scholarly journals Modelling multivariate data using product copulas and minimum distance estimators: an exemplary application to ecological traits

2022 ◽  
Author(s):  
Eckhard Liebscher ◽  
Franziska Taubert ◽  
David Waltschew ◽  
Jessica Hetzer
Keyword(s):  
Plant Traits ◽  
Plant Ecology ◽  
Ecological Modelling ◽  
Ecological Data ◽  
Multivariate Distributions ◽  
Ecological Traits ◽  
Copula Models ◽  
Global Databases ◽  
Fitting Procedure ◽  
Minimum Distance Estimators

AbstractModelling and applying multivariate distributions is an important topic in ecology. In particular in plant ecology, the multidimensional nature of plant traits comes with challenges such as wide ranges in observations as well as correlations between several characteristics. In other disciplines (e.g., finances and economics), copulas have been proven as a valuable tool for modelling multivariate distributions. However, applications in ecology are still rarely used. Here, we present a copula-based methodology of fitting multivariate distributions to ecological data. We used product copula models to fit multidimensional plant traits, on example of observations from the global trait database TRY. The fitting procedure is split into two parts: fitting the marginal distributions and fitting the copula. We found that product copulas are well suited to model ecological data as they have the advantage of being asymmetric (similar to the observed data). Challenges in the fitting were mainly addressed to limited amount of data. In view of growing global databases, we conclude that copula modelling provides a great potential for ecological modelling.

Wise use: using ecological models to understand and manage aquatic ecosystems

2020 ◽  
Vol 71 (1) ◽  
pp. 46 ◽  
Author(s):  
Rebecca E. Lester
Keyword(s):  
Aquatic Ecosystems ◽  
Ecological Models ◽  
Ecological Modelling ◽  
Ecological Data ◽  
Critical Question ◽  
Sensitivity Testing ◽  
Response Models ◽  
Ecological Response ◽  
Recommendations For Action ◽  
Ongoing Development

Using ecological-response models to understand and improve management of aquatic ecosystems is increasingly common. However, there are many questions about reliability and utility that can make the use of ecological modelling fraught. One critical question is how ecological-response models translate to what happens in practice. Many models purport to improve management by simulating ecological response to changing conditions. This suggests that tangible benefits (e.g. increased biodiversity) should flow when recommendations for action are implemented. But testing these links is rare and there are implications if those links are tenuous. One problem leading to a lack of congruence between models and reality can be a lack of ecological data for the system being modelled. Incomplete understanding, erroneous assumptions about drivers or degree of variability, and uncritical use of expert opinion can all result in models that may be more likely to mislead than inform. Explicit validation of models, sensitivity testing and ongoing development of novel solutions to deal with incomplete data can all assist. So, wise and critical use of ecological models provides one mechanism to increase our ability to quantify adverse effects on, and project future trajectories of, aquatic ecosystems.

scholarly journals Worldwide co-occurrence analysis of 17 species of the genus Brachypodium using data mining

PeerJ ◽  
2019 ◽  
Vol 6 ◽  
pp. e6193 ◽  
Author(s):  
Simon Orozco-Arias ◽  
Ana María Núñez-Rincón ◽  
Reinel Tabares-Soto ◽  
Diana López-Álvarez
Keyword(s):  
Data Mining ◽  
Association Rules ◽  
Plant Ecology ◽  
Fundamental Aspect ◽  
Data Repository ◽  
Ecological Communities ◽  
Ecological Data ◽  
Global Biodiversity Information Facility ◽  
Ecological Processes ◽  
Wide Range

The co-occurrence of plant species is a fundamental aspect of plant ecology that contributes to understanding ecological processes, including the establishment of ecological communities and its applications in biological conservation. A priori algorithms can be used to measure the co-occurrence of species in a spatial distribution given by coordinates. We used 17 species of the genus Brachypodium, downloaded from the Global Biodiversity Information Facility data repository or obtained from bibliographical sources, to test an algorithm with the spatial points process technique used by Silva et al. (2016), generating association rules for co-occurrence analysis. Brachypodium spp. has emerged as an effective model for monocot species, growing in different environments, latitudes, and elevations; thereby, representing a wide range of biotic and abiotic conditions that may be associated with adaptive natural genetic variation. We created seven datasets of two, three, four, six, seven, 15, and 17 species in order to test the algorithm with four different distances (1, 5, 10, and 20 km). Several measurements (support, confidence, lift, Chi-square, and p-value) were used to evaluate the quality of the results generated by the algorithm. No negative association rules were created in the datasets, while 95 positive co-occurrences rules were found for datasets with six, seven, 15, and 17 species. Using 20 km in the dataset with 17 species, we found 16 positive co-occurrences involving five species, suggesting that these species are coexisting. These findings are corroborated by the results obtained in the dataset with 15 species, where two species with broad range distributions present in the previous dataset are eliminated, obtaining seven positive co-occurrences. We found that B. sylvaticum has co-occurrence relations with several species, such as B. pinnatum, B. rupestre, B. retusum, and B. phoenicoides, due to its wide distribution in Europe, Asia, and north of Africa. We demonstrate the utility of the algorithm implemented for the analysis of co-occurrence of 17 species of the genus Brachypodium, agreeing with distributions existing in nature. Data mining has been applied in the field of biological sciences, where a great amount of complex and noisy data of unseen proportion has been generated in recent years. Particularly, ecological data analysis represents an opportunity to explore and comprehend biological systems with data mining and bioinformatics tools.

scholarly journals Spatial and temporal models in plant ecology: logic and causality

2022 ◽  
Author(s):  
Christian Damgaard
Keyword(s):  
Latent Variables ◽  
Hierarchical Models ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Terrestrial Ecosystems ◽  
Plant Ecology ◽  
Ecological Data ◽  
Hierarchical Framework ◽  
Temporal Models ◽  
Plant Ecological

In the paper, I argue that in order to make credible ecological predictions for terrestrial ecosystems in a changing environment, we need empirical plant ecological models that are fitted to spatial and temporal ecological data. Here, it is advocated to use structural equation models in a hierarchical framework with latent variables. Furthermore, it is an advantage that the proposed hierarchical models are analogous to well-known theoretical epistemological models of how knowledge is obtained.

scholarly journals Intraspecific variability of leaf traits and functional strategy of Himantoglossum adriaticum H. Baumann

2020 ◽  
Vol 57 (2) ◽  
pp. 105-112
Author(s):  
Mattia Baltieri ◽  
Edy Fantinato ◽  
Silvia Del Vecchio ◽  
Gabriella Buffa
Keyword(s):  
Plant Traits ◽  
Intraspecific Variability ◽  
Leaf Traits ◽  
Plant Ecology ◽  
General Validity ◽  
Dry Grasslands ◽  
Relative Contribution ◽  
Management Regime ◽  
Community Interest ◽  
Csr Strategy

Trait-based studies have become extremely common in plant ecology. In this work we analysed intraspecific trait variation of Himantoglossum adriaticum, a European endemic orchid species of Community interest, to investigate whether different populations growing on managed and abandoned semi-natural dry grasslands show differences in the CSR strategy. In seven populations occurring in Veneto Region (NE Italy), we measured H. adriaticum maximum vegetative height, leaf traits (LA, LDMC, SLA) and calculated the CSR strategy. Through CCA we investigated the relationship between plant traits and both plant community attributes (cover and height of herbs and shrubs), and geomorphologic features (aspects and slope). PERMANOVA test was used to investigate if the CSR strategy of H. adriaticum varied according to the management regime. Results showed that individuals of H. adriaticum develop different strategies when growing in different habitats. Specifically, individuals growing in managed fully sunny dry grasslands reached higher vegetative height (MH), had lower values of SLA and a higher relative contribution of the C parameter than individuals growing in abandoned dry grasslands, which, on the contrary, were shorter, had higher values of SLA (and correspondingly lower values of LDMC) and a higher relative contribution of the R parameter. Further data on reproductive traits (e.g. fruit and seed-set) may corroborate our results. Although the number of individuals addressed in this study is rather low, and our conclusions may not be considered of general validity for the species, our study demonstrated the applicability of the CSR strategy scheme in detecting functional strategies at intraspecific level.

scholarly journals Bivariate Kumaraswamy Models via Modified Symmetric FGM Copulas: Properties and Applications in Insurance Modeling

2017 ◽  
Author(s):  
Indranil Ghosh
Keyword(s):  
Structural Properties ◽  
Correlation Coefficient ◽  
Bivariate Distributions ◽  
Multivariate Distributions ◽  
Data Set ◽  
Copula Models ◽  
Representative Data ◽  
Bivariate Copula ◽  
Spearman’S Correlation ◽  
Dependence Structures

A copula is a useful tool for constructing bivariate and/or multivariate distributions. In this article, we consider a new modified class of (Farlie-Gumbel-Morgenstern) FGM bivariate copula for constructing several dierent bivariate Kumaraswamy type copulas and discuss their structural properties, including dependence structures. It is established that construction of bivariate distributions by this method allows for greater flexibility in the values of Spearman's correlation coefficient rho, and Kendall's tau . For illustrative purposes, one representative data set is utilized to exhibit the applicability of these proposed bivariate copula models.

scholarly journals Trait-based modelling in ecology: lessons from two decades of research

2019 ◽  
Author(s):  
Liubov Zakharova ◽  
Katrin M Meyer ◽  
Merav Seifan
Keyword(s):  
Species Interactions ◽  
Community Dynamics ◽  
Distribution Patterns ◽  
Plant Ecology ◽  
Ecological Modelling ◽  
Plant Interactions ◽  
Complex Species ◽  
Individual Level ◽  
Current Usage ◽  
The Individual

Trait-based approaches are an alternative to species-based approaches for functionally linking individual organisms with community structure and dynamics. In the trait‑based approach, the focus is on the traits, the physiological, morphological, or life-history characteristics, of organisms rather than their species. Although used in ecological research for several decades, this approach only emerged in ecological modelling about twenty years ago. We review this rise of trait-based models and trace the occasional transfer of trait-based modelling concepts between terrestrial plant ecology, animal and microbial ecology, and aquatic ecology. Trait-based models have a variety of purposes, such as predicting changes in species distribution patterns under climate and land-use change, planning and assessing conservation management, or studying invasion processes. In modelling, trait-based approaches can reduce technical challenges such as computational limitations, scaling problems, and data scarcity. However, we note inconsistencies in the current usage of terms in trait-based approaches and these inconsistencies must be resolved if trait-based concepts are to be easily exchanged between disciplines. Specifically, future trait-based models may further benefit from incorporating intraspecific trait variability and addressing more complex species interactions. We also recommend expanding the combination of trait-based approaches with individual-based modelling to simplify the parameterization of models, to capture plant-plant interactions at the individual level, and to explain community dynamics under global change.

scholarly journals Grouped Normal Variance Mixtures

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 103
Author(s):  
Erik Hintz ◽  
Marius Hofert ◽  
Christiane Lemieux
Keyword(s):  
Tail Dependence ◽  
R Package ◽  
Normal Mixture ◽  
Multivariate Distributions ◽  
Quasi Monte Carlo ◽  
Fitting Procedure ◽  
Mathematical Expressions ◽  
Mixing Distributions ◽  
Normal Variance ◽  
T Distribution

Grouped normal variance mixtures are a class of multivariate distributions that generalize classical normal variance mixtures such as the multivariate t distribution, by allowing different groups to have different (comonotone) mixing distributions. This allows one to better model risk factors where components within a group are of similar type, but where different groups have components of quite different type. This paper provides an encompassing body of algorithms to address the computational challenges when working with this class of distributions. In particular, the distribution function and copula are estimated efficiently using randomized quasi-Monte Carlo (RQMC) algorithms. We propose to estimate the log-density function, which is in general not available in closed form, using an adaptive RQMC scheme. This, in turn, gives rise to a likelihood-based fitting procedure to jointly estimate the parameters of a grouped normal mixture copula jointly. We also provide mathematical expressions and methods to compute Kendall’s tau, Spearman’s rho and the tail dependence coefficient λ. All algorithms presented are available in the R package nvmix (version ≥ 0.0.5).

scholarly journals Multivariate distributions of correlated binary variables generated by pair-copulas

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Huihui Lin ◽  
N. Rao Chaganty
Keyword(s):  
Binary Data ◽  
Real Life ◽  
Three Dimensions ◽  
Multivariate Distributions ◽  
Copula Models ◽  
Binary Distribution ◽  
Life Data ◽  
Scientific Disciplines ◽  
Real Life Data ◽  
Wide Range

AbstractCorrelated binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. The generalized estimating equations (GEEs) and the multivariate probit (MP) model are two of the popular methods for analyzing such data. However, both methods have some significant drawbacks. The GEEs may not have an underlying likelihood and the MP model may fail to generate a multivariate binary distribution with specified marginals and bivariate correlations. In this paper, we study multivariate binary distributions that are based on D-vine pair-copula models as a superior alternative to these methods. We elucidate the construction of these binary distributions in two and three dimensions with numerical examples. For higher dimensions, we provide a method of constructing a multidimensional binary distribution with specified marginals and equicorrelated correlation matrix. We present a real-life data analysis to illustrate the application of our results.

A goodness-of-fit test based on Kendall’s process: Durante's bivariate copula models

2021 ◽  
Vol 16 (3) ◽  
pp. 2851-2882
Author(s):  
N'dri Hubert Bian
Keyword(s):  
Goodness Of Fit ◽  
Empirical Process ◽  
Bootstrap Method ◽  
Parametric Bootstrap ◽  
Goodness Of Fit Test ◽  
Copula Models ◽  
Testing Procedures ◽  
Fitting Procedure ◽  
Fit Testing ◽  
Von Mises

The proposed goodness-of-fit testing procedures for copula models are fairly recent. The new test statistics or omnibus tests are functional of an empirical process motivated by the theoretical and empirical versions of Kendall’s or Spearman's dependence function. In this paper, we propose a fitting procedure for a symmetric and flexible copula model with a non-zero singular component using the Kendall process. The conditions under which this empirical process weakly converges are satisfied. Using a parametric bootstrap method that allows to compute approximate p-values, it is empirically shown that tests based on the Cramer-von Mises distance keeps the prescribed value for the nominal level under the null hypothesis. Simulation studies that demonstrate the power of the fit test are presented.

scholarly journals Risk Analysis of Australia’s Victorian Dairy Farms Using Multivariate Copulae

2021 ◽  
pp. 1-21
Author(s):  
Sosheel Solomon Godfrey ◽  
Ryan H. L. Ip ◽  
Thomas Lee Nordblom
Keyword(s):  
Historical Data ◽  
Cash Flows ◽  
Northern Region ◽  
Simulation Methods ◽  
Multivariate Distributions ◽  
Copula Models ◽  
South West ◽  
Comparative Risk ◽  
Positive Indicators

Abstract The study provides comparative risk analyses of Australia’s three Victorian dairy regions. Historical data were used to identify business risk and financial viability. Multivariate distributions were fitted to the historical price, production, and input costs using copula models, capturing non-linear dependence among the variables. Monte Carlo simulation methods were then used to generate cash flows for a decade. Factors that influenced profitability the most were identified using sensitivity analysis. The dairies in the Northern region have faced water reductions, whereas those of Gippsland and South West have more positive indicators. Our analysis summarizes long-term risks and net farm profits by utilizing survey data in a probabilistic manner.

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