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Microplastics Versus Natural Mineral Particles. How to Create and Test Them While Maintaining Environmental Relevance
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Microplastics (MP) are perceived as a threat to aquatic ecosystems but bear many similarities to suspended sediments which are often considered less harmful. It is, therefore pertinent to determine if and to what extent MP are different from other particles occurring in aquatic ecosystems in terms of their adverse effects. We applied meta-regressions to toxicity data extracted from the literature and harmonized the data to construct Species Sensitivity Distributions (SSDs) for both types of particles. The results were largely inconclusive due to high uncertainty but the central tendencies of our estimates still indicate that MP could be marginally more hazardous compared to suspended sediments. In part, the high uncertainty stems from the general lack of comparable experimental studies and dose-dependent point estimates. We therefore argue that until more comparable data is presented, risk assessors should act precautionary and treat MP in the 1-1000 µm size range as marginally more hazardous to aquatic organisms capable of ingesting such particles.
To fully understand the potential ecological and human health risks from nanoplastics and microplastics (NMPs) in the environment, it is critical to make accurate measurements. Similar to past research on the toxicology of engineered nanomaterials, a broad range of measurement artifacts and biases are possible when testing their potential toxicity. For example, antimicrobials and surfactants may be present in commercially available NMP dispersions, and these compounds may account for toxicity observed instead of being caused by exposure to the NMP particles. Therefore, control measurements are needed to assess potential artifacts, and revisions to the protocol may be needed to eliminate or reduce the artifacts. In this paper, we comprehensively review and suggest a next generation of control experiments to identify measurement artifacts and biases that can occur while performing NMP toxicity experiments. This review covers the broad range of potential NMP toxicological experiments, such as in vitro studies with a single cell type or complex 3-D tissue constructs, in vivo mammalian studies, and ecotoxicity experiments testing pelagic, sediment, and soil organisms. Incorporation of these control experiments can reduce the likelihood of false positive and false negative results and more accurately elucidate the potential ecological and human health risks of NMPs.
Determining the risks of microplastics is difficult because data is of variable quality and cannot be compared. Although sediments are important sinks for microplastics, no holistic risk assessment framework is available for this compartment. Here we assess the risks of microplastics in freshwater sediments worldwide, using strict quality criteria and alignment methods. Published exposure data were screened for quality using new criteria for microplastics in sediment and were rescaled to the standard 1 to 5000 µm microplastic size range. Threshold effect data were also screened for quality and were aligned to account for the polydispersity of environmental microplastics and for their bioaccessible fraction. Risks were characterized for effects triggered by food dilution or translocation, using ingested particle volume and surface area as ecologically relevant metrics, respectively. Based on species sensitivity distributions, we determined Hazardous Concentrations for 5% of the species (HC5, with 95% CI) of 4.9×109 (6.6×107 – 1.9×1011) and 1.1×1010 (3.2×108 – 4.0×1011) particles / kg sediment d.w., for food dilution and translocation, respectively. For all locations considered, exposure concentrations were either below or in the margin of uncertainty of the HC5 values. We conclude that risks from microplastics to benthic communities cannot be excluded at current concentrations in sediments worldwide.
Graphical abstract
There is definitive evidence that microplastics, defined as plastic particles less than 5 mm in size, are ubiquitous in the environment and can cause harm to aquatic organisms. These findings have prompted legislators and environmental regulators to seek out strategies for managing risk. However, microplastics are also an incredibly diverse contaminant suite, comprising a complex mixture of physical and chemical characteristics (e.g., sizes, morphologies, polymer types, chemical additives, sorbed chemicals, and impurities), making it challenging to identify which particle characteristics might influence the associated hazards to aquatic life. In addition, there is a lack of consensus on how microplastic concentrations should be reported. This not only makes it difficult to compare concentrations across studies, but it also begs the question as to which concentration metric may be most informative for hazard characterization. Thus, an international panel of experts was convened to identify 1) which concentration metrics (e.g., mass or count per unit of volume or mass) are most informative for the development of health-based thresholds and risk assessment and 2) which microplastic characteristics best inform toxicological concerns. Based on existing knowledge, it is recommended that microplastic concentrations in toxicity tests are calculated from both mass and count at minimum, though ideally researchers should report additional metrics, such as volume and surface area, which may be more informative for specific toxicity mechanisms. Regarding particle characteristics, there is sufficient evidence to conclude that particle size is a critical determinant of toxicological outcomes, particularly for the mechanisms of food dilution and tissue translocation .
Microplastic particles (MPs) are ubiquitous across a wide range of aquatic habitats but determining an appropriate level of risk management is hindered by a poor understanding of environmental risk. Here, we introduce a risk management framework for aquatic ecosystems that identifies four critical management thresholds, ranging from low regulatory concern to the highest level of concern where pollution control measures could be introduced to mitigate environmental emissions. The four thresholds were derived using a species sensitivity distribution (SSD) approach and the best available data from the peer-reviewed literature. This included a total of 290 data points extracted from 21 peer-reviewed microplastic toxicity studies meeting a minimal set of pre-defined quality criteria. The meta-analysis resulted in the development of critical thresholds for two effects mechanisms: food dilution with thresholds ranging from ~ 0.5 to 35 particles/L, and tissue translocation with thresholds ranging from ~ 60 to 4100 particles/L. This project was completed within an expert working group, which assigned high confidence to the management framework and associated analytical approach for developing thresholds, and very low to high confidence in the numerical thresholds. Consequently, several research recommendations are presented, which would strengthen confidence in quantifying threshold values for use in risk assessment and management. These recommendations include a need for high quality toxicity tests, and for an improved understanding of the mechanisms of action to better establish links to ecologically relevant adverse effects.
Ingestion of microplastics by aquatic organisms is often harmful due to the dilution of their regular food with low-calorie microplastic particles, but can also be beneficial if nutritious biofilms are present on the microplastic surface. This begs the question: is ingestion of microplastic harmful or beneficial and can the net effect of the two mechanisms be quantified? Here, we quantified these harmful and beneficial effects on Daphnia magna, using dose-response tests with clean and biofouled microplastic respectively, and determined the trade-off between these counteracting effects. A population model was developed to calculate the isoclines for zero population growth, separating the regime where adverse food dilution dominated from that where the beneficial biofilm vector mechanism dominated. Our results show that the organisms grew better when exposed to biofouled microplastic compared to pristine microplastic. Very good model predictions (R2 = 0.868–0.991) of the effects of biofouled microplastic were obtained based on literature parameter values, with optimization required only for the two sub-model parameters driving the dose-effect relationships for pristine microplastic. These results contradict previous sudies were only pristine microplastic were used and demonstrate that the ruling paradigm of unambiguously adverse microplastic effects is not ecologically justifiable.
The concern that in nature, ingestion of microplastic (MP) increases exposure of organisms to plastic-associated chemicals (the 'MP vector effect') plays an important role in the current picture of the risks of microplastic for the environment and human health. An increasing number of studies on this topic have been conducted using a wide variety of approaches and techniques. At present, the MP vector effect is usually framed as 'complex', 'under debate' or 'controversial'. Studies that critically discuss the approaches and techniques used to study the MP vector effect, and that provide suggestions for the harmonization needed to advance this debate, are scarce. Furthermore, only a few studies have strived at interpreting study outcomes in the light of environmentally relevant conditions. This constitutes a major research gap, because these are the conditions that are most relevant when informing risk assessment and management decisions. Based on a review of 61 publications, we propose evaluation criteria and guidance for MP vector studies and discuss current study designs using these criteria. The criteria are designed such that studies, which fulfil them, will be relevant to inform risk assessment. By critically reviewing the existing literature in the light of these criteria, a weight of evidence assessment is provided. We demonstrate that several studies did not meet the standards for their conclusions on the MP vector effect to stand, whereas others provided overwhelming evidence that the vector effect is unlikely to affect chemical risks under present natural conditions.
As a consequence of the global ubiquity of plastic pollution, scientists, decision‐makers, and the public often ask whether macroplastics (>5 mm) and microplastics (<5 mm) have a realized ecological threat. In 2016, we conducted a systematic review of the literature and made a call for further research testing hypotheses about ecological effects. In the subsequent years, the amount of relevant research has risen tremendously. Here, we reassess the literature to determine the current weight of evidence about the effects of plastic pollution across all levels of biological organization. Our data spans marine, freshwater, and terrestrial environments. We extracted data from 139 lab and field studies testing 577 independent effects across a variety of taxa and with various types, sizes, and shapes of plastic. Overall, 59% of the tested effects were detected. Of these, 58% were due to microplastics and 42% were due to macroplastics. Of the effects that were not detected, 94% were from microplastics and 6% were from macroplastics. We found evidence that whether or not an effect is detected, as well as the severity and direction of the effect, is driven by dose, particle shape, polymer type, and particle size. Based on our analyses, there is no doubt that macroplastics are causing ecological effects, however, the effects of microplastics are much more complex. We also assessed the environmental relevancy of experimental studies by comparing the doses used in each exposure to the concentrations and sizes of microplastics found in the environment. We determined that only 17% of the concentrations used in experimental studies have been found in nature, and that 80% of particle sizes used in experiments fall below the size range of the majority of environmental sampling. Based on our systematic review and meta‐analysis, we make a call for future work that recognizes the complexity of microplastics and designs tests to better understand how different types, sizes, shapes, doses, and exposure durations affect wildlife. We also call for more ecologically and environmentally relevant studies, particularly in freshwater and terrestrial environments.
The occurrence of microplastic in the environment is of global concern. However, the microplastic hazard assessment is hampered by a lack of adequate ecotoxicological methods because of conceptual and practical problems with particle exposure. In the environment, suspended solids (e.g., clay and cellulose) in the same size range as microplastic, are ubiquitous. Therefore, it must be established whether the addition of microplastic to these background levels of particulate material represents a hazard. We present a novel approach employing a serial dilution of microplastic and reference particles, in mixtures, which allows disentangling the effect of the microplastic from that of the other particulates. We demonstrate the applicability of the method using an immobilization test with Daphnia magna exposed to polyethylene terephthalate (test microplastic; median particle diameter ~5 µm) and kaolin clay (reference material; ~3 µm). In the range of the suspended solids test concentrations (0–10 000 mg L−1), with microplastic contributing 0–100% of total mass, the LC50 values for the plastic mixtures were significantly lower compared to the kaolin exposure. Hence, the exposure to polyethylene terephthalate was more harmful to the daphnids than to the reference material alone. The estimated threshold for the relative contribution of the test microplastic to suspended matter above which significantly higher mortality was observed was 2.4% at 32 mg of the solids L−1. This approach has a potential for standardization of ecotoxicological testing of particulates, including microplastic.
Because of their diverse sizes, shapes and densities, environmental microplastics are often perceived as complex. Many studies struggle with this complexity, and either address only a part of this diversity, or present data using discrete classifications for sizes, shapes and densities. We argue that such classifications will never be fully satisfactory, as any definition using classes does not capture the essentially continuous nature of environmental microplastic. Therefore, we propose to simplify microplastics by fully defining them through a 3D probability distribution, with size, shape and density as dimensions. Besides introducing the concept, we parameterize these probability distributions, using empirical data. This parameterization results in an approximate yet realistic representation of ‘true’ environmental microplastic. This approach to simplify microplastic could be applicable to exposure measurements, effect studies and fate modelling. Furthermore, it allows for easy comparison between studies, irrespective of sampling or laboratory setup. We demonstrate how the 3D probability distribution of environmental versus ingested microplastic can be helpful in understanding bioavailability of and exposure to microplastic. We argue that the concept of simplified microplastic will also be helpful in probabilistic risk modelling, which would greatly enhance the understanding of the risk that microplastics pose to the environment.
There is increasing scientific and public concern over the presence of microplastics (MPs) in the natural environment. Here, we present the results of a systematic review of the literature to assess the weight of evidence for MPs causing environmental harm. We conclude that MPs do occur in surface water and sediments. Fragments and fibers predominate with beads making up only a small proportion of the detected MP types. Concentrations detected are orders of magnitude lower than those reported to affect molecular level endpoints, feeding, reproduction, growth, tissue inflammation and mortality in organisms. The evidence for MPs acting as a vector for hydrophobic organic compounds (HOC) to accumulate in organisms is also weak. The available data therefore suggest that these materials are not causing harm to the environment. There is however a mismatch between the particle types, size ranges, and concentrations of MPs used in laboratory tests and those measured in the environment. Select environmental compartments have also received limited attention. There is an urgent need for studies that address this mismatch by performing better quality and more holistic monitoring studies alongside more environmentally realistic effects studies. Only then will we be able to fully characterize risks of MPs to the environment in order to support the introduction of regulatory controls that can make a real positive difference to environmental quality.
Researcher and media alarms have caused plastic debris to be perceived as a major threat to humans and animals. However, although the waste of plastic in the environment is clearly undesirable for aesthetic and economic reasons, the actual environmental risks of different plastics and their associated chemicals remain largely unknown. Here we show how a systematic assessment of adverse outcome pathways based on ecologically relevant metrics for exposure and effect can bring risk assessment within reach. Results of such an assessment will help to respond to the current public worry in a balanced way and allow policy makers to take measures for scientifically sound reasons.
Microplastic is an umbrella term that covers many particle shapes, sizes, and polymer types, and as such the physical and chemical properties of environmental microplastics will differ from the primary microbeads commonly used for ecotoxicity testing. In the present article, we discuss the physical and chemical properties of microplastics that are potentially relevant to their ecotoxicity, including particle size, particle shape, crystallinity, surface chemistry, and polymer and additive composition. Overall, there is a need for a structured approach to the testing of different properties to identify which are the most relevant drivers of microplastic toxicity. In addition, the properties discussed will be influenced by and change depending on environmental conditions and degradation pathways. Future challenges include new technologies that will enter the plastic production cycle and the impact of these changes on the composition of environmental microplastics.
Integr Environ Assess Manag 2017;13:470–475.
Dose-response analysis can be carried out using multi-purpose commercial statistical software, but except for a few special cases the analysis easily becomes cumbersome as relevant, non-standard output requires manual programming. The extension package drc for the statistical environment R provides a flexible and versatile infrastructure for dose-response analyses in general. The present version of the package, reflecting extensions and modifications over the last decade, provides a user-friendly interface to specify the model assumptions about the dose-response relationship and comes with a number of extractors for summarizing fitted models and carrying out inference on derived parameters. The aim of the present paper is to provide an overview of state-of-the-art dose-response analysis, both in terms of general concepts that have evolved and matured over the years and by means of concrete examples.
For the past 25 years NIH Image and ImageJ software have been pioneers as open tools for the
analysis of scientific images. We discuss the origins, challenges and solutions of these two programs,
and how their history can serve to advise and inform other software projects.
As microplastics may bring about adverse effects on living organisms, it is important to establish more precise quantification approaches to better understand their dynamics. One method to determine the concentration of microplastics is to estimate their mass using three-dimensional (3D) models, but its accuracy is not well known. In this study, we evaluated the shape of the particles and verified the accuracy of a 3D model-based mass estimation using samples from a tidal flat facing Tokyo Bay. The particle shape evaluation suggested that the microplastics were flat and irregular in shape; based on these data, we created two types of models to estimate their mass. As a result, an accuracy of mass estimation by our model was higher than other models that consider the slenderness and flatness of particles. The optimization of mass estimation methods based on 3D models may improve the reliability of microplastic evaluation in monitoring studies.
Although microplastics are an emerging pollutant of global concern, little is known about the environmental behavior of microplastic in sediments. This study investigated the occurrence and seasonal variation of microplastics in the sediments of Liangfeng River, China with a fluorescence staining method, and then explored the transfer of microplastics at the water and sediment interfaces during resuspension. The results showed that smaller microplastics were detected in the sediments, which were concentrated in the size range of 50−500 μm. Microplastic abundance in the sediments in the dry season were slightly higher than those from the rainy season, and the rainy season promotes the accumulation of smaller microplastics in the sediment along the river-flow direction but not for the dry season. The shape of microplastics were predominantly fibers, followed by fragments and films. Polyethylene was the most abundant polymer, accounting for more than 50 % of the total. Microplastics in the surface sediment move both to the overlying water and deeper sediment during the disturbance process. Disturbance-induced resuspension and vertical transport have significant effects on small-sized microplastics (50−500 μm). Small-sized microplastics can potentially migrate and redistribute via resuspension at different temporal and spatial scales, as some extent of resuspension is occurring in most river systems, especially in urban areas with boat traffic.
Effects of microplastics on marine taxa have become a focal point in marine experimental biology. Almost all studies so far, however, assessed the influence of microplastics on animals only in relation to a zero-particle group. Documented microplastic impacts may thus be overestimated, since many marine species also experience natural suspended solids as a stressor. Here, we compared the effects of polyvinyl chloride (PVC) and red clay (mean for both particles: ~12–14 μm) on the Mediterranean mussel Mytilus galloprovincialis across three particle concentrations (1.5, 15, 150 mg l−1). Exposure to PVC for 35 days lowered mussel body condition index by 14% in relation to clay, but no difference in byssus production, respiration and survival rates emerged between the two particle types. This suggests that the effects of synthetic particles on filter feeders may emulate those of natural suspended solids, and highlights the importance of including natural particles in microplastic exposure studies.
Freshwater sediments are a repository of microplastics (MPs) resulting from inland anthropogenic activities. Benthic invertebrates, particularly endobenthic sediment–ingesting species such as the annelid Lumbriculus variegatus (blackworm), are commonly found in contaminated sediments where they likely find and ingest MPs. In the present study, L. variegatus was exposed to concentrations between 0.51 and 20 g kg−1 dry sediment of four size-classes of irregularly-shaped polyethylene MPs (PE-MPs; size-class A: 32–63, B: 63–125, C: 125–250 and D: 250–500 μm) for 48 h to assess their sub-cellular responses to particles ingested, and for 28 days to determine chronic effects on worm's reproduction and biomass.
After the short-term exposure (48 h), number of PE-MPs in blackworms' gut were related to MPs concentration in the sediment. In general, PE-MPs ingestion by blackworms induced depletion of their energy reserves (e.g., sugars in all size classes and lipids in the size-classes of PE-MPs > 125 μm), concomitant with the activation of antioxidant and detoxification mechanisms (increased level of total glutathione in all size-classes, and increased glutathione-S-transferase activity in PE-MPs > 250 μm), preventing lipid peroxidation. In addition, it was observed a reduction of aerobic energy production (decreased activity of the electron transport system) and a slight increase in neurotransmission (cholinesterase activity). After a long-term exposure (28 d), the presence and ingestion of PE-MPs did not affect reproduction and biomass of L. variegatus.
The activation and efficiency of the antioxidant and detoxification mechanisms allied with the anatomy and physiology of L. variegatus, its feeding strategy and potentially dynamic ingestion/egestion capacity seem to be key features preventing MP deleterious effects under short- and chronic-exposures. Considering the MPs levels reported for freshwater sediments, and despite evidence of MPs ingestion and some sub-organismal effects, our results suggest no adverse impacts of PE-MPs contamination on L. variegatus populations fitness.
This study applies an integrative approach in which data concerning the ingestion of different sized MPs and subsequent sub-cellular and apical responses are delivered, raising knowledge on endobenthic invertebrates’ strategies to potentially overcome MP toxicity in field contaminated sites.
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Several studies have investigated the effects of nano- and microplastics on daphnids as key freshwater species. However, while information is abundant on the acute toxicity of plastic beads, little is known regarding the multigenerational effects of irregular microplastics. In addition, a comparison of microplastics to naturally occurring particles is missing. Therefore, we investigated the effects of irregular, secondary polystyrene microplastics (<63 mm) and kaolin as natural reference particle on the survival, reproduction, and growth of Daphnia magna over four generations under food-limited conditions. Additionally, we tested the sensitivity of the neonates in each generation to a reference compound as a proxy for offspring fitness. Exposure to high concentrations of microplastics (10,000 and 2000 particles mL-1) reduced daphnid survival, resulting in extinction within one and four generations, respectively. Microplastics also affected reproduction and growth. Importantly, an exposure to kaolin at similar concentrations did not induce negative effects. The sensitivity of neonates to potassium dichromate was not affected by maternal exposure to particles. Taken together, our study demonstrates that irregular PS particles are more toxic than natural kaolin in daphnids exposed over multiple generations under food
limitation. Thus, our work builds towards more realistic exposure scenarios needed to better understand the impacts of microplastics on zooplankton.
Microplastics are present in aquatic ecosystems the world over and may influence the feeding, growth, reproduction, and survival of freshwater and marine biota; however, the extent and magnitude of potential effects of microplastics on aquatic organisms is poorly understood. In the current study, we conducted a meta-analysis of published literature to examine impacts of exposure to microplastics on consumption (and feeding), growth, reproduction, and survival of fish and aquatic invertebrates. While we did observe within-taxa negative effects for all four categories of responses, many of the effects summarized in our study were neutral, indicating that the effects of exposure to microplastics are highly variable across taxa. The most consistent effect was a reduction in consumption of natural prey when microplastics were present. For some taxa, negative effects on growth, reproduction and even survival were also evident. Organisms that serve as prey to larger predators, e.g., zooplankton, may be particularly susceptible to negative impacts of exposure to microplastic pollution, with potential for ramifications throughout the food web. Future work should focus on whether microplastics may be affecting aquatic organisms more subtly, e.g., by influencing exposure to contaminants and pathogens, or by acting at a molecular level.
Microplastic pollution is currently perceived as an environmental hazard, and adverse effects have been reported at various levels of biological organization. However, most experimental designs do not allow plastic-specific effects to be distinguished from those caused by other particles, such as clay and cellulose, which are naturally ubiquitous in the environment. We suggest that microplastic effects reported in recent ecotoxicological studies are similar to those induced by the natural particles. To provide a sound basis for risk assessment, experimental designs must not only be able to disentangle the effects of food limitation and particle toxicity but also demonstrate whether microplastics cause impacts that differ from those induced by natural particles.
Microplastics (<5 mm) are ubiquitous in the marine environment and are ingested by zooplankton with possible negative effects on survival, feeding, and fecundity. The majority of laboratory studies has used new and pristine microplastics to test their impacts, while aging processes such as weathering and biofouling alter the characteristics of plastic particles in the marine environment. We investigated zooplankton ingestion of polystyrene beads (15 and 30 μm) and fragments (≤30 μm), and tested the hypothesis that microplastics previously exposed to marine conditions (aged) are ingested at higher rates than pristine microplastics. Polystyrene beads were aged by soaking in natural local seawater for three weeks. Three zooplankton taxa ingested microplastics, excluding the copepod Pseudocalanus spp., but the proportions of individuals ingesting plastic and the number of particles ingested were taxon and life stage specific and dependent on plastic size. All stages of Calanus finmarchicus ingested polystyrene fragments. Aged microbeads were preferred over pristine ones by females of Acartia longiremis as well as juvenile copepodites CV and adults of Calanus finmarchicus. The preference for aged microplastics may be attributed to the formation of a biofilm. Such a coating, made up of natural microbes, may contain similar prey as the copepods feed on in the water column and secrete chemical exudates that aid chemodetection and thus increase the attractiveness of the particles as food items. Much of the ingested plastic was, however, egested within a short time period (2-4 h) and the survival of adult Calanus females was not affected in an 11-day exposure. Negative effects of microplastics ingestion were thus limited. Our findings emphasize, however, that aging plays an important role in the transformation of microplastics at sea and ingestion by grazers, and should thus be considered in future microplastics ingestion studies and estimates of microplastics transfer into the marine food web.
Microplastics are omnipresent in the marine environment and sediments are hypothesized to be major sinks of these plastics. Here, over 100 articles spanning the last 50 year are reviewed with following objectives: (i) to evaluate current microplastic extraction techniques, (ii) to discuss the occurrence and worldwide distribution of microplastics in sediments, and (iii) to make a comprehensive assessment of the possible adverse effects of this type of pollution to marine organisms. Based on this review we propose future research needs and conclude that there is a clear need for a standardized techniques, unified reporting units and more realistic effect assessments.
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Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out. Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws/
When the probability of measuring a particular value of some quantity varies
inversely as a power of that value, the quantity is said to follow a power law,
also known variously as Zipf's law or the Pareto distribution. Power laws
appear widely in physics, biology, earth and planetary sciences, economics and
finance, computer science, demography and the social sciences. For instance,
the distributions of the sizes of cities, earthquakes, solar flares, moon
craters, wars and people's personal fortunes all appear to follow power laws.
The origin of power-law behaviour has been a topic of debate in the scientific
community for more than a century. Here we review some of the empirical
evidence for the existence of power-law forms and the theories proposed to
explain them.
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