Introduction to Quantitative Ecology

Modern practice of ecology, conservation, and resource management demands unprecedented levels of quantitative proficiency in mathematical modeling and statistics. This text provides foundational training in the concepts and methods of mathematical and statistical modeling used in ecology, for readers with all levels of quantitative proficiency and confidence. The first chapter presents a generalized approach to develop ecological models and introduces the “describe, explain, and interpret” framework for linking the model world to the real world. Detailed treatment of population models illustrates the myriad ways in which one can develop a model, shows how modeling choices are informed by the ecological question at hand, and emphasizes the epistemology of quantitative techniques. The second part of the book illustrates how to estimate parameters of models from data, and how to use mathematical models combined with statistics to test hypotheses. The third part of the book is devoted to an in-depth development of technical skills to implement models in two common platforms: spreadsheets and the R programming language. The book concludes by demonstrating a quantitative approach to addressing a question that spans density-dependent versus density-independent population models, fitting models to data, evaluating the strength for density dependence using model selection, and evaluating the types of dynamic behaviors that the population might exhibit.

Review of Estimating Trophic Relationships by Quantitative Fatty Acid Signature Analysis

The dynamic predator–prey relations in the food web are vital for understanding the function and structure of ecosystems. Dietary estimation is a research hotspot of quantitative ecology, providing key insights into predator–prey relationships. One of the most promising approaches is quantitative fatty acid signature analysis (QFASA), which is the first generation of statistical tools to estimate the quantitative trophic predator–prey relationships by comparing the fatty acid (FA) signatures among predators and their prey. QFASA has been continuously widely applied, refined and extended since its introduction. This article reviewed the research progress of QFASA from development and application. QFASA reflects the long-term diet of predator, and provides the quantitative dietary composition of predator, but it is sensitive to the metabolism of predator. The calibration coefficients (CCs) and the FA subset are two crucial parameters to explain the metabolism of predators, but the incorrect construction or improper use of CCs and the FA subset may cause bias in dietary estimation. Further study and refinement of the QFASA approach is needed to identify recommendations for which CCs and subsets of FA work best for different taxa and systems.

Biodiversity in Music Scores

Nature has inspired music since the dawn of humankind and has contributed to the creation and development of music as an art form. However, attempts to use the science of nature (i.e., quantitative ecology) to inform music as a broader art-science system is comparatively underdeveloped. In this paper an approach from biodiversity assessments is borrowed to quantify structural diversity in music scores. The approach is analogous in its nature and considers notations with distinct pitches and duration as equivalents of species in ecosystems, measures within a score as equivalents of ecosystems, and the sum of measures (i.e., the entire score) as a landscape in which ecosystems are embedded. Structural diversity can be calculated at the level of measures (“alpha diversity”) and the entire score (“gamma diversity”). An additional metric can be derived that quantifies the structural differentiation between measures in a score (“beta diversity”). The approach is demonstrated using music scores that vary in complexity. The method seems particularly suitable for hypothesis testing to objectively identify many of the intricate phenomena in music. For instance, questions related to the variability within and between musical genres or among individual composers can be addressed. Another potential application is an assessment of ontogenetic structural variability in the works of composers during their lifetime. Such information can then be contrasted with other cultural, psychological, and historical variables, among others. This study shows the opportunities that music and ecology offer for interdisciplinary research to broaden our knowledge of complex systems of people and nature.

A Fast and Robust Way to Estimate Overlap of Niches, and Draw Inference

The problem of quantifying the overlap of Hutchinsonian niches has received much attention lately, in particular in quantitative ecology, from where it also originates. However, the niche concept has the potential to also be useful in many other application areas, as for example in economics. We are presenting a fully nonparametric, robust solution to this problem, along with exact shortcut formulas based on rank-statistics, and with a rather intuitive probabilistic interpretation. Furthermore, by deriving the asymptotic sampling distribution of the estimators, we are proposing the first asymptotically valid inference method, providing confidence intervals for the niche overlap. The theoretical considerations are supplemented by simulation studies and a real data example.