scholarly journals Efficient algorithms for sampling feasible sets of macroecological patterns

2013 ◽  
Author(s):  
Kenneth J. Locey ◽  
Daniel J. McGlinn
Keyword(s):  
Species Abundance ◽  
Previous Method ◽  
Species Abundance Distribution ◽  
Abundance Distribution ◽  
Feasible Set ◽  
As Species ◽  
Random Samples ◽  
Feasible Sets ◽  
Sampling Algorithms ◽  
New Algorithms

Ecological variables such as species richness (S) and total abundance (N) can strongly influence the forms of macroecological patterns. For example, the majority of variation in the species abundance distribution (SAD) can often be explained by the majority of possible forms having the same N and S, i.e. the feasible set. The feasible set reveals how variables such as N and S determine observable variation and whether empirical patterns are exceptional to the majority of possible forms. However, this approach has currently only been applied to the SAD using relatively inefficient random sampling algorithms. We extend the use of the feasible set approach by developing new algorithms to efficiently generate random samples of the feasible set for the SAD and the intraspecific spatial abundance distribution (SSAD). These algorithms are often several orders of magnitude faster than a previous method, which greatly increases the size and diversity of communities that can be examined.

scholarly journals Efficient algorithms for sampling feasible sets of abundance distributions

2014 ◽  
Author(s):  
Kenneth J. Locey ◽  
Daniel J. McGlinn
Keyword(s):  
Species Abundance ◽  
Discrete Distributions ◽  
Ecological Communities ◽  
Feasible Set ◽  
As Species ◽  
Random Samples ◽  
Ecological Patterns ◽  
Feasible Sets ◽  
Sampling Algorithms ◽  
Zero Values

Ecological variables such as species richness (S) and total abundance (N) can strongly influence ecological patterns. For example, the general form of the species abundance distribution (SAD) can often be explained by the majority of possible forms having the same N and S, i.e. the SAD feasible set. The feasible set reveals how variables determine observable variation, whether empirical patterns are exceptional to the majority of possible forms, and provides a constraint-based explanation for the ubiquity of hollow-curve SADs in nature. However, use of the feasible set has been limited to inefficient sampling algorithms that prevent large ecological communities and ecologically realistic combinations of N and S from being examined. This is the primary hindrance to using this otherwise novel perspective and theoretical framework. We developed efficient computational algorithms to generate random samples of the feasible set for the SAD and similar discrete distributions of abundance, including those that allow for zero-values, e.g., absences. We provide Python and R based implementations of our algorithms and tools for testing and using them. Our algorithms are often several orders of magnitude faster than a long-standing and recently used approach. This greatly increases the size and diversity of communities that can be examined with the feasible set approach and thus advances progress using constraint-based approaches to decipher ecological patterns.

scholarly journals Efficient algorithms for sampling feasible sets of abundance distributions

2014 ◽  
Author(s):  
Kenneth J. Locey ◽  
Daniel J. McGlinn
Keyword(s):  
Species Abundance ◽  
Discrete Distributions ◽  
Ecological Communities ◽  
Feasible Set ◽  
As Species ◽  
Random Samples ◽  
Ecological Patterns ◽  
Feasible Sets ◽  
Sampling Algorithms ◽  
Zero Values

Ecological variables such as species richness (S) and total abundance (N) can strongly influence ecological patterns. For example, the general form of the species abundance distribution (SAD) can often be explained by the majority of possible forms having the same N and S, i.e. the SAD feasible set. The feasible set reveals how variables determine observable variation, whether empirical patterns are exceptional to the majority of possible forms, and provides a constraint-based explanation for the ubiquity of hollow-curve SADs in nature. However, use of the feasible set has been limited to inefficient sampling algorithms that prevent large ecological communities and ecologically realistic combinations of N and S from being examined. This is the primary hindrance to using this otherwise novel perspective and theoretical framework. We developed efficient computational algorithms to generate random samples of the feasible set for the SAD and similar discrete distributions of abundance, including those that allow for zero-values, e.g., absences. We provide Python and R based implementations of our algorithms and tools for testing and using them. Our algorithms are often several orders of magnitude faster than a long-standing and recently used approach. This greatly increases the size and diversity of communities that can be examined with the feasible set approach and thus advances progress using constraint-based approaches to decipher ecological patterns.

scholarly journals Attenuation of species abundance distributions by sampling

2015 ◽  
Vol 2 (4) ◽  
pp. 140219 ◽  
Author(s):  
Hideyasu Shimadzu ◽  
Ross Darnell
Keyword(s):  
Random Sampling ◽  
Species Abundance ◽  
Sampling Bias ◽  
Theoretical Studies ◽  
Limited Time ◽  
Species Abundance Distribution ◽  
Abundance Distribution ◽  
As Species ◽  
Species Abundance Distributions ◽  
Important Challenge

Quantifying biodiversity aspects such as species presence/ absence, richness and abundance is an important challenge to answer scientific and resource management questions. In practice, biodiversity can only be assessed from biological material taken by surveys, a difficult task given limited time and resources. A type of random sampling, or often called sub-sampling, is a commonly used technique to reduce the amount of time and effort for investigating large quantities of biological samples. However, it is not immediately clear how (sub-)sampling affects the estimate of biodiversity aspects from a quantitative perspective. This paper specifies the effect of (sub-)sampling as attenuation of the species abundance distribution (SAD), and articulates how the sampling bias is induced to the SAD by random sampling. The framework presented also reveals some confusion in previous theoretical studies.

Using a Macroecological Approach to Study Geographic Range, Abundance and Body Size in the Fossil Record

2010 ◽  
Vol 16 ◽  
pp. 117-141 ◽  
Author(s):  
S. Kathleen Lyons ◽  
Felisa A. Smith
Keyword(s):  
Body Size ◽  
Fossil Record ◽  
Species Abundance ◽  
Geographic Range ◽  
Species Abundance Distribution ◽  
Abundance Distribution ◽  
Geographic Ranges ◽  
Spatial And Temporal Scales ◽  
Geographic Range Size ◽  
Fossil Data

Macroecology is a rapidly growing sub-discipline within ecology that is concerned with characterizing statistical patterns of species' abundance, distribution and diversity at spatial and temporal scales typically ignored by traditional ecology. Both macroecology and paleoecology are concerned with answering similar questions (e.g., understanding the factors that influence geographic ranges, or the way that species assemble into communities). As such, macroecological methods easily lend themselves to many paleoecological questions. Moreover, it is possible to estimate the variables of interest to macroecologists (e.g., body size, geographic range size, abundance, diversity) using fossil data. Here we describe the measurement and estimation of the variables used in macroecological studies and potential biases introduced by using fossil data. Next we describe the methods used to analyze macroecological patterns and briefly discuss the current understanding of these patterns. This chapter is by no means an exhaustive review of macroecology and its methods. Instead, it is an introduction to macroecology that we hope will spur innovation in the application of macroecology to the study of the fossil record.

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