AUSTRALIAN FRONTIERS OF SCIENCE, 2003

Canberra, 31 July to 1 August 2003

AUSTRALIAN FRONTIERS OF SCIENCE, 2003
Canberra, 31 July to 1 August 2003

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New approaches to the 'evolution' of complex ecological systems kangaroo population dynamics
by Professor Hugh Possingham

Hugh Possingham is a Professor in Mathematics and Zoology at the University of Queensland, where he is the Director of the Ecology Centre. Hugh completed Applied Mathematics Honours at the University of Adelaide and his DPhil at Oxford University in 1987 as a Rhodes Scholar. Postdoctoral research periods followed at Stanford University and the Australian National University (QEIII Fellow). In 1991 he moved to Applied Mathematics at the University of Adelaide and in 1995 he was appointed Foundation Chair and Professor of Environmental Science. In July 2000 he took his current position at the University of Queensland where he was recently awarded an ARC Professorial Research Fellowship. Hugh has received the Australian Academy of Science's inaugural Fenner Medal, Australian Mathematics Society medal, a Eureka prize and a medal from the Modelling and Simulation Society of Australia. The Possingham lab includes five postdoctoral researchers and eleven PhD students working on empirical and theoretical aspects of applied population ecology.

While I was listening then to the talks I made the mistake of reading the back of the program which says, 'Over the course of the symposium these gifted young scientists' so that lets me out 'will explain what they do and why.' So I thought I might actually say a bit about why I do what I do, as well as what I do.

I am going to go through some specific examples, but before I do that I want to make a few points about all the people involved in this research. The research program is very interdisciplinary. The people who have contributed come from Zoology, Geography and Mathematics. Indeed a lot of the people are in themselves interdisciplinary people. Professor Gordon Grigg is a physiologist who has become more of an ecologist, I and Ms Cindy Hauser are mathematicians who have become ecologists, and Dr Tony Pople is an ecologist who has become a mathematical modeller.

Another thing I want to say is that, while I will talk about kangaroo issues and kangaroo population dynamics, I also want to try and lace what I do with the philosophy of the way we think quite different, I think, from a lot of the philosophy of the way that people think in the talks we have heard so far. Possibly we are more similar to the paleo people and geologists than to the molecular people, in the way we approach our science. Partly the differences are to do with time and spatial scales, our access to data, and whethjer we think mechanistically or holistically.

The other thing I should say is that this is one of about six different research programs of work within my group. I can't, obviously, go through all of them. What I want to do is use this research to illustrate some philosophical points, and also to point out that population ecology is actually quite an applied science. One of the questions is we should ask ourselves is 'Why? Why do we do science?' It is not just to write papers in scientific journals. Population ecology drives is the science behind many things that are important to this country, for example, weed and pest management, fisheries, conservation of threatened species. Our kangaroo work can be interpreted as a problem of harvesting, pest control and conservation depending on your perspective or geographical location.

A lot of the work our research group has done in the past has had quite major implications for resource utilisation in this country. Work, for example, on population modelling for threatened species, with my colleague David Lindenmayer, has had an enormous influence on forestry debates in this country. Work on reserve design, by one of my former PhD students, Dr Ian Ball, has now underpinned the entire redesign of the Great Barrier Reef Marine Park. We are here to talk science and I am going to focus on the science side, but what I am talking about in these research programs has actually changed the face of Australia and the way Australia is managed.

I think a lot of people in the general public think ecologists look at lions eating zebras: it's very interesting and it's natural history and it's not particularly useful. We often get the question, 'Can ecologists get jobs? Who would employ them?' I suppose I will be arguing quite strongly that they are very employable and very important.

I suppose Tim Flannery's words on that were quite important. His argument was that until you can feed, clothe and house yourself sustainably, you can't call yourselves Australians. And we're not. We are running down the natural capital of this country at a vast rate, on the assumption, presumably, that we can go to another continent once we have exhausted this one. So his view was that until you are actually managing the country sustainably, you can't call yourself an Australian. I think that is a good point, and it is part of the philosophy behind what we do.

There are seven parts to my talk:

1. Background and history

2. Visualisation of the patterns

3. The confrontation of models with data

4. Why model - prediction, utility or understanding?

5. The evolutionary impact of harvesting a 'just so' story

6. Optimal adaptive monitoring

7. Learning while managing a new discipline applied theoretical ecology

I want to highlight now one of the key things that I think is a bit of a revolution in the field of ecology: the confrontation of models with data. We have very limited data, and it is really noisy, noisy data. We cannot just go and do another experiment to resolve an issues about the long-term dynamics of red kangaroosbecause it takes you 20 years to get the data. So we have got to think hard about what models we build and how we refine those models. Because we are waiting from year to year for the data points we have a lot of time to synthesise and analyse. We really want to maximise the value we get out of that data. We cannot sort out our problems by just collecting more data and or doing more experiments.

We adopt an approach championed by Ray Hilborn and Marc Mangel in their book The Ecological Detective. They argue that null hypothesis testing is of limited value to the applied ecologist. You can't accept a null-hypothesis; you can only reject it, which means you never have a predictive model that you can use to manage your system of interest (eg kangaroos). You are just waiting to reject a null-hypothesis. In our research we try to have several alternative models at any point in time, and we assign a relative belief in those models, which means that at any point in time, with the data and the information we have got, we can actually say, 'This is the best model. Go and manage the planet with this model until we find out some more information, and we may change our mind later on.

Also, coming from a maths background, I want to talk a bit about the reason for modelling. Why are we modelling? Is it just to understand the world? Is it to predict things? Is it to manage things?

Data on the distribution and abundance of red kangaroos has, fortuitously, been collected for a long time. We have data going back to 1978, through the foresight of a large number of people, particularly Gordon Grigg with respect to aerial surveys. It is unusual for us to have that much data for a long period of time. So this is a bit of a luxury. For kangaroos we have data overlong temporal scales and large spatial scales. There is not a lot of ecology that goes on at this sort of large scale. We are talking about ecology at the scale of the a continent. Most population ecology, some of the classic stuff, occurs for example in the rocky intertidal, at the scale of metres. Scaling up our ecological knowledge from this small scale to the landscape scale is very important.

Another interesting thing is that a lot of what I am talking about is very similar to what fisheries people do. One thing where we have an advantage is that for a lot of fisheries population, the only data they have is the fish that is caught. We actually have the kangaroos that are shot; we also have independent surveys of that population.

Click on image for a larger version of figure 1

This slide gives you a quick idea of how the data is collected. People fly fixed transects and count, over many hours and days. This happens in at least three states of Australia fairly consistently, and it has happened for a long time in slightly different ways in different places. It is a fairly consistent and robust counting method. There have been a lot of research into the methodology of counting kangaroos.

One of the interesting things I have found about the last day or so has been people's approaches to visualisation. In this research we are involved with remote sensing and geography people, who are always saying, 'Let's look at the data. Let's look at it in interesting ways, and see what can we discover?' I must admit I was a big cynic about visualisation, but we have actually looked into it and sometimes clever visualisation can expose things that otherwise would have been hard to see.

Click on image for a larger version of figure 2

This is the kind of data we have, and we can visualise lots of it (thanks to Norbet Menke and Stuart Phinn). I just want to quickly show a couple of the things that are quite interesting in this animated data set, just to give you an idea of the scale of the problem and the processes that are going on. It is certainly very complicated. In this visualisation, every three seconds we are going forward another year. The size of the dot is the size of the red kangaroo population in part of a transect in South Australia. You can see an enormous amount of variability In space and time.

I just want you now to pay attention as the numbers are increasing. In 1981 there is a surge in abundance, and then we go into a drought in 1982-83. If you look at that jump from 1980 to 1981, one of the most interesting things that the visualisation tells us is, that despite the current dogma that red kangaroos are fairly sedentary, it is impossible to get those increases in numbers without fairly large-scale movement. So the visualisation has been informative. The visualisation also gives you a far better idea of how the variability plays out in time and space, and it can inform how you then construct various models.

Click on image for a larger version of figure 3

Moving from the spatial visualisation we can simply plot the dynamics of kangaroo numbers for the whole region. The x-axis is time and the y-axis is a scaled value. The blue line is kangaroo abundance and we are interested in comparing that abundance with the national digitised vegetation index which is collected by satellite and is believed to be a measure of food availability. Visualising these patterns it is fairly clear that kangaroo abundance is strongly correlated with how green the region is 6-12 months beforehand. This makes sense because kangaroo numbers will take this long to respond, the time it takes for birth and growth of an individual to a point at which it can be seen in an arial survey.

You might think, 'Oh, this is a pretty easy modelling exercise. Just put in a 12-month time lag, put in the rainfall and we're away. That tells us everything about kangaroo numbers.' But if you look hard around the year 2000, and in other places, you see the relationship breaks down. So it is more than just rainfall. What is it? Is it density dependence (competition between kangaroos), is it the harvesting, is the sheep stocking rates? What other things can we get out of these time series?

In terms of confronting the model with data, the idea is now to create a series of different models, or if you like, nested subsets of models, with and without certain parameters in them, to try and work out what variables drive kangaroo abundance. And from a theoretical perspective this asks quite fundamental questions about things, like: what is the plausible time lag? Can we explain that in terms of the physiology and growth rate of kangaroos? Do sheep compete with kangaroos? You might guess yes, they both eat grass, but maybe not. What about density dependence the impact of abundance on per capita birth and death rates? Australian ecologists led the world in arguing about density dependence Nicholson, Andrewartha and Birch. We are leaders in that discussion, and the issue is still in dispute.

Click on image for a larger version of figure 4

What I am going to show is models built for the north-east pastoral district, then we will go to some broader models where we are modelling all the regions. Again it is an interesting scaling question here. We can model all of South Australia's population people have done that. We can model it region by region. We can try and model every one of those red dots and see how that is fluctuating. But of course you couldn't model that in isolation, because there is movement. The question of the appropriate scale to build a model is intruiging.

We will now compare two models, a ratio model developed by Tony Pople, and a more mechanistic model following work by Graeme Caughley. The ratio has theoretical support but is very simple. The "interactive" model developed by Caughley has a lot more mechanism and would certainly appeal more to an empirical ecologist.

Click on image for a larger version of figure 5

In this slide we use maximum likelihood methods to parameterise the ratio model using the first half of the data, and then we see how well it predicts for the rest of the data. In this particular case the ratio model seems to do a good job at prediction. Does that mean it is a useful model? It is good at prediction. Is it informative? Will it be useful for management? Well, it didn't have a lot of mechanism in it.

Click on image for a larger version of figure 6

The interactive model, which has more mechanism in it is a poor predictor of kangaroo population dynamics. Is it good for management? In fact, if we just took a purely statistical view of this, we would say, 'Throw away the interactive model.' But there is more to models than absolute prediction, which we shall see.

This work is three or four years old, more recently Niclas Jonzen has worked with us to build a more complex and general time-series model of kangaroo population growth that includes harvesting, sheep numbers, rainfall, density-dependence and environmental variability. The model is shown in the slide below.

Click on image for a larger version of figure 7

We used Akaike's information criteria to interrogate the data and determine the model that explains the data in the most parsimonious fashion. The bottom line in all this modelling is that if you throw in more parameters, you will get a better fit. That is almost a truism. Akaike's information criteria actually give you the most parsimonious model. It tells you which one is not overfitting the data, and that has become an extremely popular and powerful tool in ecology in the last two or three years.

The 'best' model has 50% of our support but does some funny things. The statistics say it is a great model and there is strong density dependence. Well, that's fine. It is unusual but plausible to get strong density dependence. Harvesting matters; if you shoot kangaroos they die. That's good to know. But kangaroos seem to eat sheep, because the d term, which should be negative if sheep compete with kangaroos, is positive. The more sheep there are, the faster the kangaroo population grows. That's a worry: I don't think kangaroos eat sheep. Dr Jonzen also found inexplicable correlations between regions that cannot be explained by the rainfall patterns. Inexplicable correlations what are they?

So it really leads us to saying, 'There are a lot of things about kangaroo population dynamics we don't know.' We think that the reason why kangaroos are appearing to respond positively to sheep is actually that the people who manage the pastoral properties are much better at deciding when to put sheep on a paddock than we could determine than just by lagged rainfall. This makes some sense and also implies a quite weak affect of sheep on kangaroos, if any.

So why are we modelling? Are we just trying to make an accurate forecast? No. This last model is the best one we have from a statistical perspective, it supersedes the other two. In this case it seems that the better a model is at predicting, the less sense it makes ecologically.

Click on image for a larger version of figure 8

There is a final reason why we model, aside from prediction and explanation. The main government and industry interest in these models is how well they perform at making robust management decisions. Let's say we do use the models to make some decisions, and let's go back to the first two fairly simple models, the ratio model which was theoretically interesting but very simple and the interactive model, which had a lot of mechanism in it (see figure). The interactive model tells us to harvest around 15%, while the model that had more predictive power, the ratio model, suggests a harvest about 35%. There is a clear flaw in the latter, due to an excessive capacity of that model to allow low kangaroo populations to recover rapidly. The final curve is what we would predict using a simple logistic model, which was classically used in fisheries, and while that suggests about the same quota, it predicts unreasonably high abundances.

Finally we turn briefly to an even more applied question, how often should we monitor kangaroo populations to avoid overharvesting?

Click on image for a larger version of figure 9

Here we (in particular Tony Pople again) have used the models to look at the consequences of monitoring less, which saves us money, on the probability of population collapse. Obviously less monitoring means we are less certain about the size of a population and we are more likely to set a quota that is too large resulting in over-harvesting. Using the model in this way allows us to trade-off the savings from less monitoring with the cost of population collapse.

This leads me to the research issue that I am most passionate about at the moment active adaptive management. When you have got very little data one of the most interesting things about ecology and applied ecology is the idea that we can manage the system to learn things faster. So if we don't understand what is going on with the sheep, maybe we can manage the system to learn some of those parameters faster through changing sheep numbers experimentally at a large spatial scale. This will incur a management cost in the short term but may lead to better predictive models in the long term which means better management. Ultimately what is the price we are willing to pay to have more understanding of a system and better predictive models?. We call that active adaptive management, and probably the only prospect in this country of our getting better natural resource management understanding is that we deliberately manipulate the system but not just to get profits and gains. We manipulate these large-scale systems to maximise the rate of information gain. That is an interesting mathematical problem, and it is stuff that we are currently working on at the moment. The problem is intruiging and mathematically
quite hard.

Session 5 discussion