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

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

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

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

If you have questions, please contact [e-mail] or [e-mail]

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

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

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

If you have questions, please contact [e-mail], [e-mail], or [e-mail]