Predicting unexpected outcomes in invasive species control – poster at #neobiota2016

At Neobiota2016, I presented a poster on the early work that I’ve managed to do for the Christmas Island project. While I can’t upload the poster since the results are very preliminary and need refinement, I would like take the opportunity and introduce the general problem of invasive species control and give an description of the methods which intend to use.

With my poster at #Neobiota2016 – yes I did try to attract people’s attention with invasive species biscuits :)


The most common questions I received since arriving in Europe in the lead up to the conference was: “Why do you eradicate cats?”. In Europe cats are mostly seen as pets: while wild house cats (feral cats) exist there too, the problem is less severe as in Australia or other places where cats don’t occur naturally.

Cats were originally introduced to Australia take care of other pests like rats and mice, but now they threaten the survival of many native animals. A recent article has found feral cats to be the worst invasive predator threatening at least 430 animal species and having caused the extinction of at least 63 species.

The most severely impacted species are found on islands, and Christmas Island is no exception; here cats are a major threat to many native birds, but as generalist predators, they also feed on reptiles, amphibians and small mammals. Removing this threat is key to ongoing management for conserving threatened natives, such as the Christmas Island owl or the Lister’s gecko.


Christmas Island hawk owl. © List Preston

But cats are not the only introduced predator on Christmas Island: 20 other introduced species have turned invasive and threaten native wildlife either through predation or by changing the native habitat. Cats are the top-predator on the island, and their removal could lead to unintended negative outcomes as they have occurred on other islands in the past. To ensure that the removal of cats results in conserving threatened species, we need to predict the result of an eradication in advance. But how do we predict responses of several species to a management actions, especially when we know little about the species’ interactions and population dynamics?

This is where my research comes in: I’m currently adapting a method by Christopher Baker and colleagues for the Christmas Island case. In their article, they provide a framework for predicting the outcome of reintroductions of species to existing communities when we only know if an interaction between the species involved is positive or negative.

Here, I’ll give a short overview over one of their case studies: the well-known and widely studied Yellowstone network after the reintroduction of wolves. Check out Chris’ publication for a more detailed description and another case study (a dingo reintroduction). Also, if you’re keen to run the analysis yourself, check out Chris’ blog post.

1) In a first step, we require a network of interacting species and this can be done through eliciting it with experts or searching the literature. For the Yellowstone case study the network was modified from Ripple et al. 2014 Science (Figure 1).

Figure 1. Network of species in Yellowstone NP. Solid lines indicate interactions pre-reintroduction, dashes lines are new interactions after reintroduction. Black arrows show positiv interactions, while red arrows show negative interactions. Figure is reproduced from Baker et al. 2016 Cons Biol

2) Once we know the structure of the network, we can translate it into a matrix with all species occurring in rows and columns. Each cell shows if a species receives either a positive effect (+1), a negative effect (-1) or no effect (0) from interacting with another species.

Figure 2. Matrix shows the effect of an interaction between each species: -1 interactions = predation pressure or competition, +1  feeding or mutualistic benefit. 0 when species don’t interact directly. Read from column to row, e.g. wolves have a negative effect on elks, but elks have a positive effect on bears.

3) With this information a generalised Lotka-Volterra model is parameterised. Only the direction of the interactions is known, hence, interaction strength was sampled from a uniform distribution between 0 and +1 or -1.

Lotka-Volterra equation for simulating community dynamics. Growth rates ri and interaction terms aij have to be parameterised. The interaction term includes all interactions between species (interspecific interactions) and within a species (infraspecific competition)

4) Growth rates estimates were available for wolves, elks and bears, and they allowed a wide variation to include all potential community dynamics. Unknown growth rates can be sampled randomly from wide, realistic distributions.

5) Sample a set of parameters for the community without wolves (pre-reintroduction).

6) Two post hoc tests check for model viability:

  1. All species have to be present in the community (current state)
  2. System has to have stable equilibrium (more information in supplement – this is not the right place for a large chunk of maths).

7) Many different realisations need to be generated to cover a wide parameter uncertainty. In total Baker et al. (2016) generated 10,000 viable models.

8) Next, wolves were reintroduced to the system and the new equilibrium of the system was solved for.

9) The relative changes for each ecosystem element from pre-reintroduction to reintroduction systems are saved.

10) Lastly the community dynamics are solved with the integration function ode45 in Matlab. As initial conditions the pre-reintroduction equilibrium is used and the wolves are reintroduced with 10% of their smallest equilibrium abundance.

11) The results for all 10,000 (viable) models are then combined to get the overall results of the system.

For the Yellowstone case study, 11 species showed over 2,000 qualitatively different long-term responses, but ecosystem-wide results were limited to four (Figure 3 a). The most frequently predicted responses were observed in reality: bears and woody plants increased in abundance and stream morphology improved.

Figure 3 shows a) the proportion of times of all models that a species abundance increased (light bars) or decreased (dark bars). All possible ecosystem outcomes are represented by the dynamics of two species: elks and beers. Here a subset of the outcomes is shown where elks b) increased or c) decreased.

The four different responses could be combined based on the relative changes of only two species: bears and elks. For example, whenever, elks increased the abundance of bears was lower than when elks decreased (Figure 3 b). Further, when elks increased birds, beavers, berries, and woody plants decreased and stream morphology got worse (Figure 3 c).

Even simple interaction networks produce many different possible community dynamics, which highlights the need to parameterise models with as much information as possible. Systematic methods like these help synthesise results from many predictions which helps to make decisions when little information is available.

Since the Christmas Island network is even larger (see here), the possible network dynamics are even more variable. To reduce this variation, I am currently searching for literature about interaction strengths between the species (e.g., scat analysis for predator diets) and growth rate estimates of all species.

Although Neobiota2016 was mainly about invasive weeds and drivers of invasion, I managed to meet the other “cat lady”, Pauline Palmas, who is studying the cats’ diet in New Caledonia. This is great, because we have started thinking about using diet information to parameterise the interaction strengths and it will be very useful to compare cat diet from different islands in similar climatic conditions. So stay tuned for future results on the Christmas Island project.


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