# Reconstructing the historical fauna of a large continental island: a multispecies reintroduction risk analysis

## Citation

Peterson, Katie et al. (2021), Reconstructing the historical fauna of a large continental island: a multispecies reintroduction risk analysis, Dryad, Dataset, https://doi.org/10.5061/dryad.t1g1jwt2p

## Abstract

1. Reintroduction projects, which are an important tool in threatened species conservation, are becoming more complex, often involving the translocation of multiple species. Ecological theory predicts that the sequence and timing of reintroductions will play an important role in their success or failure. Following the removal of sheep, goats and feral cats, the Western Australian government is sequentially reintroducing 13 native fauna species to restore the globally important natural and cultural values of Dirk Hartog Island.

2. We use ensembles of ecosystem models to compare 23 alternative reintroduction strategies on Dirk Hartog Island, in Western Australia. The reintroduction strategies differ in the order, timing, and location of releases on the island. Expert elicitation informed the model structure, allowing for use of different presumed species interaction networks which explicitly incorporated uncertainty in ecosystem dynamics.

3. Our model ensembles predict that almost all of the species (~12.5 out of 13, on average) will successfully establish in the ecosystem studied, regardless of which reintroduction strategy is undertaken. The project can therefore proceed with greater confidence and flexibility regarding the reintroduction strategy. However, the identity of the at-risk species varies between strategies, and depends on the structure of the species interaction network, which is quite uncertain. The model ensembles also offer insights into why some species fail to establish on Dirk Hartog Island, predicting that most unsuccessful reintroductions will be the result of competitive interactions with extant species.

4. *Synthesis and applications:* Our model ensembles allow for the comparison of outcomes between reintroduction strategies and between different species interaction networks. This framework allows for inclusion of high uncertainty in dynamics. Finally, an ensemble modelling approach also creates a foundation for formal adaptive management as reintroduction projects proceed.

## Methods

This is the code and data that generates the models and figures used in the manuscript and supplementary documents.

We begin by generating an ensemble of models for each transition matrix, which are associated with the same dynamic behaviours determined through expert elicitation. To do this we first determine a scalar multiple for each transition matrix, that will be multiplied along the diagonal of the coefficient matrix and ensure that one thousand models are generated in approximately 24 hours. This is done using the Matlab script *FindMultiplier.m* in which a user selects the transition matrix to investigate (and its type: 1 if all signs are defined, 2 if the sign is uncertain).

The ensemble of models is then generated using the Matlab script *CreateModelsForAll.m*. This script requires the user to define the transition matrix to investigate and the number of models which we want to generate. The user must also change the save name at the bottom of the script. This script uses Multipliers.mat (generated by the user by running *FindMultiplier.m*), IM’X’.xlsx, where *‘X’∈{1,…,7}*, and Rvector.xlsx. This script also uses the functions and scripts *ExtractCoexistenceConstraints.m*, *Coexistence_constraint.m*, *check_stability.m*, and *GrowthRateConstraint.m*, which are used to determine if models match the elicited dynamic constraints. We will discuss these constraints in more detail later. Finally this script outputs *ModelEnsembleIM’X’.mat*, where *‘X’∈{1,…,7}*, which contains the ensemble of models (and their associated parameters) for interaction matrix *‘X’*.

Finally, we use the ensemble of models to simulate the reintroduction strategies. This is done using the script, *Spatial_reintroduction_simulation.m*. This script uses *ModelEnsembleIM’X’.mat*, where *‘X’∈{1,…,7}*, along with elicited dispersal data in DispTimeDelay.xlsx, DispUpperBound.xlsx, DispLowerBound.xlsx. The translocation strategies are loaded in using AlternativeNames.xlsx, and Alt’Y’.xlsx, where *‘Y’∈{1,…,23}*. This script then uses *species_DE_spatial.m* to simulate the system. The output of *Spatial_reintroduction_simulation.m* saves *OutcomesSetBIGIM’X’.mat* (the set of species which failed in a given simulation for a given translocation alternative), and *SimulationSetBIGIM’X’.mat* (the timeseries abundance and time data for every simulation), where *‘X’∈{1,…,7}*.

To then analyse these simulations and generate the figures used in the manuscript and supplementary materials we use the following scripts and functions:

- Manuscript Figures:
- Fig 2:
*VisuallyCmpareMatrices.m* - Fig 3:
*Figure_key_timeseries_SUBSET.m* - Fig 4:
*Figure_4.m* - Fig 5:
*ExplainWhyExtinct_quantiles.m* - Fig 6:
*Figure_checkerbard_particular_species.m*

- Fig 2:
- Supplementary Figures
- Supplementary Infrmation 2:
*SUPPFIG_Figure_key_timeseries_AllSupps.m* - Supplementary Infrmation 3:
*SUPPFIG_matrix_vilins.m* - Supplementary Infrmation 4:
*SUPPFIG_Figure_checkerbards_bars.m* - Supplementary Infrmation 5:
*ExplainWhyExtinct_quantiles.m*

- Supplementary Infrmation 2:

Input parameters are specified at the beginning of major scripts/functions.

If you have questions, please contact **kpeter10@umd.edu or michael.bode@qut.edu.au**

This is the code and data that generates the models and figures used in the manuscript and supplementary documents.

We begin by generating an ensemble of models for each transition matrix, which are associated with the same dynamic behaviours determined through expert elicitation. To do this we first determine a scalar multiple for each transition matrix, that will be multiplied along the diagonal of the coefficient matrix and ensure that one thousand models are generated in approximately 24 hours. This is done using the Matlab script *FindMultiplier.m* in which a user selects the transition matrix to investigate (and its type: 1 if all signs are defined, 2 if the sign is uncertain).

The ensemble of models is then generated using the Matlab script *CreateModelsForAll.m*. This script requires the user to define the transition matrix to investigate and the number of models which we want to generate. The user must also change the save name at the bottom of the script. This script uses Multipliers.mat (generated by the user by running *FindMultiplier.m*), IM’X’.xlsx, where *‘X’∈{1,…,7}*, and Rvector.xlsx. This script also uses the functions and scripts *ExtractCoexistenceConstraints.m*, *Coexistence_constraint.m*, *check_stability.m*, and *GrowthRateConstraint.m*, which are used to determine if models match the elicited dynamic constraints. We will discuss these constraints in more detail later. Finally this script outputs *ModelEnsembleIM’X’.mat*, where *‘X’∈{1,…,7}*, which contains the ensemble of models (and their associated parameters) for interaction matrix *‘X’*.

Finally, we use the ensemble of models to simulate the reintroduction strategies. This is done using the script, *Spatial_reintroduction_simulation.m*. This script uses *ModelEnsembleIM’X’.mat*, where *‘X’∈{1,…,7}*, along with elicited dispersal data in DispTimeDelay.xlsx, DispUpperBound.xlsx, DispLowerBound.xlsx. The translocation strategies are loaded in using AlternativeNames.xlsx, and Alt’Y’.xlsx, where *‘Y’∈{1,…,23}*. This script then uses *species_DE_spatial.m* to simulate the system. The output of *Spatial_reintroduction_simulation.m* saves *OutcomesSetBIGIM’X’.mat* (the set of species which failed in a given simulation for a given translocation alternative), and *SimulationSetBIGIM’X’.mat* (the timeseries abundance and time data for every simulation), where *‘X’∈{1,…,7}*.

To then analyse these simulations and generate the figures used in the manuscript and supplementary materials we use the following scripts and functions:

- Manuscript Figures:
- Fig 2:
*VisuallyCmpareMatrices.m* - Fig 3:
*Figure_key_timeseries_SUBSET.m* - Fig 4:
*Figure_4.m* - Fig 5:
*ExplainWhyExtinct_quantiles.m* - Fig 6:
*Figure_checkerbard_particular_species.m*

- Fig 2:
- Supplementary Figures
- Supplementary Infrmation 2:
*SUPPFIG_Figure_key_timeseries_AllSupps.m* - Supplementary Infrmation 3:
*SUPPFIG_matrix_vilins.m* - Supplementary Infrmation 4:
*SUPPFIG_Figure_checkerbards_bars.m* - Supplementary Infrmation 5:
*ExplainWhyExtinct_quantiles.m*

- Supplementary Infrmation 2:

Input parameters are specified at the beginning of major scripts/functions.

If you have questions, please contact **kpeter10@sesync.org**,** cailan.jeynessmith@hdr.qut.edu.au**,** **or** michael.bode@qut.edu.au**

## Usage Notes

We provide a summary of all functions with their inputs, dependent functions/data, and outputs.

To generate models:

- FindMultiplier.m
- Determines the diagnal multiplier ‘
*FinalMult*’ fr a given transition matrix, IM’X’.xlsx, to generate 1000 samples in approximately 24 hours when used in CreateModelsForAll.m. - Inputs: Select a transitin matrix, IM’X’.xlsx, to investigate (and its type: 1 if all signs are defined, 2 if there is sign uncertainty),
- Lads Rvector.xlsx, IM’X’.xlsx
- Runs ExtractCexistenceConstraint.m, Coexistence_constraint.m, check_stability.m, GrowthRateConstraint.m

- Determines the diagnal multiplier ‘
- CreateModelsForAll.m
- Finds mdels which meet dynamic constraints for a selected transition matrix.
- Inputs: select transitin matrix, IM’X’.xlsx, to investigate (and its type: 1 if all signs are defined, 2 if there is sign is uncertain) and number of coexisting matrices which we want. Change output save name at the bottom of the file
- Lads Multipliers.mat, IM’X’.xlsx, Rvector.xlsx,
**Cexistence_constraints_list.mat** - Runs Cexistence_constraint.m, check_stability.m, GrowthRateConstraint.m, ExtractCoexistenceConstraints.m
- Saves MdelEnsembleIM’X’.mat

- Spatial_reintroduction_simulation.m
- This generates simulatins of the ecosystems which are then used to generate figures
- Lads in DispTimeDelay.xlsx, DispUpperBound.xlsx, DispLowerBound.xlsx, AlternativeNames.xlsx, AltX.xlsx, ModelEnsembleIMX.mat,
- Runs species_DE_spatial.m
- Saves OutcmesSetBIGIMX.mat, SimulationSetBIGIMX.mat

- ExtractCoexistenceConstraints.m
- Generates a matrix with abundance cnstraints
- Lads Coexistence_constraints_CS_SC.xlsx
- Saves Cexistence_constraints_list.mat

- Check_stability.m
- Checks the stability f a system
- Is run by CreateMdelsForAll.m and Coexistence_constraint.m

- Coexistence_constraint.m
- Checks if a subset f species can coexist together
- Runs Check_stability.m
- Is run by CreateMdelsForAll.m

- GrowthRateConstraint.m
- Checks if species have grwth rates which exist within the bounds identified by Rvector.xlsx
- Is run by CreateMdelsForAll.m

- species_DE_spatial.m
- Runs a simulatin of a translocation strategy, taking into account spatial factors such as translocation
- is run by Spatial_reintrduction_simulation.m

Manuscript Figures:

- Fig 2: VisuallyCompareMatrices.m
- Input: Change ‘i’ t range from 1:6 to 1:7 (line 53) to obtain all Figures found in manuscript
- Lads
__DHINames.xlsx, DHINames_shrt.xlsx, DHINames_medium.xlsx__, IM’X’.mat,

- Fig 3: Figure_key_timeseries_SUBSET.m
- Lads
__AlternativeNames_23.xlsx__, SimulatinSetBIGIMX.mat, OutcomesSetBIGIMX.mat, DHINames.xlsx - Calls Make_TIFF.m, tight_subplt.m
- Saves Reintr_timeseries_LowRes.tiff, Reintro_timeseries.tiff

- Lads
- Fig 4: Figure_4.m
- Lads AlternativeNames_23.xlsx, OutcomesSetBIGIMX.mat, DHINames.xlsx, OUTCOMES_BLOCK.mat
- Calls TranslcationAlternativesNames.m, Make_TIFF.m
- Saves Figure_4_LwRes.tiff, Figure_4.tiff

- Fig 5: ExplainWhyExtinct_quantiles.m
- Lads ModelEnsembleIMX.mat, OutcomesSetBIGIMX.mat, SimulationSetBIGIMX.mat, DHINames.xlsx, DHINames_short.xlsx, DHINames_medium.xlsx, AlternativeNames_23.xlsx
- Calls Make_TIFF.m
- Saves ‘SpeciesName’_failure_ExpertMatrix_’X’.tiff

- Fig 6: Figure_checkerboard_particular_species.m
- Lads AlternativeNames_23.xlsx, OutcomesSetBIGIMX.mat, DHINames.xlsx, DHINames_short.xlsx, DHINames_medium.xlsx
- Calls TranslcationAlternativesNames.m, Make_TIFF.m, tight_subplot.m
- Figure_6_LwRes.tiff, Figure_6.tiff

- ManuscriptFigure_checkerboards_bars_consensus.m:
- Input: set variable
*PLOT_checker_SameMat = 1* - Lads AlternativeNames_23.xlsx, OutcomesSetBIGIM’X’.mat, DHINames_short.xlsx, DHINames_medium.xlsx
- Saves OUTCOMES_BLOCK.mat which is used in Figure_4.m

- Input: set variable
- TranslocationAlternativesNames.m:
- Input: ALTNAME (defined in functins which call it)
- Lads ALTNAME.xlsx
- Defines the names used in figures

Supplementary Figures

- Supplementary Information 2: SUPPFIG_Figure_key_timeseries_AllSupps.m
- Lads AlternativeNames_23.xlsx, SimulationSetBIGIMX.mat, OutcomesSetBIGIMX.mat, DHINames.xlsx, DHINames_short.xlsx
- Calls Make_TIFF.m, tight_subplt.m
- Saves SuppFig_Reintr_timeseries_X.tiff

- Supplementary Information 3: SUPPFIG_matrix_violins.m
- Lads AlternativeNames_23.xlsx, OutcomesSetBIGIMX.mat, DHINames.xlsx,
- Calls Make_TIFF.m, TranslcationAlternativesNames.m
- Saves SuppFig_vilin_X.tiff

- Supplementary Information 4: SUPPFIG_Figure_checkerboards_bars.m
- Lads AlternativeNames_23.xlsx, OutcomesSetBIGIMX.mat, DHINames.xlsx, DHINames_short.xlsx, DHINames_medium.xlsx
- INPUT: PLOT_checker_SameSpp, PLOT_checker_SameAlt, PLOT_checker_SameMat are binary variables at the tp of the file, which are set to 1 if the desired figure is to be generated
- Calls TranslcationAlternativesNames.m, Make_TIFF.m, tight_subplot.m
- Saves SuppFig_MatrixAlternativeChecquerbard.tiff, SuppFig_MatrixSpeciesChecquerboard.tiff, SuppFig_AlternativeSpeciesChecquerboard.tiff

- Supplementary Information 5: ExplainWhyExtinct_quantiles.m
- Lads ModelEnsembleIMX.mat, OutcomesSetBIGIMX.mat, SimulationSetBIGIMX.mat, DHINames.xlsx, DHINames_short.xlsx, DHINames_medium.xlsx, AlternativeNames_23.xlsx
- Calls Make_TIFF.m
- Saves ‘SpeciesName’_failure_ExpertMatrix_’X’.tiff

External Function:

- tight_subplot.m:
- generates subplts with minimised whitespace.
- Dwnloaded from MathWorks