In this post Sam Nicol discusses his recent article with Regis Sabbadin, Nathalie Peyrard and Iadine Chadès Finding the best management policy to eradicate invasive species from spatial ecological networks with simultaneous actions

Lots of invasive species live in spatial networks, which means that they live in a series of discrete habitat sites, but occasionally move between the sites. Managing invasive species in these networks requires a lot of decision-making. Firstly, there are lots of places where you could try to control the species. At each site you have to decide whether or not to control the species, so the number of combinations of potential management locations is very large, particularly as the network size increases. Secondly, you have to decide where to manage through time, and the species moves around while you’re trying to control it. If you manage in the wrong place, the invasive species is likely to recolonise, undoing all your hard work.

Despite the complexity of these systems, making the right decisions can mean that the species can be controlled more effectively at a lower cost. This can translate to cheaper control, better agricultural productivity or better protection for endangered species impacted by the invasive species. Optimal control approaches try to find the best possible set of management actions (called the optimal policy) to control the species through time. Given the number of combinations of strategies that are possible, the optimal policy is a very small needle in a series of very large haystacks, so we need to use smart algorithms to help us find good strategies.

Habitat of the red-finned blue-eye—one of seven artesian springs that make up the global distribution of this remarkable desert-dwelling fish species. (Photo credit: May-Le Ng).

Our new study published in Journal of Applied Ecology introduces a new technique to plan invasive species control actions these networks.  The study makes use of the graph-based Markov decision process (GMDP), which finds a near-optimal policy for applying multiple actions simultaneously in spatial networks across time. Since the policy returned by the GMDP can be difficult to interpret, we also created a way to extract a simpler policy using classification trees.

The method was applied to the challenge of eradicating invasive mosquitofish (Gambusia holbrooki) from the habitat of the red-finned blue-eye (Scaturiginichthys vermeilipinnis), a critically endangered fish with a global population that is restricted to just seven artesian springs in Queensland, Australia. After simplifying the GMDP policy, the best policy was to manage springs occupied by mosquitofish and their connected neighbours, unless the neighbours were occupied by red-finned blue-eyes.

Invasive mosquitofish (Gambusia holbrooki) out-compete red-finned blue-eyes and are a major threat to red-fin persistence. Mosquitofish are established on every inhabited continent and are among world’s worst pest fish species. (Photo credit: Sam Nicol).

Controlling invasive species costs billions of dollars worldwide (Pimentel et al 2005), so finding the most effective and efficient ways to control them is a challenge worth solving. To date, the problem of optimal control in spatially connected networks has been constrained to small networks or a limited number of management actions per year. This study demonstrates how we can use the GMDP to explore a much richer set of management policies and provides a technique to simplify the resulting policies into simple rules of thumb that can be easily communicated to managers.