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Questions tagged [diversity]

measures of diversity (or uniformity or inequality) such as: biodiversity in ecology, income inequality in economic. Examples are entropy and simpson's indices.

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How to do rarefaction analysis for sample-based abundance data?

I would like to compare plant richness of different forest stands via rarefaction. The data is collected in a plot-based manner. I set 4 equal-sized plots in each stand, counted all plant individuals ...
Sitta's user avatar
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Calculating Diversity Indices at a Specific Taxonomic Level Using Richness Tables without OTU Association Information

I have a question concerning the calculation of indices, such as the Shannon index, Inverse Simpson, etc., at a specific taxonomic level (e.g., family level) using a richness table of that particular ...
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Testing the hypothesis that $\sum_i^N p_i^2 =(N-1)/2N$ given $\sum_i^N p_i=1$

In ecology there is a simple index for measuring diversity known as the Simpson index. In it simplest formula, it takes a series of proportions, representing the relative abundance (number of ...
JMenezes's user avatar
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Unsure of statistics needed while working with replicates

I apologize if the question is considered too broad, but I'm hoping to get at least a basic starting point as I'm somewhat stuck with how to approach this. I am working with community ecological data-...
user390865's user avatar
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Why don't vegan::vegdist and vegan::metaMDS produce equivalent results?

This question has been discussed before but the proposed solution (https://stats.stackexchange.com/a/459820/170801) is no longer reproducible for some reason. As a refresher - it has been suggested ...
befriendabacter's user avatar
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Hazard ratios - one unit increase for a continuous variable measuring diversity (Blau index/ coefficient of variation), how to interpret?

I am having difficulty understanding how to interpret a one-unit increase/decrease for continuous variables in a Cox model. Specifically, I have created the variables gender, age & nationality ...
Laura Hill's user avatar
2 votes
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93 views

How to fit GLMM or LMM models to analyze alpha diversity metrics (Hill numbers)?

I am studying alpha diversity (Hill numbers) using shotgun metagenomic data. The sampling design has multiple levels of nesting, as follows: 2 years > 3 locations > 2 conditions > 1 transect &...
Éder Rodrigues's user avatar
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Can Shannon-Wiener index be used for measuring temporal differences? [closed]

I understand the Shannon diversity index being used in spatial analysis when comparing multiple sites of measurement, but can it be used to measure abundances, richness, diversity, etc. on a temporal ...
user390865's user avatar
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Why should a valid diversity measure be independent of the target variable?

Consider an ensemble of weak learners (i.e. regressors or classifiers) whose predictions are aggregated (e.g. via averaging or majority vote) into an ensemble estimate. This gives rise to the question ...
ngmir's user avatar
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14 votes
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Quantifying diversity of bird species

I’m wondering if anyone could recommend a diversity index to look at the differences in breeding bird territories between two sites. These are my data - the numbers represent the number of breeding ...
luciano's user avatar
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Characterizing and comparing the heterogeneity of ordinal responses from survey

Let us consider the following setting: We have two groups Q1 and Q2 of questions Several participants answer all questions using a single ordinal scale A, B, C or D for all questions. Then, I want ...
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Is this definition of the Herfindahl index related to its usual definition?

For me, the usual definition of the Herfindahl index is this one. See also this question. Here, on page 26, it is defined as a function of the coefficient of variation: Are these definitions of the ...
Quodly's user avatar
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Calculate Herfindahl-Hirschman Index when you know the total but only observe the largest few

The Herfindahl–Hirschman Index (HHI) is a concentration measure defined as $$H = \sum_i p_i^2,$$ where $p_i$ is the market share of firm $i$. However this assumes knowing all $p_i$ for an industry. ...
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Ways to measure deviation from a discrete uniform distribution [duplicate]

I'm looking for a way to characterize the deviation from a discrete uniform distribution. Example: 50 balls are distributed over 10 urns. In the most equal case, all urns get 5 balls. In the most ...
cosine's user avatar
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What is the appropriate way to statistically analyse diversity indexes?

I have been working with a soil-derived viral metagenomic data set and am looking for advice on the appropriate statistical approach to the results. I have 2 different sample areas. Within both areas ...
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How to measure if a categorical distribution is concentrated in a very few bins

I'm trying to think of a way to measure that a categorical distribution of any size is concentrated in only a few bins, so not uniform. The best way I can think of is checking entropy, but that's kind ...
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Dissimilarity only between different treatments in dataset

I am studying the impact of wildfires on vegetation species composition. I have surveyed the burnt and unburnt areas on six sites which burned at different points in time from which I now have species ...
user340096's user avatar
1 vote
1 answer
223 views

Metrics to compare diversity of groups on multiple characteristics

When I search for 'diversity metrics' it seems like most work has focused on ecological diversity, and I most frequently see the Simpson diversity index. This is equivalent to the economics metric, ...
Dr. Beeblebrox's user avatar
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316 views

Diversity index and ordinal variables?

Is it possible to calculate a diversity index (Simpson's or eventually Shannon's index) from ordinal data? As in, we surveyed 50 transects and recorded several species' "abundance" in 4 ...
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How do I decide if it's ok to pool data?

I have biodiversity data (fish species, and their individual length, through electrofishing) from 8 different stretches of the same river, for 7 different seasons. We would like to see if it's ok to ...
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How to include standard deviations in diversity calculations?

I have community abundance data where each species has a mean and a standard deviation (determined by replicate samples). I am comparing the diversity of two communities. The various diversity metrics ...
rrr's user avatar
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Clustering as a diversity metric?

I have this idea where I want to compute the number of clusters in subsets of the full dataset and compare this number with the total number of clusters for the full dataset as a metric for the ...
Evan's user avatar
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2 votes
1 answer
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I have diversity index values and I wish to test for statistical significance between the zones readings. How can I statistically analyse this?

I have produced a graph for each Zone, x axis = years, y axis = diversity. I would primarily like to analyse the difference in diversity between the zones, but would also be interested in analysing ...
jack23's user avatar
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1 answer
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ecologists, if I have diversity data (Shannon's index) for years and sites how can I produce data just for the sites (explained better below)

I have 3 sites each split into the same 3 zones. With abundance data taken on 4 different years. I have produced diversity index readings for each zone at each site, for each year. If I'm not trying ...
jack23's user avatar
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1 answer
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How can I use R to asses the biodiversity of reef zones?

I wish to analyse my dataset, and concluded with the information I have, biodiversity would be good choice. I have 3 sites each are a reef and have the same zonation (split into 3 zones). I am aiming ...
jack23's user avatar
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235 views

Significance test for the difference in Simpson's Diversity Index values?

I've taken several samples of categorical data and calculated the spread of each using Simpson's Diversity Index. I would now like to perform a significance test to see if these spreads are similar or ...
joshisanonymous's user avatar
1 vote
1 answer
778 views

Comparing species communities between sites with different numbers of replicates

I'm working with ecological community data collected from different sites and want to make comparisons between the sites using descriptors like richness, Shannon Weiner's diversity, and Simpson's ...
Fragilaria's user avatar
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138 views

Is the Bray-Curtis dissimilarity/similarity independent of richness/diversity?

I was told about potential issues with the Bray-Curtis dissimilarity/similarity measure. Specifically, I have been asked if Bray-Curtis is independent of richness/diversity. I am unsure how to answer ...
ecology's user avatar
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Build tree to calculate beta diversity

I am trying to calculate beta diversity using the UniFrac distance on my data, each sample having OTUs values. To calculate it, I saw it required building a tree with percentages that represented the ...
odyssey's user avatar
5 votes
1 answer
124 views

Clustering on n features while maximizing the heterogeneity on m remaining features

We have a random vector $X\sim p(X)$, and a set of realizations of the random vector $S=\{X_i\}_{i=1}^N$. The random vector has $n$ continuous and $m$ categorical features. I want to cluster $S$ so ...
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Continuous (not categorical) measures of diversity?

Which measures of diversity are used where? When I search for diversity indicators I find the Simpson and Shannon index, but these are both for categorical data. If I have data with some structure (e....
Lochend's user avatar
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24 views

Statistical Test for Trends in Samples from a Possibly Changing Distribution

I have some data of quantitative measurements of the language in books from the years 1800 to 2000. For each year I have between 0 and 50 samples, mostly about 10 samples per year. If I bin the data ...
chasmani's user avatar
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1 vote
1 answer
86 views

Remove points, but preserve diversity

Given a finite set of points in $\mathbb{R}^n$, all at finite distances from each other I would like to remove a certain proportion of points, in such a way as to penalise clustering. For example for $...
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How to compare community diversity of longitudinal and independent samples?

We are wanting to compare the diversity of biofouling species on longitudinal and independent samples. The first set of samples is repeated measures data, as we measured percent cover of species on ...
Emmerson Wilson's user avatar
4 votes
1 answer
215 views

Distance matrix time series analysis? (Ecology/diversity)

I am trying to analyze a time series of ecological data. Each time point in the series is a matrix of animals-by-foods (that they were observed to eat). For each of these time points, I compute the ...
Matt's user avatar
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500 views

How should I deal with spatial autocorrelation in beta GLMM (glmmTMB)? (Bird diversity)

I am trying to compare certain a taxonomic diversity index (for bird communities) calculated for squares in a map grid system (a total of 34 squares) for two different years: 1998 and 2018. My ...
KO 88's user avatar
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How to interpret rarefaction results?

I have applied rarefaction analysis with R's package iNext. I got these results: ...
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3 votes
0 answers
70 views

A reference request for a population statistic---experienced population density?

We all know that countries (for example) have population densities, but suppose we want to know what is the actual experienced population density (that is, if, say, in Sweden 95% of the population ...
Igor Rivin's user avatar
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0 answers
293 views

Which test should I use to compare the effect of a parasite infection on gut microbiome across time serie data point

I am interested in the effect of an intestinal parasite infection on the rat gut bacterial community. I have two groups of rats ("infected" and "non-infected") each consists of 6 ...
Vince Bil's user avatar
6 votes
2 answers
957 views

How to measure whether a discrete distribution is uniform or not?

Say I have two vectors [1,2,1,2,2] and [1,2,1,1,1]. The number at each dimension is the frequency of one element. How do I measure whether these two vectors are close to the uniform distribution? I ...
hidemyname's user avatar
2 votes
2 answers
510 views

How to include the observed values, not just their probabilities, in information entropy?

Shannon entropy measures the unpredictability in a random variable's outcome as the weighted average of the probabilities of that variable's outcomes or observed values. However, it discards the ...
develarist's user avatar
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751 views

PCoA/MDS on sqrt transformed Bray-Curtis dissmilarity using cmdscale

I would like to use PCoA to visualize beta diversity of a large community. I chose Bray-Curtis as distance measure to calculate the dissimilarity matrix and would like to apply a square root ...
mucl's user avatar
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1 vote
1 answer
214 views

Test homogeneity of multivariate dispersion with regard to the Modified Raup-Crick Metric

Please find a citation for the modified Raup-Crick Metric below Modified Raup-Crick Metric (Chase et al. 2011 As an extremely brief review, this metric generates a dissimilarity matrix containing ...
Alex Romer's user avatar
1 vote
1 answer
87 views

Is there a minimum number for the calculation of the Herfindahl index?

Is there a minimum number of observations in order to assess concentration or not?
adrCoder's user avatar
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1 answer
131 views

What are the ways to normalize the vegetation data when the plot sizes of samples are different?

I have collected data on mangrove tree species density and composition from two habitat categories (sample groups) by using belt transects of various lengths between 100 x 10 M to 500 x 10 m. (3 & ...
Nehru's user avatar
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7 votes
4 answers
2k views

How is the Herfindahl-Hirschman index different from entropy?

The Herfindahl–Hirschman Index (HHI) is a concentration measure defined as $$H = \sum_i p_i^2,$$ where $p_i$ is the market share of firm $i$. It's maximized when one firm has a monopoly and minimized ...
bjarkemoensted's user avatar
3 votes
2 answers
2k views

Use vegdist function before metaMDS?

I am trying to do calculate beta-diversity of bacterial community data. I have been following numerous tutorials regarding this subject and I am getting mixed advice. I am trying to calculate beta-...
Roelof Coertze's user avatar
1 vote
1 answer
118 views

Understanding the assumptions of a Poisson regression model? Modeling plant diversity

I have data on plant diversity in response to a fully crossed treatments of fertilizer and light in grassland systems: ...
Ryan's user avatar
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1 answer
156 views

Zero Denominator in Yule's Q-statistics?

In Concept Drift Adaptation by Exploiting Historical Knowledge they use Yule's Q-statistics to compute diversity between a collection of predictions. I think the context is not really important. I ...
gmp's user avatar
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1 vote
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Creating a fair coefficient for prize competition

I am trying to boost sales in our sales divisions by creating a small competition between them. However, the elaboration is quite tricky in order to guarantee a fair competition. There are 20 sales ...
schiseb's user avatar
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