxa, a process which might trigger changes in the male genital morphology, thus possibly promoting speciation as a by‐product. It can therefore be hypothesized that interspecific distances in allometries and, possibly, in other morphological traits mirror phylogenetic distances. In this study we first assessed the phylogenetic relationships amongst three closely related taxa belonging to the so‐called ‘Onthophagus fracticornis‐similis‐opacicollis’ species‐complex by sequencing the mitochondrial gene cytochrome oxidase subunit 1 (cox1). Biomolecular results indicated three independent lineages, the closest relationships being found between Onthophagus similis and Onthophagus opacicollis. Then we assessed the extent to which divergence pattern of horn static allometries and size and shape divergence patterns of one genital (paramere) and two nongenital (head and epipharynx) structures mirrored the phylogenetic relationships. Interspecific divergence patterns of horn static allometries, paramere, and head shape were found to be congruent with the evolutionary relationships inferred from biomolecular data. Nevertheless, paramere size and epipharynx shape showed patterns not consistent with the phylogeny. Furthermore, the relative size of nongenital structures showed little interspecific divergence compared to their shapes. Our results suggest that size and shape interspecific divergence mirror phylogeny only in part; they also indicate that distinct morphological traits may differ in their tendency to evolve in concert, and that size and shape of the same trait can evolve independently across species. © 2011 The Linnean Society of London, Zoological Journal of the Linnean Society, 2011, 162 , 482–498.     

Density dependent and density independent relationships during a twenty-seven year study of the population dynamics of the benthic macroinvertebrate community of a chemically unstable lake

Data are given on net precipitation, water chemistry, vegetation cover and the population dynamics of 20 taxa of benthic macroinvertebrates from the total of 40 recorded ln the lake. The relationships between data sets were investigated by bivariate analysis. The relationships between abiotic factors are best described by linear equations as are some relationships between Sigara concinna, Sigara dorsalis, Potamopyrgus jenkinsi and environmental factors. The relationships of numbers of Gammarus tigrinus with temperature, Sigara stagnalis with conductivity, Corixidae with time and Sigara lateralis, Theromyzon tessulatum and Piscicola geometra with vegetation cover are best described by exponential equations. The relationships between the population dynamics of pairs of certain taxa viz. Gammarus tigrinus and G. duebeni, G. tigrinus and Asellus aquaticus, G. tigrinus and Corixidae, Sigara dorsalis and S. concinna, are best described by power equations. The relationship of vegetation cover with time and the population dynamics of many taxa are best described by logarithmic logistic equations.Both density dependent and density independent relationships appear to be responsible for changes in numbers and taxa within the total community. Density independent relationships are most important at times of environmental change while density dependent relationships, though operating continuously, are most important when conditions are stable.     

Scaling of Frond Form in Hawaiian Tree Fern Cibotium glaucum: Compliance with Global Trends and Application for Field Estimation

Large‐fronded tree ferns are critical components of many tropical forests. We investigated frond and whole‐plant allometries for Hawaiian keystone species Cibotium glaucum, for prediction and to compare with global scaling relationships. We found that C. glaucum fronds maintain geometric proportionality across a wide range of plant and frond sizes. These relationships result in strong allometries that permit rapid field estimation of frond size from simple linear dimensions. C. glaucum frond allometries complied with intra‐ and interspecific global trends for leaf area versus mass established for much smaller‐leafed species, indicating ‘diminishing returns’ in photosynthetic area per investment in mass for larger fronds. The intraspecific trend was related to declining water content in larger fronds, but not to a significantly larger investment in stipe or rachis relative to lamina. However, C. glaucum complied with the global interspecific trends for greater allocation to support structures in larger leaves. Allometries for frond number and size versus plant height showed that as plants increase in height, frond production and/or retention progressively declines, and the increases of leaf size tend to level off. These frond and whole plant‐level relationships indicate the potential for estimating frond area and mass at landscape scale to enrich studies of forest dynamics.     

Ecological scaling laws link individual body size variation to population abundance fluctuation

Scaling research has seen remarkable progress in the past several decades. Many scaling relationships were discovered within and across individual and population levels, such as species–abundance relationship, Taylor's law, and density mass allometry. However none of these established patterns incorporate individual variation in the formulation. Individual body size variation is a key evolutionary phenomenon and closely related to ecological diversity and species adaptation. Using a macroecological approach, I test 57 Long‐Term Ecological Research data sets and show that a power‐law and a generalized power‐law function describe well the mean‐variance scaling of individual body mass. This relationship connects Taylor's law and density mass allometry, and leads to a new scaling pattern between the individual body size variation and population abundance fluctuation, which is confirmed using freshwater fish and forest tree data. Underlying mechanisms and implications of the proposed scaling relationships are discussed. This synthesis shows that integration and extension of existing ecological laws can lead to the discovery of new scaling patterns and complete our understanding of the relation between individual trait and population abundance. Synthesis Scaling relationships are useful for community ecology as they reveal ubiquitous patterns across different levels of biological organizations. This work extends and integrates two existing scaling laws: Taylor's law and density‐mass allometry, and derives a new variance allometry between individual body mass and population abundance. The result shows that diverse individual body size is associated with stable population fluctuation, reflecting the effect of individual traits on population characteristics. Confirmed by several empirical data sets, these scaling relationships suggest new ways to study the underlying mechanisms of Taylor's law and have profound implications for fisheries and other applied sciences.     

Conservative whole‐organ scaling contrasts with highly labile suborgan scaling differences among compound eyes of closely related Formica ants

Static allometries determine how organ size scales in relation to body mass. The extent to which these allometric relationships are free to evolve, and how they differ among closely related species, has been debated extensively and remains unclear; changes in intercept appear common, but changes in slope are far rarer. Here, we compare the scaling relationships that govern the structure of compound eyes of four closely related ant species from the genus Formica. Comparison among these species revealed changes in intercept but not slope in the allometric scaling relationships governing eye area, facet number, and mean facet diameter. Moreover, the scaling between facet diameter and number was conserved across all four species. In contrast, facet diameters from distinct regions of the compound eye differed in both intercept and slope within a single species and when comparing homologous regions among species. Thus, even when species are conservative in the scaling of whole organs, they can differ substantially in regional scaling within organs. This, at least partly, explains how species can produce organs that adhere to genus wide scaling relationships while still being able to invest differentially in particular regions of organs to produce specific features that match their ecology.     

Dichotomy of eutherian reproduction and metabolism

How anatomical, physiological and ecological (life history) features scale with body mass is a fundamental question in biology. There is an ongoing debate in the scientific literature whether allometric scaling follows a universal pattern that can be described in a single model, or differs between groups. However, recently some analyses were published demonstrating a change in scaling across the body mass range: brain‐size allometry of mammals indicates that scaling follows a curvilinear pattern in double‐logarithmic space, and a quadratic pattern in double‐logarithmic space was found in one of the largest physiological datasets, on basal metabolic rate (MR) in mammals. Here, we analysed a variety of independent datasets on anatomical, physiological and ecological characteristics in mammals, birds and reptiles to answer the question whether the quadratic scaling is a universal biological law, or a pattern unique to mammals. The pattern was present in mammalian basal and field MR, brain size, and reproduction parameters, but neither in other organ allometries in mammals, nor in the scaling of MR in birds and reptiles. However, the curvature was better explained by separate allometric scaling of three different mammalian reproduction strategies: marsupials, and eutherian mammals with one and with many offspring. The two latter strategies are distributed unequally over the body mass range in eutherian mammals. Our findings show that a quadratic model, as well as a traditional allometric model with a universal scaling exponent (such as 0.67 or 0.75), may be inappropriate in mammals as they are a result of different scalings within these three reproductive groups. We propose that the observed distribution pattern is the result of the eutherian mammal clade's uniquely pronounced dichotomy of reproductive strategies.     

Scale-Adjusted Metrics for Predicting the Evolution of Urban Indicators and Quantifying the Performance of Cities

More than a half of world population is now living in cities and this number is expected to be two-thirds by 2050. Fostered by the relevancy of a scientific characterization of cities and for the availability of an unprecedented amount of data, academics have recently immersed in this topic and one of the most striking and universal finding was the discovery of robust allometric scaling laws between several urban indicators and the population size. Despite that, most governmental reports and several academic works still ignore these nonlinearities by often analyzing the raw or the per capita value of urban indicators, a practice that actually makes the urban metrics biased towards small or large cities depending on whether we have super or sublinear allometries. By following the ideas of Bettencourt et al. [PLoS ONE 5 (2010) e13541], we account for this bias by evaluating the difference between the actual value of an urban indicator and the value expected by the allometry with the population size. We show that this scale-adjusted metric provides a more appropriate/informative summary of the evolution of urban indicators and reveals patterns that do not appear in the evolution of per capita values of indicators obtained from Brazilian cities. We also show that these scale-adjusted metrics are strongly correlated with their past values by a linear correspondence and that they also display crosscorrelations among themselves. Simple linear models account for 31%–97% of the observed variance in data and correctly reproduce the average of the scale-adjusted metric when grouping the cities in above and below the allometric laws. We further employ these models to forecast future values of urban indicators and, by visualizing the predicted changes, we verify the emergence of spatial clusters characterized by regions of the Brazilian territory where we expect an increase or a decrease in the values of urban indicators.     

Mass,phylogeny, and temperature are sufficient to explain differences in metabolic scaling across mammalian orders?

Whether basal metabolic rate‐body mass scaling relationships have a single exponent is highly discussed, and also the correct statistical model to establish relationships. Here, we aimed (1) to identify statistically best scaling models for 17 mammalian orders, Marsupialia, Eutheria and all mammals, and (2) thereby to prove whether correcting for differences in species’ body temperature and their shared evolutionary history improves models and their biological interpretability. We used the large dataset from Sieg et al. (The American Naturalist 174 , 2009, 720) providing species’ body mass (BM), basal metabolic rate (BMR) and body temperature (T). We applied different statistical approaches to identify the best scaling model for each taxon: ordinary least squares regression analysis (OLS) and phylogenetically informed analysis (PGLS), both without and with controlling for T. Under each approach, we tested linear equations (log‐log‐transformed data) estimating scaling exponents and normalization constants, and such with a variable normalization constant and a fixed exponent of either ? or ¾, and also a curvature. Only under temperature correction, an additional variable coefficient modeled the influence of T on BMR. Except for Pholidata and Carnivora, in all taxa studied linear models were clearly supported over a curvature by AICc. They indicated no single exponent at the level of orders or at higher taxonomic levels. The majority of all best models corrected for phylogeny, whereas only half of them included T. When correcting for T, the mathematically expected correlation between the exponent (b) and the normalization constant (a) in the standard scaling model y = a x ^b was removed, but the normalization constant and temperature coefficient still correlated strongly. In six taxa, T and BM correlated positively or negatively. All this hampers a disentangling of the effect of BM, T and other factors on BMR, and an interpretation of linear BMR‐BM scaling relationships in the mammalian taxa studied.     

Property relations: alien land laws and the racial formation of Filipinos as aliens ineligible to citizenship

Because Filipino Americans are racially categorized as Asians today, many scholars presume that they were automatically included within the provisions of the alien land laws at the time of their legislation. The following article suggests that the racial status of Filipino Americans, during this early period, was much more ambiguous. Instead, most Americans perceived Filipinos in relation to Native and African-Americans. The Alien Land Laws (1913–1952) were, together with anti-miscegenation laws and the Tydings-McDuffie Act, a regime of legal policies that eventually transformed Filipinos into Asians by 1934. Meanwhile, their racial ambiguity provided early Filipino immigrants with significant opportunities to challenge their exclusion in American society, and especially the alien land laws.     

Spatial scaling laws do not structure strongyloid nematode communities in macropodid hosts

The characteristics of species within a community can influence the number of species that can coexist within that community. In particular, body size can constrain how many individuals can 'fit' into a community, and overlap in resource use between species depends on differences in their body sizes. Here, using data from 18 communities of strongyloid nematodes living in the stomachs of macropodid marsupials, we test key predictions derived from spatial scaling laws regarding the minimum similarity in body size between coexisting species believed to control how many species can coexist in a community. These communities are ideal systems for such a test: they consist of huge numbers of individuals from numerous species, all belonging to the same family (Chabertiidae) and living in the same host organ. Within these communities, we found that mean abundance correlated negatively with body size across all nematode species, whether body size was measured as length or volume. However, we found no support for the predictions of spatial scaling laws. First, the size ratios of pairs of adjacent-sized species did not decrease as a function of the size of the largest species in a pair. The few significant relationships observed were all positive, suggesting that the relative difference in size between adjacent species in the size hierarchy may in fact increase toward the upper end of the size spectrum. Second, the frequency distributions of body sizes were predominantly right-skewed amongst the communities investigated: within the size spectrum observed in a nematode community, small-bodied species greatly outnumber large-bodied ones, in sharp contrast to the predictions of spatial scaling laws. Nematode body size may thus determine the abundance achieved by a species but not how many species can coexist; the limiting similarity between coexisting species must depend on other biological traits.     

Allometric scaling laws for water uptake by plant roots

This paper develops scaling laws for plant roots of any arbitrary volume and branching configuration that maximize water uptake. Water uptake can occur along any part of the root network, and thus there is no branch-to-branch fluid conservation. Maximizing water uptake, therefore, involves balancing two flows that are inversely related: axial and radial conductivity. The scaling laws are tested against the root data of 1759 plants from 77 herbaceous species, and compared with those from the WBE model. I further discuss whether the scaling laws are invariant to soil water distribution. A summary of some of the results follows. (1) The optimal radius for a single root (no branches) scales with volume as . (2) The basic allometric scaling for root radius branches (r_i+1=β*r_i) is of the form , where f(N)=A(N)/(n_b*(1+A(N))), n_b is the number of branches, and A(N) and ε(N) are functions of the number of root diameter classes (not constants as in the WBE model). (3) For large N, β converges to the β from the WBE model. For small N, the β's for the two models diverge, but are highly correlated. (4) The fractal assumption of volume filling of the WBE model are also met in the root model even though they are not explicitly incorporated into it. (5) The WBE model for rigid tubes is an asymptotic solution for large root systems (large N and biomass). (6) The optimal scaling solutions for the root network appears to be independent of soil water distribution or water demand. The data set used for testing is included in the electronic supplementary archive of the journal.     

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.