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# WK 34 - Cooccurrence Analysis and Beta Diversity with a Novel Metric Based on Statistical Theory

**Session Description**: Ecologists and biogeographers have used ~80 indices to estimate association in a cooccurrence data. However, the indices systematically presented severe challenges in the interpretation. We recently exhibited that this problem emerges from a highly inconsistent mapping of the indices to the cumulative probability distribution of the null model (Mainali et al. 2022, Science Advances 8:1–9). Consequently, we recently developed a novel metric of association called alpha hat, which (a) is a statistical estimator of a model parameter mechanistically interpretable as a degree of association because alpha hat is the log ratio of the relative probability of preference, and (b) resolves the challenges of the traditional indices and various standardization techniques. We subsequently developed an installable R package (https://github.com/kpmainali/CooccurrenceAffinity) and a vignette (https://www.biorxiv.org/content/10.1101/2022.11.01.514801v1).

In this workshop, participants (a) will engage in analyzing a*2*×*2* contingency table of occurrence/co-occurrence counts and a *m*×*n* presence-absence matrix to compute beta diversity and species-pair affinity, (b) will participate in discussion to understand each of the quantities computed, and (c) will discuss the utility and relevance of these methods in ecological/biogeographic research.

**Interactive Analysis:** Specifically, the participants will compute, understand and learn to use in their research the following quantities:

(1) affinity (MLE of alpha metric) and its p-value

(2) four types of CI of alpha MLE

(3) median interval of alpha MLE

(4) coverage probability of a chosen CI

**Interactive **

**Discussion: ** The participants will engage in discussion of the quantities listed above. I will present a brief discussion of the four types of CI and our recommendation for most research applications. I will explain why caution is required in interpretation of the most extreme positive and negative co-occurrences.

**Interactive Plotting: **The participants will generate:

(1) a square heatmap of affinity, traditional indices and other computed quantities analyzing*m*×*n* presence-absence matrix

(2) a coverage probability of a chosen CI, actually showing in a plot how robustly the CI performs

**Outcome:** At the end of the workshop, the participants will be able to analyze a *2*×*2* contingency table of occurrence/co-occurrence counts and a *m*×*n* presence-absence matrix. They will be able to compute and understand the meaning of affinity, its median interval, its four types of CIs and coverage probability of the CIs, and good practices in this analysis, especially the most useful CI. The participants will also be able to plot the results and the coverage probability of CI.

Workshop

Career Track

Wednesday, August 9, 2023

1:30 PM – 3:00 PM PDT

Location: C124

- KM
Kumar Mainali

Senior Data Scientist

Chesapeake Conservancy, Conservation Innovation Center, 716 Giddings Avenue, Suite 42, Annapolis, MD 21401

Annapolis, Maryland, United States

In this workshop, participants (a) will engage in analyzing a

(1) affinity (MLE of alpha metric) and its p-value

(2) four types of CI of alpha MLE

(3) median interval of alpha MLE

(4) coverage probability of a chosen CI

(1) a square heatmap of affinity, traditional indices and other computed quantities analyzing

(2) a coverage probability of a chosen CI, actually showing in a plot how robustly the CI performs