Estructura espacial y dinámica del bosque montano del sur del Ecuador. Interacciones bióticas y limitaciones abióticas

Muchos estudios han descrito la composición y diversidad de los bosques montanos tropicales, pero los patrones espaciales y las diferentes tipos de relaciones de estos, entre especies o entre grupos funcionales ha sido poco documentada. El presente trabajo se realizó en tres parcelas completamente censadas del bosque de la Estación Biológica “Chamusquin” (Zamora Chinchipe, Ecuador), y se plantea como objetivo principal conocer la estructura espacial y dinámica del bosque montano tropical del sur del Ecuador, así como las interacciones bióticas y limitaciones abióticas que influyen en esta dinámica, para ello se planteó cuatro objetivos de estudio que son: conocer los patrones espaciales de los gremios ecológicos dentro de la zona de estudio; conocer la influencia de la dependencia negativa de la densidad sobre dos especies de helechos arborescentes (Cyatheaceae); conocer si existen especies o grupos ecológicos acumuladoras o repulsoras de diversidad en el área de estudio; y conocer cómo influyen la diversidad filogenética y la densidad del vecindario en la incidencia de herbivoría y parasitismo sobre las fases iniciales del establecimiento forestal (brinzales) así como en la supervivencia de los mismos Como paso previo para el análisis del resto de objetivos, dentro de cada parcela se marcaron todos los individuos con DAP ≥5 cm y se tomaron sus coordenadas (X, Y). Además se tomaron datos de variables superficiales y muestras del suelo. Las especies encontradas se clasificaron de acuerdo a sus características biológicas, asignándolas a cada uno de los cuatro gremios forestales usualmente distinguidos en los bosques tropicales: tolerantes a la sombra (TS), tolerantes parciales a la sombra (TPS), pioneras de vida larga (PVL) y pioneras de vida corta (PVC). Para el estudio del primer objetivo tas se emplearon funciones K de Ripley inhomogéneas, ajustando la heterogeneidad en base a la variación espacial de las variables ambientales registradas . Los resultados demostraron que tanto la frecuencia relativa como el patrón espacial de las diferentes estrategias funcionales varían a lo largo de la sucesión y que éste además está influido por la variación ambiental. En adición, tanto el patrón espacial como la respuesta a la variación ambiental de los diferentes gremios es distinta entre adultos y juveniles. Todo ello sugiere que el ensamblaje de la diversidad en los bosque montanos andinos está controlado por procesos deterministas más que por procesos neutrales. Para responder el segundo objetivo se estudiaron los efectos de la dependencia negativa de la densidad (DND) y la heterogeneidad ambiental en las poblaciones de dos especies de helechos arborescentes abundantes, Cyathea caracasana y Alsophila engelii, y cómo estos efectos cambian a través de un gradiente sucesional. Los patrones de especies albergan información sobre procesos tales como la competencia que puede ser revelado fácilmente utilizando técnicas de análisis de patrones punto. Sin embargo, su detección puede ser difícil debido a los efectos de factores de confusión heterogeneidad del hábitat. Aquí, empleamos funciones K y funciones de correlación de par homogéneas y no homogéneas para cuantificar el cambio en el patrón espacial de diferentes clases de tamaño con un diseño de casos-controles para estudiar las asociaciones entre helechos arborescentes jóvenes y adultos. Usando estimaciones espaciales de la biomasa de los cuatro tipos de gremios ecológicos (PVC, PVL, TPS, TS) como covariables, hemos ajustado modelos de Poisson heterogéneos a los patrones de puntos de de los helechos juveniles y los adultos y hemos explorado además la existencia de dependencia del hábitat en estos patrones. Nuestro estudio reveló efectos de la DND para C. caracasana y un fuerte filtrado ambiental que subyace al patrón de A. engelii. Encontramos también que las poblaciones de adultos y juveniles de ambas especies respondieron de manera diferente a la heterogeneidad del hábitat y en la mayoría de los casos esta heterogeneidad se asoció con la distribución espacial de la biomasa de los cuatro tipos de gremios. Estos resultados muestran la eficacia de controlar los efectos de la heterogeneidad ambiental para evitar su confusión con los patrones derivados de interacciones biológicas cuando se estudia la DND y demuestran la utilidad de los mapas de covariables derivados de comunidades biológicas como resumen de la heterogeneidad ambiental. Para nuestro tercer objetivo nos centramos en explorar cómo influyen las especies más abundantes en la organización espacial de la diversidad a lo largo de un gradiente sucesional en el bosque montano del sur del Ecuador. Para ello utilizamos la función ISAR (Individual Species Area Relationship). Encontramos que la frecuencia de especies neutras, repulsoras y acumuladoras de diversidad taxonómica varía dependiendo del grado de sucesión. Además se comprobó que la mayoría de los gremios forestales se comportó de forma neutral, pero la proporción de acumuladores, aumentó al avanzar la sucesión hacia estados más maduros, lo que indica el establecimiento de fuertes procesos competitivos a medida que avanza la sucesión y la mayor importancia del papel de las especies individuales en dichos estados. Finalmente, examinamos el efecto de la vecindad taxonómica y filogenética, así como la estrategia de vida, sobre la incidencia de la herbivoría y el parasitismo en las poblaciones de brinzales de tres fragmentos forestales en una secuencia sucesional del bosque montano húmedo. Evaluamos además los efectos de herbivoría, parasitismo, estrategia de vida y diferentes indicadores de la vecindad sobre la supervivencia de los brinzales. Por último contrastamos la posible existencia de una tendencia compensatoria de la comunidad (CCT) a nivel de fragmento forestal. Nuestros análisis no consiguieron detectar una CCT pero si pusieron de manifiesto la existencia de efectos locales de dependencia negativa de la densidad. Por ejemplo, la presencia de herbivoría y parasitismo sobre los brinzales se relacionó significativamente con una menor supervivencia de estos. Por otro lado, indicadores del efecto de la vecindad como la densidad de brinzales del mismo género y el área basal de árboles vecinos del mismo género incrementaron la prevalencia de la herbivoría o el parasitismo en los brinzales. El incremento de la incidencia de la herbivoría o el parasitismo no está exclusivamente ligado a tener una vecindad taxonómicamente idéntica (vecinos de la misma especie) sino que categorías taxonómicas más laxas como el "género" o simplemente relaciones de semejanza filogenética son capaces de predecir los efectos negativos de la vecindad. Los efectos detectados variaron en los diferentes grupos funcionales distinguidos. Los resultados que hemos obtenido en este trabajo parecen indicar que el funcionamiento de las comunidades de brinzales del bosque montano tropical no difiere mucho del reportado para comunidades de plántulas en otros bosques tropicales y cumple las predicciones de la hipótesis de Janzen y Connell, aunque matizadas por la mayor resistencia de los brinzales al efecto de herbivoría y parasitismo. ABSTRACT Many studies have described the composition and diversity of tropical montane forests, but the different spatial patterns and types of relationships between species or between functional groups has been poorly documented. This work was made in three completely surveyed forest plots at Biological Station "Chamusquin" (Zamora Chinchipe, Ecuador). Our main objective was to know the spatial structure and dynamics of the tropical montane forest in southern Ecuador, as well as the biotic interactions and abiotic constraints affecting this dynamic. More specifically, we aimed to understand the spatial patterns of ecological guilds; to explore the influence of negative density dependence on two species of tree ferns (Cyatheaceae); to determine whether some species or ecological groups structure spatially plant diversity in these forests; and to test the effects of biological neighborhood on the incidence of herbivory and parasitism and on the survival of saplings. We mapped within each plot all trees with DBH ≥5 cm. Besides, surface data variables and soil samples they were taken. The species found were classified according to their biological characteristics in four forest guilds: shade-tolerant (ST), partial shade tolerant (PST), long-lived pioneer (LLP) and short-lived pioneer (SLP). To analyze the spatial patterns of the ecological guilds, we employed the inhomogeneous version of Ripley's K-function and adjusted heterogeneity surfaces based on the spatial variation of the measured environmental variables. The results showed that both the relative frequency of each functional guild as well as their spatial pattern varied throughout succession and that the spatial pattern is explained by environmental variation. In addition, both spatial pattern and the response to spatial variation of each guild varied throughout ontogeny. All in all suggest that diversity assembly in the studied forests is ruled by deterministic instead of neutral processes. We also addressed the negative effects of density dependence (NDD) and environmental heterogeneity in populations of two species of abundant tree ferns, Cyathea caracasana and Alsophila engelii, and how these effects change across a successional gradient.. Here, we used homogeneous and inhomogeneous K and pair-correlation functions to quantify the change in the spatial pattern of different size classes with a case-control design to study associations between young and adult tree ferns. Using spatial estimates of the biomass of the four types of ecological guilds (SLP, LLP, PST, ST) as co-variables, we fitted heterogeneous Poisson models to juvenile and adult tree fern point patterns and explored the existence of habitat dependence. Our study revealed NDD effects for C. caracasana and strong environmental filtering underlying the pattern of A. engelii. We found that adult and juvenile populations of both species responded differently to habitat heterogeneity and in most cases this heterogeneity was associated with the spatial distribution of biomass of the four functional tree types. These findings show the effectiveness of factoring out environmental heterogeneity to avoid confounding factors when studying NDD and demonstrate the usefulness of covariate maps derived from mapped communities. For our third objective we focused on exploring how the most abundant species influence the spatial organization of tree diversity in these forests. For this, we used the individual species-area relationship function (ISAR). We found that the proportion of accumulator, repeller and neutral species, varied depending on the degree of succession. We found also that most guilds behaved neutrally but the proportion of accumulator guilds increased as succession advanced to more mature stages. This point, to the existence of strong competitive effects mediated by individual species in these mature forests. Finally, we examined the effects of life strategies and taxonomic and phylogenetic neighborhood on the incidence of herbivory and parasitism in the communities of saplings in the same forest fragments. We evaluated also the effects of life strategies, herbivory, parasitism and some indicators of neighborhood on sapling survival. Finally we tested for the existences of a compensatory community trend at plot scale. We did not found a CCT but we found proof of local NND effects. For instance, the prevalence of herbivory and parasitism were related to lower sapling survival. On the other hand the density of con-generic saplings and the basal area of neighbor con-generic trees were related to a higher prevalence of herbivory or parasitism in the saplings. We demonstrated that the increase in the prevalence of herbivory or parasitism it s not exclusive of a conspecific neighborhood but instead larger taxonomic categories such as "genus" or simple phylogenetic relationships are also able to predict NND effects. The NND effects varied among functional guilds. Our results show that the dynamic of sapling communities in Ecuadorian montane forests is similar to seedling dynamics in other tropical forest and follows the predictions of Janzen-Connell hypothesis, although softened by the strong resilience of saplings in comparison to seedlings.

A global budget for fine root biomass, surface area, and nutrient contents

Global biogeochemical models have improved dramatically in the last decade in their representation of the biosphere. Although leaf area data are an important input to such models and are readily available globally, global root distributions for modeling water and nutrient uptake and carbon cycling have not been available. This analysis provides global distributions for fine root biomass, length, and surface area with depth in the soil, and global estimates of nutrient pools in fine roots. Calculated root surface area is almost always greater than leaf area, more than an order of magnitude so in grasslands. The average C:N:P ratio in living fine roots is 450:11:1, and global fine root carbon is more than 5% of all carbon contained in the atmosphere. Assuming conservatively that fine roots turn over once per year, they represent 33% of global annual net primary productivity.

Nonuniformity of the constitutive law parameters for shear rupture and quasistatic nucleation to dynamic rupture: a physical model of earthquake generation processes.

Based on the recent high-resolution laboratory experiments on propagating shear rupture, the constitutive law that governs shear rupture processes is discussed in view of the physical principles and constraints, and a specific constitutive law is proposed for shear rupture. It is demonstrated that nonuniform distributions of the constitutive law parameters on the fault are necessary for creating the nucleation process, which consists of two phases: (i) a stable, quasistatic phase, and (ii) the subsequent accelerating phase. Physical models of the breakdown zone and the nucleation zone are presented for shear rupture in the brittle regime. The constitutive law for shear rupture explicitly includes a scaling parameter Dc that enables one to give a common interpretation to both small scale rupture in the laboratory and large scale rupture as earthquake source in the Earth. Both the breakdown zone size Xc and the nucleation zone size L are prescribed and scaled by Dc, which in turn is prescribed by a characteristic length lambda c representing geometrical irregularities of the fault. The models presented here make it possible to understand the earthquake generation process from nucleation to unstable, dynamic rupture propagation in terms of physics. Since the nucleation process itself is an immediate earthquake precursor, deep understanding of the nucleation process in terms of physics is crucial for the short-term (or immediate) earthquake prediction.

Dynamic friction and the origin of the complexity of earthquake sources.

We study a simple antiplane fault of finite length embedded in a homogeneous isotropic elastic solid to understand the origin of seismic source heterogeneity in the presence of nonlinear rate- and state-dependent friction. All the mechanical properties of the medium and friction are assumed homogeneous. Friction includes a characteristic length that is longer than the grid size so that our models have a well-defined continuum limit. Starting from a heterogeneous initial stress distribution, we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for a few 1000 events. The style of seismicity produced by this model is determined by a control parameter associated with the degree of rate dependence of friction. For classical friction models with rate-independent friction, no complexity appears and seismicity is perfectly periodic. For weakly rate-dependent friction, large ruptures are still periodic, but small seismicity becomes increasingly nonstationary. When friction is highly rate-dependent, seismicity becomes nonperiodic and ruptures of all sizes occur inside the fault. Highly rate-dependent friction destabilizes the healing process producing premature healing of slip and partial stress drop. Partial stress drop produces large variations in the state of stress that in turn produce earthquakes of different sizes. Similar results have been found by other authors using the Burridge and Knopoff model. We conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.

Analysis of a metallic pedestrian bridge under dynamic human loads in pre and post reinforcement phases

The purpose of this work is to study the dynamic behavior of a pedestrian bridge in Alicante, Spain. It is a very slender footbridge with vertical and horizontal vibration problems during the passage of pedestrians. Accelerations have been recorded by accelerometers installed at various locations of the bridge. Two scenarios, in free vibration (after the passage of a certain number of pedestrians on the bridge) and forced vibration produced by a fixed number of pedestrians walking on the bridge at a certain speed and frequency. In each test, the effect on the comfort of the pedestrians, the natural frequencies of vibration, the mode shapes and damping factors have been estimated. It has been found that the acceleration levels are much higher than the allowable by the Spanish standards and this should be considered in the restoration of the footbridge.

The evolution of mass tourism destinations: new approaches beyond deterministic models in Benidorm (Spain)

Although deterministic models of the evolution of mass tourism coastal resorts predict an almost inevitable decline over time, theoretical frameworks of the evolution and restructuring policies of mature destinations should be revised to reflect the complex and dynamic way in which these destinations evolve and interact with the tourism market and global socio-economic environment. The present study examines Benidorm because its urban and tourism model and large-scale tourism supply and demand make it one of the most unique destinations on the Mediterranean coast. The investigation reveals the need to adopt theories and models that are not purely deterministic. The dialectic interplay between external factors and the internal factors inherent in this destination simultaneously reveals a complex and diverse stage of maturity and the ability of destinations to create their own future.

Applying reactive models to column experiments to assess the hydrogeochemistry of seawater intrusion: optimising ACUAINTRUSION and selecting cation exchange coefficients with PHREEQC

Three sets of laboratory column experimental results concerning the hydrogeochemistry of seawater intrusion have been modelled using two codes: ACUAINTRUSION (Chemical Engineering Department, University of Alicante) and PHREEQC (U.S.G.S.). These reactive models utilise the hydrodynamic parameters determined using the ACUAINTRUSION TRANSPORT software and fit the chloride breakthrough curves perfectly. The ACUAINTRUSION code was improved, and the instabilities were studied relative to the discretisation. The relative square errors were obtained using different combinations of the spatial and temporal steps: the global error for the total experimental data and the partial error for each element. Good simulations for the three experiments were obtained using the ACUAINTRUSION software with slight variations in the selectivity coefficients for both sediments determined in batch experiments with fresh water. The cation exchange parameters included in ACUAINTRUSION are those reported by the Gapon convention with modified exponents for the Ca/Mg exchange. PHREEQC simulations performed using the Gains-Thomas convention were unsatisfactory, with the exchange coefficients from the database of PHREEQC (or range), but those determined with fresh water – natural sediment allowed only an approximation to be obtained. For the treated sediment, the adjusted exchange coefficients were determined to improve the simulation and are vastly different from those from the database of PHREEQC or batch experiment values; however, these values fall in an order similar to the others determined under dynamic conditions. Different cation concentrations were simulated using two different software packages; this disparity could be attributed to the defined selectivity coefficients that affect the gypsum equilibrium. Consequently, different calculated sulphate concentrations are obtained using each type of software; a smaller mismatch was predicted using ACUAINTRUSION. In general, the presented simulations by ACUAINTRUSION and PHREEQC produced similar results, making predictions consistent with the experimental data. However, the simulated results are not identical to the experimental data; sulphate (total S) is overpredicted by both models, most likely due to such factors as the kinetics of gypsum, the possible variations in the exchange coefficients due to salinity and the neglect of other processes.

Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.

Modelling a biomass supply chain through discrete-event simulation

The organizational structure of the companies in the biomass energy sector, regarding the supply chain management services, can be greatly improved through the use of software decision support tools. These tools should be able to provide real-time alternative scenarios when deviations from the initial production plans are observed. To make this possible it is necessary to have representative production chain process models where several scenarios and solutions can be evaluated accurately. Due to its nature, this type of process is more adequately represented by means of event-based models. In particular, this work presents the modelling of a typical biomass production chain using the computing platform SIMEVENTS. Throughout the article details about the conceptual model, as well as simulation results, are provided

Forest-based supply chain modelling using the SimPy simulation framework

Proper management of supply chains is fundamental in the overall system performance of forestbased activities. Usually, efficient management techniques rely on a decision support software, which needs to be able to generate fast and effective outputs from the set of possibilities. In order to do this, it is necessary to provide accurate models representative of the dynamic interactions of systems. Due to forest-based supply chains’ nature, event-based models are more suited to describe their behaviours. This work proposes the modelling and simulation of a forestbased supply chain, in particular the biomass supply chain, through the SimPy framework. This Python based tool allows the modelling of discrete-event systems using operations such as events, processes and resources. The developed model was used to access the impact of changes in the daily working plan in three situations. First, as a control case, the deterministic behaviour was simulated. As a second approach, a machine delay was introduced and its implications in the plan accomplishment were analysed. Finally, to better address real operating conditions, stochastic behaviours of processing and driving times were simulated. The obtained results validate the SimPy simulation environment as a framework for modelling supply chains in general and for the biomass problem in particular.

Comparing fiscal multipliers across models and countries in Europe. National Bank of Belgium Working Paper No. 278, March 2015

This paper employs fifteen dynamic macroeconomic models maintained within the European System of Central Banks to assess the size of fiscal multipliers in European countries. Using a set of common simulations, we consider transitory and permanent shocks to government expenditures and different taxes. We investigate how the baseline multipliers change when monetary policy is transitorily constrained by the zero nominal interest rate bound, certain crisis-related structural features of the economy such as the share of liquidity-constrained households change, and the endogenous fiscal rule that ensures fiscal sustainability in the long run is specified in terms of labour income taxes instead of lump-sum taxes.

Eurozone Crisis and Social Models: What We Can Learn from Italy and Spain. CES Papers - Open Forum #20, 2013-2014

This paper considers the role of social model features in the economic performance of Italy and Spain during the run-up to the Eurozone crisis, as well as the consequences of that crisis, in turn, for the two countries social models. It takes issue with the prevailing view - what I refer to as the “competitiveness thesis” - which attributes the debtor status of the two countries to a lack of competitive capacity rooted in social model features. This competitiveness thesis has been key in justifying the “liberalization plus austerity” measures that European institutions have demanded in return for financial support for Italy and Spain at critical points during the crisis. The paper challenges this prevailing wisdom. First, it reviews the characteristics of the Italian and Spanish social models and their evolution in the period prior to the crisis, revealing a far more complex, dynamic and differentiated picture than is given in the political economy literature. Second, the paper considers various ways in which social model characteristics are said to have contributed to the Eurozone crisis, finding such explanations wanting. Italy and Spain ́s debtor status was primarily the result of much broader dynamics in the Euro- zone, including capital flows from richer to poorer countries that affected economic demand, with social model features playing, at most, an ancillary role. More aggressive reforms responding to EU demands in Spain may have increased the long term social and economic costs of the crisis, whereas the political stalemate that slowed such reforms in Italy may have paradoxically mitigated these costs. The comparison of the two countries thus suggests that, in the absence of broader macro-institutional reform of the Eurozone, compliance with EU dictates may have had perverse effects.

Family Models of In(ter)dependence: Cultural Change and the Question of Universal Needs

I will start by discussing some aspects of Kagitcibasi’s Theory of Family Change: its current empirical status and, more importantly, its focus on universal human needs and the consequences of this focus. Family Change Theory’s focus on the universality of the basic human needs of autonomy and relatedness and its culture-level emphasis on cultural norms and family values as reflecting a culture’s capacity for fulfilling its members’ respective needs shows that the theory advocates balanced cultural norms of independence and interdependence. As a normative theory it therefore postulates the necessity of a synthetic family model of emotional interdependence as an alternative to extreme models of total independence and total interdependence. Generalizing from this I will sketch a theoretical model where a dynamic and dialectical process of the fit between individual and culture and between culture and universal human needs and related social practices is central. I will discuss this model using a recent cross-cultural project on implicit theories of self/world and primary/secondary control orientations as an example. Implications for migrating families and acculturating individuals are also discussed.

Dynamic D-Vine copula model with applications to Value-at-Risk (VaR)

Regular vine copulas are multivariate dependence models constructed from pair-copulas (bivariate copulas). In this paper, we allow the dependence parameters of the pair-copulas in a D-vine decomposition to be potentially time-varying, following a nonlinear restricted ARMA(1,m) process, in order to obtain a very flexible dependence model for applications to multivariate financial return data. We investigate the dependence among the broad stock market indexes from Germany (DAX), France (CAC 40), Britain (FTSE 100), the United States (S&P 500) and Brazil (IBOVESPA) both in a crisis and in a non-crisis period. We find evidence of stronger dependence among the indexes in bear markets. Surprisingly, though, the dynamic D-vine copula indicates the occurrence of a sharp decrease in dependence between the indexes FTSE and CAC in the beginning of 2011, and also between CAC and DAX during mid-2011 and in the beginning of 2008, suggesting the absence of contagion in these cases. We also evaluate the dynamic D-vine copula with respect to Value-at-Risk (VaR) forecasting accuracy in crisis periods. The dynamic D-vine outperforms the static D-vine in terms of predictive accuracy for our real data sets.

Spatially explicit estimates of stock size, structure and biomass of North Atlantic albacore tuna (Thunnus alalunga) in the North Atlantic for the period 1987-2011, compiled from statistics about ICCAT fishery region L6

The development of the ecosystem approach and models for the management of ocean marine resources requires easy access to standard validated datasets of historical catch data for the main exploited species. They are used to measure the impact of biomass removal by fisheries and to evaluate the models skills, while the use of standard dataset facilitates models inter-comparison. North Atlantic albacore tuna is exploited all year round by longline and in summer and autumn by surface fisheries and fishery statistics compiled by the International Commission for the Conservation of Atlantic Tunas (ICCAT). Catch and effort with geographical coordinates at monthly spatial resolution of 1° or 5° squares were extracted for this species with a careful definition of fisheries and data screening. In total, thirteen fisheries were defined for the period 1956-2010, with fishing gears longline, troll, mid-water trawl and bait fishing. However, the spatialized catch effort data available in ICCAT database represent a fraction of the entire total catch. Length frequencies of catch were also extracted according to the definition of fisheries above for the period 1956-2010 with a quarterly temporal resolution and spatial resolutions varying from 1°x 1° to 10°x 20°. The resolution used to measure the fish also varies with size-bins of 1, 2 or 5 cm (Fork Length). The screening of data allowed detecting inconsistencies with a relatively large number of samples larger than 150 cm while all studies on the growth of albacore suggest that fish rarely grow up over 130 cm. Therefore, a threshold value of 130 cm has been arbitrarily fixed and all length frequency data above this value removed from the original data set.