# Inverse priority effects: A role for historical contingency during species losses

## Cite this dataset

Torres, Agostina et al. (2023). Inverse priority effects: A role for historical contingency during species losses [Dataset]. Dryad. https://doi.org/10.5061/dryad.h44j0zpsb

## Abstract

Communities worldwide are losing multiple species at an unprecedented rate, but how communities reassemble after these losses is often an open question. It is well established that the order and timing of species arrival during community assembly shapes forthcoming community composition and function. Yet, whether the order and timing of species losses can lead to divergent community trajectories remains largely unexplored. Here, we propose a novel framework that sets testable hypotheses on the effects of the order of species losses inverse priority effects and suggests its integration into the study of community assembly. We propose that the order of species losses within a community can generate alternative reassembly trajectories, and suggest mechanisms that may underlie these inverse priority effects. To formalize these concepts quantitatively, we used a three-species Lotka-Volterra competition model, enabling to investigate conditions in which the order of species losses can lead to divergent reassembly trajectories. The inverse priority effects framework proposed here promotes the systematic study of the dynamics of species losses from ecological communities, ultimately aimed to better understand community reassembly and guide management decisions in light of rapid global change.

## README

### * File name:

README_Dataset-Historical-contingency-during-species-losses.txt *

Authors: Agostina Torres, Sara E. Kuebbing, Katharine L. Stuble,

Samantha A. Catella, Martin A. Nuñez, and Mariano A. Rodriguez-Cabal *

Date created: 2023-10-30 * Date modified: 2023-12-01

Dataset Attribution and Usage

-----------------------------

* Dataset Title: Data for the article "Inverse priority effects: A role for historical contingency during species losses"

* Persistent Identifier: 10.5061/dryad.h44j0zpsb

* Dataset creators: Agostina Torres, Sara E. Kuebbing, Katharine L.Stuble, Samantha A. Catella, Martin A. Nuñez, and Mariano A. Rodriguez-Cabal

* Suggested Citations:

* Dataset citation: > Torres, A., Kuebbing, S. E., Stuble, K. L.,Catella, S. A., Nuñez, M. A., Rodriguez-Cabal, M. A. 2023. Data for the article " Inverse priority effects: A role for historical contingency during species losses", Dryad, Dataset, DOI: 10.5061/dryad.h44j0zpsb

* Corresponding publication: > Torres, A., Kuebbing, S. E., Stuble, K. L., Catella, S. A., Nuñez, M. A., Rodriguez Cabal, M. A. 2023. Inverse priority effects: A role for historical contingency during species losses. Ecology Letters. Accepted

Contact Information -------------------

* Name: Agostina Torres * Affiliations: Instituto de Investigaciones en Biodiversidad y Medioambiente, CONICET, Universidad Nacional del Comahue, Bariloche, Argentina. * ORCID ID:

https://orcid.org/0000-0001-9682-7296 * Email:

torresa@comahue-conicet.gob.ar * Address: e-mail preferred

Dataset Metadata ===========================

Dates and Locations -------------------

* Dates of data collection: Simulated data

* Geographic locations of data collection: Simulated data

#### Methodological Information ==========================

* Methods: we use a phenomenological Lotka-Volterra model of three competing species to demonstrate how and when inverse priority effects can arise in a community based solely on intrinsic dynamics of species interactions, represented as competition coefficients. The model takes the form: (dN_i)/dt=r_i N_i (1-∑_(j=1)^n▒〖α_ij N_j 〗) where N_i is the abundance of species i (i=1,2,3), r_i is the intrinsic growth rate of species i in the absence of competition, n is the total number of species in the system, and α_ij is the competitive effect of species j on species i for i,j=1,2,3. We chose to set all r_i to 1 and limit all α_ij to fall between 0 and 2. We designated one species as the focal and varied removal order of the two nonfocal species (A and B). Then, we assessed prevalence of inverse priority effects that arose specifically when the focal species was excluded when nonfocal species B was removed first (i.e., because the focal was excluded by nonfocal species A), but persisted when nonfocal species A was removed first (i.e., because it could persist with or excluded nonfocal species B).

Data and File Overview ======================

Summary Metrics ---------------

* Code file format: .R * Code file count: 4 * Output file formats:

.RData * Output file count: 3

* Total file count: 7 (4+3)

Naming Conventions ------------------

* File naming scheme: - First part: denotes the type of file:

Code/Output - Second part: denotes the type of information provided in

each file.

--> Parts in naming schemes are separated by '-'. * Throughout, IPE is an acronym for inverse priority effect.

Table of Contents -----------------

* Code files: - Code-IPE_LinearStabilityAnalysis.R -

Code-IPE_IdentifyIPEs.R - Code-IPE_Figure3.R - Code-IPE_Figure4.R

* Output files: - Output-GoodAndSkipParams.RData -

Output-IPE_LinearStabilityAnalysis_Output.RData -

Output-alldat_stable.RData

Setup -----

* Unpacking instructions: n/a

File/Folder Details ===================

1. Code File Code__IPE_LinearStabilityAnalysis.R is the code used to find combinations of competition coefficients leading to a locally stable 3-species equilibrium. There are two output files:

1.1. Output-GoodAndSkipParams.RData has the parameter combinations used in the analysis saved in the "good" matrix, and all other parameter combinations saved in the "skip" matrix (these are parameter combinations that do not meet the criteria for a real solution given in the Supplemental methods).

1.2. Output-IPE_LinearStabilityAnalysis_Output.RData contains three

matrices:

1.2.1. coexistingAlphas

Rows are all parameter combinations we used in the analysis (from the "good" matrix described above).

Columns 1-9 are the competition coefficients with notation α_ij, for species pair i,j for all pairwise interactions between i,j, and k, where '1' indicates the focal species, '2' indicates nonfocal A, and '3' indicates nonfocal B.

1.2.2. coexistingEqpoints

- Rows are all parameter combinations we used in the analysis (from the "good" matrix described above).
- Columns are the equilibrium abundances of the three species given by equation 2 in the Supplemental methods; N1 is the focal, N2 is nonfocal A, and N3 is nonfocal B.

1.2.3. STABLE3SpsEq

Rows are all parameter combinations we used in the analysis (from the "good" matrix described above).

Column is a binary variable indicating whether the real part of all three eigenvalues from the Jacobian given by equation 3 in the Supplemental methods was negative (1 for yes, 0 for no).

2. File IPE_IdentifyIPEs.R loads in the data from the linear stability analysis and then provides a detailed step-by step process of identifying the parameter combinations that yield an inverse priority effect, including visualizations along the way. There is one output file saved as:

2.1. alldat_stable.RData, which is a matrix.

Rows represent a parameter combination that leads to a locally stable 3-species coexistence equilibrium.

Columns 1-9 are the competition coefficients with notation α_ij, forspecies pair i,j for all pairwise interactions between i,j, and k, where'1' indicates the focal species, '2' indicates nonfocal A, and '3' indicates nonfocal B.

Columns 10-12 ("N1eq", "N2eq", "N3eq") are the equilibrium abundances of the three species given by equation 2 in the Supplemental methods; N1 is the focal, N2 is nonfocal A, and N3 is nonfocal B.

Column 13 ("STABLE3spsEq") is a binary variable indicating whether the real part of all three eigenvalues from the Jacobian given by equation 3 in the Supplemental methods was negative (1 for yes, 0 for no; this matrix only contains locally stable combinations so all values should =1).

Column 14-19 are values of niche overlap ("rho_ij", or ρ_ij in the main text) and relative fitness differences ("fit_ij", or f_j/f_i in the main text) for species pairs i,j for all pairwise combinations of i, j, and k, where '1' indicates the focal species, '2' indicates nonfocal A, and '3' indicates nonfocal B.

Columns 20-21 contain a binary variable indicating whether that parameter combination yielded an inverse priority effect (1 for yes, 0 for no). "guaranteedIPE1" and "guaranteedIPE2" correspond to scenarios 1 and 2, respectively, discussed in the Supplemental methods.

Columns 22-24 contain a binary variable indicating whether that parameter combination yielded an inverse priority effect (1 for yes, 0 for no). "p1IPE", "p2IPE", and "p3IPE" correspond to scenarios 3-5, respectively, discussed in the Supplemental methods.

Column 25 ("anyIPE") is a summary column indicating whether any of the 5 scenarios from the previous columns yielded an inverse priority effect (binary, 1 for yes, 0 for no).

Column 26-28 are stabilization potential values (1-ρ_ij) for species pairs i,j for all pairwise combinations of i, j, and k, where '1' indicates the focal species, '2' indicates nonfocal A, and '3' indicates nonfocal B.

3. Code File IPE_Figure3.R is the code that produced Figure 3.

4. Code File IPE_Figure4.R is the code that produced Figure 4.