How Simple Should a Model Be?

Should scientists make simplifying assumptions in complex models? This is a debate as old as the hills, and one that everyone seems to have strong opinions about. Some argue that because even the most simplistic model based on the best available estimates is objective, it is better than relying solely on “gut feelings”. In such a model, estimates based on expert opinion or simplifying assumptions can at least be included in a transparent fashion. Others argue that such an approach can miss important emergent properties as a result of missed complexity, making any results misleading and potentially even worse than not using a model at all.

Models to Support Management: Invasive Horses, Cats and Deer

Wild horses in the Australian alps. © Regina Magierowski
Wild horses in the Australian Alps. © Regina Magierowski

Both sides are right in their own way, of course, but perhaps unusually (as an applied mathematics graduate working in ecology), I’ve found myself leaning towards the former view as my career progresses. During my last postdoc, I was confronted with a large, vexing problem: the incursion of wild horses in the Australian Alps. The species was already impacting bogs and wetlands, overpopulated in some places to the point of starvation, and spreading to previously pristine areas of National Park. The issue was (and still is) highly contentious, with activists applying considerable political pressure against lethal forms of control. Knowledge of population densities across the horses’ range was patchy and ability to predict their likely movements equally unreliable. Even predicting their demographics was difficult, with most values for population growth rates conflicting and spatially variable.

As a result, park managers were faced with potentially catastrophic results for their protected areas but were unable to readily quantify these or even empirically explore potential options for management. To help, we developed a spatially explicit population model called SPADE – the Spatial Population Abundance Dynamics Engine. We used this model in concert with some sensitivity analyses to predict the spread of the population, the effects of different management strategies and the associated costs based on various assumptions.

Modelled (red and grey) hunting-only culling rates of feral cats vs. actual culling by hunting rate before (black) and after (white) the addition of trapping and poisoning © Nick Beeton
Modelled (red and grey) hunting-only culling rates of feral cats vs. actual culling by hunting rate before (black) and after (white) the addition of trapping and poisoning © Nick Beeton

As it became clear that SPADE would be a useful tool in a wide variety of applications, we worked with multiple collaborators to make sure that it was as user-friendly as we could make it. We hope that this will allow landscape managers to explore scenarios with a minimum of assistance or difficulty. To introduce the model to the literature in Methods in Ecology and Evolution, we looked for a case study with high quality spatial data to validate it and demonstrate its potential use. We ended up working with a dataset of the successful Marion Island cat eradication program in the late ’80s and early ’90s – the largest island eradication of feral cats anywhere in the world to date.

Marion Island is a sub-Antarctic island halfway between South Africa and the Antarctic mainland, with breeding populations of seabirds threatened by domestic cat predation. Using SPADE, we successfully managed to predict the observed broad-scale decline of cats on the island as a result of hunting, showed that the decline was influenced by cat dispersal and demonstrated that hunting would not have been successful without the later addition of trapping and poisoning approaches as the population declined.

Fallow Deer have become widespread at Five Rivers Reserve in Tasmania’s Central Highlands . © Tony Hisgett
Fallow Deer have become widespread at Five Rivers Reserve in Tasmania’s Central Highlands . © Tony Hisgett

However, the original purpose of SPADE was always to provide estimates of likely scenarios based on whatever data is available. Another controversial local issue where this approach has been useful is the issue of fallow deer in Tasmania. These are partially protected as a hunting resource despite increasing concerns about their population spread. Little information is available about their demography or location other than numbers of hunting permits issued. Though they have been in Tasmania since the 1830s, their population has remained suppressed until recent decades, at which point it has apparently increased rapidly.

We used the best available information and conservative estimates of deer reproductive rates to estimate their spread and found it likely that they could become well established across the state with a population over 1 million by mid-century. Without heavy control they could cause untold damage to both conservation and agriculture in the state. This alarming scenario is one that managers may have been unable or unwilling to face without a simple model.

But is Our Simple Model Wrong?

Some have argued that our model isn’t complex enough and we are ignoring or unaware of key processes, resulting in potentially biased and alarmist predictions for deer populations. Though they may well be right, the precautionary principle tells us that in the absence of clear evidence, we must assume and plan for the worst. This places the burden of proof squarely on those arguing for the status quo. An advantage of models like SPADE is that it is simple to modify an existing model based on new data or different assumptions in order to re-analyse data if new information is brought to light.

Moving Forward

The simplest models require the most careful justification and the process of adaptive management means that these are constantly being updated with new information and assumptions. In addition there are plenty of new potential applications to try SPADE on, such as the spread of orange hawkweed in southern Australia and buffalo in the north. Some processes, such as water currents and wind-based dispersal, will require additional work to the model. The modeller’s work is never done though, and I can only sigh from behind my computer as I hear field ecologist colleagues tell stories about the far-flung places that my models are being used in.

To find out more about SPADE, read the full article HERE.

This manuscript is being highlighted as part of our promotion of Southern Hemisphere authors coinciding with the 8th Southern Connection Congress in Chile (18-23 January 2016). Follow us on Twitter, Facebook and Google+ to see other great articles that we’re highlighting this week!