Taylor's Law Research Articles

Analyzing Taylor's Scaling Law: qualitative differences of social and territorial behavior on colonization/extinction dynamics

AbstractThe power law relation between the mean population count and its variance (Taylor's Power Law, TPL) is among the few general patterns in population ecology. While the TPL has been described to be pervasive across taxa, the causes of variation of the exponent describing this relation is not well understood. We compare the TPL exponents for two species with different social systems and behavior: Piñon jays (Gymnorhinus cyanocephalus) and Western scrub‐jays (Aphelocoma californica). We analyze the underlying processes that generate the expected values of population size and its variance. Using a probabilistic model, we identify and estimate important processes involved in the generation of the TPL exponents. While both species show a scaling relationship between their mean and abundance, share a common negative relation between mean abundance and colonization–extinction rates, they differ greatly in the statistical distributions of colonization, extinction, the mean number of colonists, the probability of zero abundance and population sizes. We show how different aspects of the processes that generate abundance affect the TPL exponent, thereby providing empirical guidelines to interpret differences in the scaling relation between mean and variance of population size.

Petition for Writ of Certiorari: Re; Constitutional Challenge to the 'Taylor Law' Cert. Denied.

Petition for Writ of Certiorari: Re; Constitutional challenge to the Taylor Law Cert. Denied.

Taylor's power law and fluctuation scaling explained by a central-limit-like convergence

A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.

Hydrogen-bond network formation of water molecules and its effects onthe glass transitions in the ethylene glycol aqueous solutions: failureof the Gordon–Taylor law in the water-rich range and absence of theTg = 115 K rearrangement process in bulk pure water

Enthalpy relaxation processes proceeding in ethylene glycol (EG) aqueous solutions[(EG)x(H2O)1 − x] within silica-gel nanopores were studied by adiabatic calorimetry. While thex = 0.25 solution within pores with diameter of 52 nm showed a glass transition atTg = 139 K, ageing of the solution at 160 K caused a phase separation to reveal glass transitions atTg = 145 and 160 K for EG-rich and water-rich regions, respectively: the water moleculesare understood to form a more developed hydrogen-bond network, andconsequently force the EG molecules in between the water-rich regions. TheTg = 160 K is in goodagreement with the Tg value of the internal (not interfacial) water confined within poreswith thickness of 1.1 nm. The ageing further remarkably diminished theTg = 115 K glass transition. This indicates that, while the molecules responsible for the glasstransition are the mobile water ones forming a lower number of hydrogen bonds than four,the fraction of such water molecules is reduced in association with the development of thenetwork and the glass transition is absent in bulk pure water. When the samex = 0.25 solution was confined within 1.1- and 12 nm pores, the water molecules developed ahydrogen-bond network in the pore centre due to the presence of the pore wall and pushed theEG molecules onto the pore surface even at higher temperatures: the water-rich region gaveTg = 155 K close to 160 K. It is concluded that the hydrogen-bond network inherentto water structure is developed/collapsed remarkably in the range nearx = 0; consequently, the composition dependence ofTg inthe bulk system deviates sharply in the range from the Gordon–Taylor empirical law followed for largex > 0.2.

The Long Haul Effects of Interest Arbitration: The Case of New York State's Taylor Law

The authors examine debates about the effects of mandatory interest arbitration on police and firefighters in New York State under the Taylor Law from 1974 to 2007. Comparing experience with interest arbitration in the first three years after the law was adopted with experiences from 1995 to 2007, the authors find that no strikes occurred under arbitration and that rates of dependence on arbitration declined considerably. Moreover, the effectiveness of mediation prior to and during arbitration remained high, the tripartite arbitration structure continued to foster discussion of options for resolution among arbitration panel members, and wage increases awarded under arbitration matched those negotiated voluntarily by the parties. Econometric estimates of the effects of interest arbitration on wage changes in a national sample suggest wage increases differed little in states with arbitration from those without it. The authors therefore propose a role for interest arbitration in national labor policy.

Origins of Taylor’s power law for fluctuation scaling in complex systems

Taylor's fluctuation scaling (FS) has been observed in many natural and man-made systems revealing an amazing universality of the law. Here, we give a reliable explanation for the origins and abundance of Taylor's FS in different complex systems. The universality of our approach is validated against real world data ranging from bird and insect populations through human chromosomes and traffic intensity in transportation networks to stock market dynamics. Using fundamental principles of statistical physics (both equilibrium and nonequilibrium) we prove that Taylor's law results from the well-defined number of states of a system characterized by the same value of a macroscopic parameter (i.e., the number of birds observed in a given area, traffic intensity measured as a number of cars passing trough a given observation point or daily activity in the stock market measured in millions of dollars).

Opposition to 12(B)6 Motion

Opposition to Authorities Motion to Dismiss for failure to state a claim. 1983 Constitutional complaint against New York Taylor Law. Quotes Dred Scott, Plessy v. Ferguson, Chinese Exclusion Act, Holocaust etc.

Constitutional Challenge to Taylor Law

Complainant alleges violations of Ku Klux Klan Act of 1871 a.k.a. The Civil Rights Act of 1871 and Title 42 Chapter 21 Subchapter I § 1983. Civil action for Deprivation of Rights. In addition Fed. R. Civ. P. 5.1 Constitutional Challenge to a Statute. In addition Title 28 Part VI Chapter 161 § 2403 (b). Intervention by United States or a State; constitutional question. The United States Constitutional Amendments violated by the Defendants (State Actors) include, but are not limited to, I, IV, V, VI, VII, VIII, IX, X, XIII, XIV. Plaintiff contends The Public Employees Fair Employment Act, Article 14 of the New York State Civil Service Law, a.k.a. The Taylor Law was, is, and will be facially and as applied unconstitutional under said Amendments.

A GENERAL MODEL FOR ANALYZING TAYLOR'S SPATIAL SCALING LAWS

Taylor's spatial scaling law concerns the relation between the variance and the mean population counts within areas of a given size. For a range of area sizes, the log of the variance often is an approximately linear function of the mean with a slope between 1 and 2, depending on the range of areas considered. In this paper, we investigate this relationship theoretically for random quadrat samples within a large area. The model makes a distinction between the local point process determining the position of each individual and the population density described by a spatial covariance function. The local point process and the spatial covariance of population density both contribute to the general relationship between the mean and the variance in which the slope may begin at 1, increase to 2, and decrease to 1 again. It is demonstrated by an example that the slope theoretically may exceed 2 by a small amount for very regular patterns that generate spatial covariance functions that increase in certain intervals. We also show how properties of population dynamics in space and time determine this relationship.

Public Sector Labor Law in the Kaye Court

This presentation was delivered at the 40th Anniversary of the Taylor Law Conference sponsored by the NYS Public Employment Relations Board (PERB) in Albany in May 2008. The presentation dealt with the New York Court of Appeals' approach to public sector labor law. Professor Vincent M. Bonventre identified patterns and trends in the decisions of the Court of Appeals, the state's highest court, over the fifteen year period during which Judith S. Kaye has served as Chief Judge. A review of those decisions is revealing. Overall patterns for the fifteen years, as well as recent trends, emerge from the court's rulings when reviewed in light of certain considerations: unanimous versus divided decisions, pro-employee versus pro-management ones, pro versus con-collective bargaining rulings, decisions in which public policy was deemed to prohibit versus permit collective bargaining or arbitration or certain terms or conditions of employment. All of the foregoing is illustrated in graphs that underscore these contrasts in the cases collectively, as well as highlight the recent trends suggesting a pro-management change in the court's direction.

Fluctuation scaling in complex systems: Taylor's law and beyond1

Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form ‘fluctuations ≈ constant × averageα’, where the exponent α is predominantly in the range [1/2, 1]. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names Taylor's law or fluctuation scaling. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling.

Distribuição espacial da meleira do mamoeiro em zonas de trópico úmido e trópico semi-árido

O vírus da meleira, transmitido por Bemisia tabaci, é um dos maiores problemas da cultura do mamoeiro (Carica papaya), sendo responsável por perdas de até 100% na produção. Com o objetivo de compreender melhor sua epidemiologia e gerar subsídios para estudos da influência de fatores culturais e bioecológicos na dinâmica da doença, avaliou-se a distribuição espacial de plantas afetadas pela meleira em zonas de Trópico Úmido e Trópico Semi-árido, em 15 plantios comerciais em Eunápolis-BA e Petrolina-PE, entre jan. 2000 e mar. 2001. As áreas foram mapeadas anotando-se a posição de cada planta e a presença ou ausência de sintomas. Foram consideradas doentes aquelas que apresentavam frutos com exsudação espontânea do látex, látex muito fluido, frutos borrados e/ou folhas do ápice com o bordo necrosado. Pelas análises de seqüências ordinárias, índice de dispersão, áreas isópatas e ajuste dos logaritmos das variâncias binomial e de acordo com a lei de Taylor, observaram-se maior agregação nas linhas de plantio que entre linhas e uma agregação de mediana a forte em sub-áreas (1,4 < ID < 3,1). Na maioria dos lotes, as áreas de maior incidência concentraram-se nas bordas dos talhões, o que indica que a migração de vetores assume um papel importante na disseminação da doença. Em alguns casos foi possível detectar a presença de focos isolados no interior dos lotes, o que sugere a formação de colônias dos vetores e transmissão planta a planta a partir de inóculo secundário. Não foram observadas diferenças significativas na distribuição espacial de plantas doentes entre as áreas das duas regiões.

Determination of the Material Intrinsic Length Scale of Gradient Plasticity Theory

The enhanced gradient plasticity theories formulate a constitutive framework on the continuum level that is used to bridge the gap between the micromechanical plasticity and the classical continuum plasticity. The later cannot predict the size effects since it does not posses an intrinsic length scale. To assess the size effects, it is indispensable to incorporate an intrinsic material length parameter l into the constitutive equations. However, the full utility of gradient-type theories hinges on one's ability to determine the constitutive length-scale parameter l that scales the gradient effects. Thus, the definition and magnitude of the intrinsic length scale are keys to the development of the new theory of plasticity that incorporates size effects. The classical continuum plasticity is also unable to predict properly the evolution of the material flow stress since the local deformation gradients at a given material point are not accounted for. The gradient-based flow stress is commonly assumed to rely on a mixed type of dislocations: those that are initially randomly or statistically distributed, which are referred to as statistically stored dislocations (SSDs), and those formed to account for the additional strengthening mechanism associated with the deformation gradients, which are referred to as geometrically necessary dislocations (GNDs). In this work two micromechanical models to assess the coupling between SSDs and GNDs are discussed. One in which the SSDs and GNDs are simply summed (model-I) and one in which, implicitly, their accompanying strength are added (model-II). These two dislocation interaction models, which are based on Taylor's hardening law, are then used to identify the deformation-gradient-related intrinsic length-scale parameter l in terms of measurable microstructural physical parameters. The paper also presents a method for identifying the material intrinsic length parameter l from micro hardness results obtained by conical or pyramidal indenters.

Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro- and nano-indentation experiments

The enhanced gradient plasticity theories formulate a constitutive framework on the continuum level that is used to bridge the gap between the micromechanical plasticity and the classical continuum plasticity. They are successful in explaining the size effects encountered in many micro- and nano-advanced technologies due to the incorporation of an intrinsic material length parameter into the constitutive modeling. However, the full utility of the gradient-type theories hinges on one's ability to determine the intrinsic material length that scales with strain gradients, and this study aims at addressing and remedying this situation. Based on the Taylor's hardening law, a micromechanical model that assesses a nonlinear coupling between the statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) is used here in order to derive an analytical form for the deformation-gradient-related intrinsic length-scale parameter in terms of measurable microstructural physical parameters. This work also presents a method for identifying the length-scale parameter from micro- and nano-indentation experiments using both spherical and pyramidal indenters. The deviation of the Nix and Gao [Mech. Phys. Solids 46 (1998) 411] and Swadener et al. [J. Mech. Phys. Solids 50 (2002) 681; Scr. Mater. 47 (2002) 343] indentation size effect (ISE) models’ predictions from hardness results at small depths for the case of conical indenters and at small diameters for the case of spherical indenters, respectively, is largely corrected by incorporating an interaction coefficient that compensates for the proper coupling between the SSDs and GNDs during indentation. Experimental results are also presented which show that the ISE for pyramidal and spherical indenters can be correlated successfully by using the proposed model.

Dinâmica temporal da Clorose Variegada dos Citros em três regiões do Estado de São Paulo

Este trabalho objetivou esclarecer se o progresso da Clorose Variegada dos Citros (CVC) diferia entre três regiões de São Paulo, distintas quanto à incidência da CVC em citrus (Citrus spp.). Foram avaliadas três áreas, Noroeste, Centro e Sul de São Paulo, durante dois anos, em avaliações quinzenais, quando eram mapeadas as plantas sintomáticas. Tentou-se o ajuste de nove modelos ao progresso da doença, além do ajuste de três modelos a segmentos das curvas originais. Foram estimadas também as diferenciais e as diferenciais secundárias de cada curva de progresso. Apenas quando as curvas foram divididas é que foram obtidos bons ajustes aos modelos de progresso. A diferencial (velocidade da doença) e diferencial secundária (aceleração do aparecimento de novas plantas doentes) apresentaram diversos picos ao longo do tempo. Esses picos ocorreram em meses de Primavera e Verão. Levanta-se aqui a hipótese de que os picos de diferencial - incomuns na quantidade encontrada - estejam relacionados a determinados picos de emissão de brotações, já que as novas brotações são o local preferido de alimentação dos vetores de Xylella fastidiosa.

Distribution and sampling of Maruca vitrata (Fabricius) (Lep., Pyralidae) larvae on Lonchocarpus sericeus (Poir) H.B. and K.

The spatio-temporal distribution of the pod borer Maruca vitrata was assessed on Lonchocarpus sericeus over a period of 6 months, in order to develop sampling plans and facilitate sampling on this host plant. Lonchocarpus sericeus, one of the preferred alternative host plants of M. vitrata is widely spread in Benin and should therefore be included in the ecological management of the insect. Some experiments were conducted at an ecological site in south Benin, where L. sericeus can be found. The analysis of 17 weekly samples showed that tree canopy did not have a significant effect (P = 0.3471) on larval distribution. Significant differences (P = 0.0001) were obtained between the sizes of flowers (10, 20, 30 and 40 racemes). Geographical quadrants consisting of the upper east branches, lower east branches, upper west branches and lower west branches did not differ significantly (P = 0.8713). The time of infestation of L. sericeus by M. vitrata was investigated by taking samples every 2 days. Data analysis of these samples revealed that L. sericeus was infested at the open flower stage. Temporal distribution of larvae showed the greatest abundance of larvae occurred in June. The index of aggregation was 1.37 with the TAYLOR law and 1.26 with the Iwao procedure. These values showed that the larval dispersion pattern is negative binomial. On this basis, sequential sampling plans were developed and these could permit an accurate estimate of tree data for sampling.

Collective bargaining in the public sector: the experience of eight states

1. INTRODUCTION AND OVERVIEW Joyce M. Najita and James L. Stern Introduction Extent of Organization and Representation The Law of Public Sector Bargaining Scope of Bargaining Right to Strike Impasse Resolution/Interest Arbitration Grievance Arbitration Concluding Thoughts 2. JUDICIAL REVIEW AND LEGISLATIVE RESPONSE: THE NEW JERSEY PUBLIC SECTOR COLLECTIVE BARGAINING EXPERIENCE Joan Parker Jurisdiction Representation Unfair Practices Scope of Negotiations Mediation and Factfinding Interest Arbitration Grievance Arbitration Conclusion 3. GRIEVANCE AND INTEREST ARBITRATION IN PENNSYLVANIA'S PUBLIC SECTOR Joan Parker Act 195 Jurisdiction Representation Issues Scope of Bargaining Dispute Resolution Dispute Resolution-Act 88 Grievance Arbitration Act 111 Jurisdiction Representation Questions Dispute Resolution Grievance Arbitration Conclusion 4. INTEREST ARBITRATION AND MUNICIPAL EMPLOYEE BARGAINING-THE WISCONSIN EXPERIENCE William C. Houlihan Legislative Background Bargaining Units and Representation The Impact of Interest Arbitration Organizing The Changed Nature of Bargaining Municipal Employment Relations Act Impasse Procedure under MIA (Police and Firefighters Except Milwaukee Police) Impasse Procedure under MERA (MED/ARB and INT/ARB) Impasse Procedure Covering Milwaukee Police Law Enforcement Employees of the Milwaukee Police Department Police and Fire Arbitration Experience under MIA Municipal Employees Arbitration Experience under MERA Teachers and the QEO The Narcotic Effect, Issues, and Comparables Conclusion 5. PUBLIC SECTOR COLLECTIVE BARGAINING IN MICHIGAN: LAW AND RECENT DEVELOPMENTS Gregory M. Saltzman and Shlomo Sperka Evolution of Michigan's Public Sector Bargaining Policy Extent of Unionism Strike Experience Scope of Bargaining under PERA Mediation and Factfinding Act 312: Compulsory Interest Arbitration for Police and Firefighter Units Act 112: Legislative and Judicial History Act 112 and Strikes Act 112 and the Scope of Bargaining Act 112: Other Provisions and Effects Proposal A: A Major Change in School Financing State Civil Service Employees Conclusion 6. COLLECTIVE BARGAINING IN CALIFORNIA'S PUBLIC SECTOR Carol A. Vendrillo Early Legislation George Brown Act Winton Act Meyers-Milias-Brown Act Right to Strike Binding Interest Arbitration Past Efforts to Get Comprehensive Labor Law Aaron Commission Educational Employment Relations Act Dills Act Higher Education Employer-Employee Relations Act Agency Fees Excluded Employees Act Extent of Organization Public Schools State Employees Higher Education Local Government Future Trends 7. PUBLIC SECTOR LABOR LAW AND EXPERIENCE IN NEW YORK STATE Janet McEneaney and Robert P. Hebdon A Brief Look Back The Regulatory Agencies The Public Employment Relations Board The New York City Office of Collective Bargaining The Duty To Bargain and the Scope of Bargaining The Duty To Bargain Maintaining the Status Quo after a Contract Expires The Scope of Bargaining The Management Rights Clause of the NYCCBL Impasse Resolution under the Taylor Law Procedure Evidence on Mediation and Factfinding Impasse Resolution under the NYCCBL Arbitration and Contract Enforcement Strikes The Privatization of New York's Public Services Summary and Conclusion 8. ILLINOIS PUBLIC SECTOR COLLECTIVE BARGAINING LEGISLATION: THE FIRST FIFTEEN YEARS R. Theodore Clark, Jr. and F. Donal O'Brien Senate Bill 536 and House Bill 1530 Extent of Unionization in the Illinois Public Sector Subsequent Amendments to the IPLRA and the IELRA Administration of the Acts Representation Cases Duty to Bargain Cases Treatment of Alleged Unilateral Action Cases Statutory Impasse Procedures Contract Administration and Grievance Arbitration Questions Yet To Be Answered under the IPLRA and/or IELRA Concluding Observations 9. ESSENTIAL EMPLOYEE STRIKES AND STATUTORY ARBITRATION PROCEDURES: THE HAWAI'I PUBLIC SECTOR COLLECTIVE BARGAINING EXPERIENCE Joyce M. Najita, William J. Anzenberger, and Helene S. Tanimoto Introduction The Legal Framework for Collective Bargaining in Hawai'i's Public Sector Administering Agency: HPERB/HLRB Statutory Bargaining Units Scope of Bargaining The Public Employer Grievance Arbitration Limited Right to Strike Negotiation Impasse Resolution Impact of Strikes and Adoption of Statutory Arbitration Procedures Statewide Teachers Strike, 1973 The Firefighter Sickout and Strike Threats, 1974-1979 Blue-Collar Workers' Strike, 1979 HGEA Strike, 1994 Protecting the Public Health and Safety: Who Are Essential Employees? Firefighters (Decision No. 80) Blue-Collar Workers (Decision No. 119) Teachers (Decision Nos. 181, 186, and 383) HGEA Workers (Decision No. 212 and Order No. 1033) Statutory Arbitration As Strike Alternative Summary and Conclusions

A power law for cells.

Darwin observed that multiple, lowly organized, rudimentary, or exaggerated structures show increased relative variability. However, the cellular basis for these laws has never been investigated. Some animals, such as the nematode Caenorhabditis elegans, are famous for having organs that possess the same number of cells in all individuals, a property known as eutely. But for most multicellular creatures, the extent of cell number variability is unknown. Here we estimate variability in organ cell number for a variety of animals, plants, slime moulds, and volvocine algae. We find that the mean and variance in cell number obey a power law with an exponent of 2, comparable to Taylor's law in ecological processes. Relative cell number variability, as measured by the coefficient of variation, differs widely across taxa and tissues, but is generally independent of mean cell number among homologous tissues of closely related species. We show that the power law for cell number variability can be explained by stochastic branching process models based on the properties of cell lineages. We also identify taxa in which the precision of developmental control appears to have evolved. We propose that the scale independence of relative cell number variability is maintained by natural selection.

Size Dependence of the Stability of Emulsion Drops Pressed against a Large Interface

In this work we study experimentally the lifetime of oil droplets pressed by buoyancy against a large oil/water interface, in a system containing protein (bovine serum albumin). The stability of the drops depends strongly on their size, which can be explained with the hydrodynamics of thinning of the gap region. Two distinct size intervals with different thinning regimes may be discerned: (i) Very small drops (below ∼20 μm). They remain practically nondeformed up to coalescence; in this case the lifetime diminishes with increase of the drop radius. The latter trend may be described qualitatively in terms of the Taylor law (or mixed Stokes−Taylor law) for viscous resistance. (ii) Large drops. They form films, and the lifetime rises with the increase of the size, which complies with the Reynolds law for the friction in the gap. The overall dependence of the lifetime on the drop radius passes through a shallow and broad minimumhere for the first time this is proved by direct measurement in a real system: o...

Dispersion Statistics and Sample Size Estimates for Three Fish Species (Symphodus ocellatus, Serranus scriba and Diplodus annularis) in the Lavezzi Islands Marine Reserve (South Corsica, Mediterranean Sea)

For the correct management of the future International Marine Park of Bonifacio, a sampling strategy must be adopted to follow the population fluctuations of certain species of fish. This sampling will be carried out by SCUBA visual census using the fixed point method. The information to be gleaned using this method will include estimates of biomass. These data will subsequently be used to perform both spatial comparisons between sites and temporal comparisons over periods of several years. In order to reveal the existence of statistically significant differences, the sampling strategy adopted must allow accurate means to be obtained which possess relatively low coefficients of variability. The calculation of this optimum sampling depends on the spatial distribution of the species examined. The Taylor law (s2 = a ×xb), which represents a much utilized mean‐variance relationship, will be used to compare the aggregation of three species of fish (Symphodus ocellatus,Serranus scriba and Diplodus annularis) on two different substrate types (Posidonia oceanica meadows and rocks) and for four sites in the Lavezzi Islands. The goodness of fit of this law to the biomass data will allow an optimum sampling strategy to be determined for each species with coefficients of variability of 10 and 25%.