Blog by James Millington, PhD

Things got a bit crazy this month as I made the transition from my Leverhulme Fellowship to a permanent position at King’s as Lecturer in Physical and Quantitative Geography. I’m now Programme Director on the MSc in Environmental Monitoring, Modelling and Management (which I completed 10 years ago this month!) and preparing for of new modules on which I’m teaching this term has kept me busy. Specifically, this term I’m teaching on the postgraduate module ‘Methods for Environmental Research’ and the undergraduate modules ‘Principles of Geographical Inquiry II’ and ‘Current Research in… Ecosystem Services’ (which I taught last year also). So it’s been busy, but also stimulating to be putting thought into how best to communicate and illuminate ideas.

As part of the Intro for our new postgraduate students, and so that can find out more about the research that we do in the department, this week the Earth and Environmental Dynamics research group seminar series was given over to several short presentations by members of staff. The slides from mine is below.

July was a busy month of writing. Unfortunately, it wasn’t busy writing on this blog and I failed on my New Year’s resolution to make at least one blog post each calendar month this year.

The writing I was doing was for my contribution to a new Landscape Ecology textbook I’m co-authoring with Dr Rob Francis. I’ve written and contributed to individual chapters for edited books previously (the latest highlighted below), but a whole book is a larger challenge. In particular, it’s been a useful experience thinking about how to structure the presentation of the ideas we want to address, which order they come in, what goes in each chapter, and so forth. I’ve mainly been working on the chapters on scale and disturbance, but have also been thinking about material for the heterogeneity and landscape evolution chapters. I’ve been learning a lot, revisiting old notes (including from my undergraduate lectures with Dr Perry!) and reviewing the content of others’ books. It’s been good thinking about some of the broader issues – such as the shifting-mosaic steady state and diversity-disturbance relationships – as it helps to frame more focused questions and work I’ve been thinking about and doing (including my ongoing research using Mediterranean disturbance-succession simulation modelling). When I get the chance (in amongst other things) I’ll post more here about the progression of the book, it’s aims and how it will fit in with teaching we have planned.

One of the interesting things we show with the model, which was not readily at the outset of our investigation, is that parent agents with above average but not very high spatial mobility fail to get their child into their preferred school more frequently than other parents – including those with lower mobility. This is partly due to the differing aspirations of parents to move house to ensure they live in appropriate neighbourhoods, given the use of distance (from home to school) to ration places at popular schools. In future, when better informed by individual-level data and used in combination with scenarios of different education policies, our modelling approach will allow us to more rigorously investigate the consequences of education policy for inequalities in access to education.

I’ve pasted the abstract below and because JASSS is freely available online you’ll be able to read the entire paper in a few months when it’s officially published. Any questions before then, just zap me an email.

Millington, J.D.A., Butler, T. and Hamnett, C. (forthcoming) Aspiration, Attainment and Success: An agent-based model of distance-based school allocation Journal of Artificial Societies and Social Simulation

AbstractIn recent years, UK governments have implemented policies that emphasise the ability of parents to choose which school they wish their child to attend. Inherently spatial school-place allocation rules in many areas have produced a geography of inequality between parents that succeed and fail to get their child into preferred schools based upon where they live. We present an agent-based simulation model developed to investigate the implications of distance-based school-place allocation policies. We show how a simple, abstract model can generate patterns of school popularity, performance and spatial distribution of pupils which are similar to those observed in local education authorities in London, UK. The model represents ‘school’ and ‘parent’ agents. Parental ‘aspiration’ to send their child to the best performing school (as opposed to other criteria) is a primary parent agent attribute in the model. This aspiration attribute is used as a means to constrain the location and movement of parent agents within the modelled environment. Results indicate that these location and movement constraints are needed to generate empirical patterns, and that patterns are generated most closely and consistently when schools agents differ in their ability to increase pupil attainment. Analysis of model output for simulations using these mechanisms shows how parent agents with above-average – but not very high – aspiration fail to get their child a place at their preferred school more frequently than other parent agents. We highlight the kinds of alternative school-place allocation rules and education system policies the model can be used to investigate.

The main aim of visiting Assoc. Profs. David O’Sullivan and George Perry was to continue on from where we left off with our recent work on agent-based modelling (including that published inGeoforum on narrative explanation and in the ABM of Geographical systems book chapter). The paper on narrative explanation was actually initiated in a previous trip I made to Auckland in 2005 – takes a while for these things to come to fruition (but in my defence I was busy with otherthings for several years and there were otheroutcomes from that trip). Hopefully, such a concrete outcome as a publication from our modelling and discussions won’t be so long in coming this time around! In particular, we’ll continue to examine the idea that, just as we fail to maximise the value of spatial models by not using spatial analysis of their output, we fail to maximise the value of agent-based models by not using agent-based analysis of their output. Identifying means of understanding how agent interactions and attributes influence path dependency in system dynamics seems and interesting place to start…

While in Auckland I also made good progress on the manuscript I’m writing with John Wainwright on the value of agent-based modelling for integrating geographical understanding (which I mentioned previously). I presented the main ideas from this manuscript in a seminar to members of the School of Environment and got some useful feedback. The slides from my presentation are below and I’m sure I’ll discuss that more here in future.

Another area I made progress on with George is the continuing use of the Mediterranean disturbance-succession modelling platform developed during my PhD. We think there are some interesting questions we can use an enhanced version of the original model to investigate, including examining the controls on Mediterranean vegetation competition and succession during the Holocene. One of the most sensitive aspects of the original model was the importance of soil moisture for succession dynamics and I’ve started on updating the model to use the soil-water balance model employed in the LandClim model. Enhancing the model in this way will also improve it’s applicability to explore fire-vegetation interactions with human activity and to explore questions regarding fire-vegetation-terrain interactions (i.e., ecogeomorphology).

So, lots to be going on with and hopefully I’ll be able to visit again in another few years time.

Most of my participation at the meeting was related to the Land Systems Science Symposium sessions (which ran across four days) and the Agent-Based and Cellular Automata Model for Geographical Systems sessions. It was good to discuss and meet new people wrestling with similar issues to those in my own research. Unfortunately, the ABM sessions were scheduled for the last day which meant it was only late in the conference that I got to properly meet people I’d encountered online (e.g., Mike Batty, Andrew Crooks, Nick Magliocca) and others. Despite being scheduled for the last day there was a good turnout in the sessions and my presentation (below) seemed to go down well. Researchers from the group at George Mason University were most well-represented, with much of their work using the MASON modelling libraries (which I’m going to have to looking into more to continue the work initiated during my PhD).

It’s hard to concentrate on 20-minute paper sessions continuously for five days though, and I found the discussion panels and plenaries a nice relief, allowing a broader picture to develop. For example, David O’Sullivan (whom I’m currently visiting at the University of Auckland) chaired and interesting panel discussion on ABM for Land Use/Cover Change. Participants included, Chris Bone who discussed the need for better representation of model uncertainty from multiple simulation (via temporal variant-invariant analysis – coming soon in IJGIS); Dan Brown who suggested we’re missing mid-level models that are neither abstract ‘toys’ nor beholden to mimetic reproduction of specific empirical data (e.g., where are the ABM equivalents of von Thunen and Burgess type models?); and Moira Zellner who highlighted problems of using ABM for decision-making in participatory approaches (Moira’s presentation in the ABM session was great, discussing the ‘blow-up’ in her participatory modelling project when the model got too complicated and stakeholders no longer wanted to know what the model was doing under the hood).

I also really enjoyed Mike Goodchild’s Progress in Human Geography annual lecture, in which he reviewed the development of GIScience through his long career and where he thought it should go next (‘Old Debates, New Opportunities’). Goodchild argued (I think) that Geography cannot (and should not) be an experimental science in the mold of Physics, and that rather than attempting to identify laws in social (geographical) science, we should aim to find things that can be deemed to be ‘generally true’ and used as a norm for reducing uncertainty. This is possible because geography is ‘neither uniform nor unique’, but it is repeating. Furthermore, he argued it was time for GIScience to rediscover place and that a technology of place is needed to accompany the (existing) technology of space. This technology of place might use names rather than co-ordinates, hierarchies of places rather than layers of coverages, and produce sketch maps rather than planimetric maps. The substitution of names of places for co-ordinates of locations is particularly important here, as names are social constructs and so multiple (local) maps are possible (and needed) rather than a single (global) map. Goodchild exemplified this using Google Maps, which differs depending on which country you view it from (e.g., depending on what the State views as its legitimate borders). He talked about loads of other stuff, including critical GIS, but these were the points I found most intriguing.

Another way to break up the constant stream of 20-minute project summaries would have been organised fieldtrips around the LA area. However, unlike the landscape ecology conference there is no single time set aside for fieldtrips, and while there are organised trips they’re scheduled throughout the week (simultaneous with sessions). Given such a large conference I guess it would be hard to fit all the sessions into a single week if time were set aside. I didn’t make it to any of the formal fieldtrips, but with Ben Clifford (checkout his new book, The Collaborating Planner?) and Kerry Holden I did manage to find time to hit the beach for some sun. It was a long winter in the UK after all! Now I’m in Auckland it’s warm but stormy; an update about activities here to come in May.

This week I visited one of my former PhD advisors, Prof John Wainwright, at Durham University. We’ve been working on a manuscript together for a while now and as it’s stalled recently we thought it time we met up to re-inject some energy into it. The manuscript is a discussion piece about how agent-based modelling (ABM) can contribute to understanding and explanation in geography. We started talking about the idea in Pittsburgh in 2011 at a conference on the Epistemology of Modeling and Simulation. I searched through this blog to see where I’d mentioned the conference and manuscript before, but to my surprise, before this post I hadn’t.

In our discussion of what we can learn through using ABM, John highlighted the work of Kurt Godel and his incompleteness theorems. Not knowing all that much about that stuff I’ve been ploughing my way through Douglas Hofstadter’s tome ‘Godel, Escher and Bach: An Eternal Golden Braid’ – heavy going in places but very interesting. In particular, his discussion of the concept of recursion has taken my notice, as it’s something I’ve been identifying elsewhere.

The general concept of recursion involved nesting, like Russian dolls, stories within stories (like in Don Quixote) and images within images:

Computer programmers of take advantage of recursion in their code, calling a given procedure from within that same procedure (hence their love of recursive acronyms like PHP [PHP Hypertext Processor]). An example of how this works is in Saura and Martinez-Millan’s modified random clusters method for generating land cover patterns with given properties. I used this method in the simulation model I developed during my PhD and have re-coded the original algorithm for use in NetLogo [available online here]. In the code (below) the grow-cover_cluster procedure is called from within itself, allowing clusters of pixels to ‘grow themselves’.

However, rather than get into the details of the use of recursion in programming, I want to highlight two other ways in which recursion is important in social activity and its simulation.

The first, is in how society (and social phenomena) has a recursive relationship with the people (and their activities) composing it. For example, Anthony Gidden’s theory of structuration argues that the social structures (i.e., rules and resources) that constrain or prompt individuals’ actions are also ultimately the result of those actions. Hence, there is a duality of structure which is:

“the essential recursiveness of social life, as constituted in social practices: structure is both medium and outcome of reproduction of practices. Structure enters simultaneously into the constitution of the agent and social practices, and ‘exists’ in the generating moments of this constitution”. (p.5 Giddens 1979)

Another example comes from Andrew Sayer in his latest book ‘Why Things Matter to People’ which I’m also progressing through currently. One of Sayer’s arguments is that we humans are “evaluative beings: we don’t just think and interact but evaluate things”. For Sayer, these day-to-day evaluations have a recursive relationship with the broader values that individuals hold, values being ‘sedimented’ valuations, “based on repeated particular experiences and valuations of actions, but [which also tend], recursively, to shape subsequent particular valuations of people and their actions”. (p.26 Sayer 2011)

However, while recursion is often used in computer programming and has been suggested as playing a role in different social processes (like those above), its examination in social simulation and ABM has not been so prominent to date. This was a point made by Paul Thagard at the Pittsburgh epistemology conference. Here, it seems, is an opportunity for those seeking to use simulation methods to better understand social patterns and phenomena. For example, in an ABM how do the interactions between individual agents combine to produce structures which in turn influence future interactions between agents?

Second, it seems to me that there are potentially recursive processes surrounding any single simulation model. For if those we simulate should encounter the model in which they are represented (e.g., through participatory evaluation of the model), and if that encounter influences their future actions, do we not then need to account for such interactions between model and modelee (i.e., the person being modelled) in the model itself? This is a point I raised in the chapter I helped John Wainwright and Dr Mark Mulligan re-write for the second edition of their edited book “Environmental Modelling: Finding Simplicity in Complexity”:

“At the outset of this chapter we highlighted the inherent unpredictability of human behaviour and several of the examples we have presented may have done little to persuade you that current models of decision-making can make accurate forecasts about the future. A major reason for this unpredictability is because socio-economic systems are ‘open’ and have a propensity to structural changes in the very relationships that we hope to model. By open, we mean that the systems have flows of mass, energy, information and values into and out of them that may cause changes in political, economic, social and cultural meanings, processes and states. As a result, the behaviour and relationships of components are open to modification by events and phenomena from outside the system of study. This modification can even apply to us as modellers because of what economist George Soros has termed the ‘human uncertainty principle’ (Soros 2003). Soros draws parallels between his principle and the Heisenberg uncertainty principle in quantum mechanics. However, a more appropriate way to think about this problem might be by considering the distinction Ian Hacking makes between the classification of ‘indifferent’ and ‘interactive’ kinds (Hacking, 1999; also see Hoggart et al., 2002). Indifferent kinds – such as trees, rocks, or fish – are not aware that they are being classified by an observer. In contrast humans are ‘interactive kinds’ because they are aware and can respond to how they are being classified (including how modellers classify different kinds of agent behaviour in their models). Whereas indifferent kinds do not modify their behaviour because of their classification, an interactive kind might. This situation has the potential to invalidate a model of interactive kinds before it has even been used. For example, even if a modeller has correctly classified risk-takers vs. risk avoiders initially, a person in the system being modelled may modify their behaviour (e.g., their evaluation of certain risks) on seeing the results of that behaviour in the model. Although the initial structure of the model was appropriate, the model may potentially later lead to its own invalidity!” (p. 304, Millington et al. 2013)

The new edition was just published this week and will continue to be a great resource for teaching at upper levels (I used the first edition in the Systems Modeling and Simulation course I taught at MSU, for example).

More recently, I discussed these ideas about how models interact with their subjects with Peter McBurney, Professor in Informatics here at KCL. Peter has written a great article entitled ‘What are Models For?’, although it’s somewhat hidden away in the proceedings of a conference. In a similar manner to Epstein, Peter lists the various possible uses for simulation models (other than prediction, which is only one of many) and also discusses two uses in more detail – mensatic and epideictic. The former function relates to how models can bring people around a metaphorical table for discussion (e.g., for identifying and potentially deciding about policy trade-offs). The other, epideictic, relates to how ideas and arguments are presented and leads Peter to argue that by representing real world systems in a simulation model can force people to “engage in structured and rigorous thinking about [their problem] domain”.

John and I will be touching on these ideas about the mensatic and epideictic functions of models in our manuscript. However, beyond this discussion, and of relevance here, Peter discusses meta-models. That is, models of models. The purpose here, and continuing from the passage from my book chapter above, is to produce a model (B) of another model (A) to better understand the relationships between Model A and the real intelligent entities inside the domain that Model A represents:

“As with any model, constructing the meta-model M will allow us to explore “What if?” questions, such as alternative policies regarding the release of information arising from model A to the intelligent entities inside domain X. Indeed, we could even explore the consequences of allowing the entities inside X to have access to our meta-model M.” (p.185, McBurney 2012)

Thus, the models are nested with a hope of better understanding the recursive relationship between models and their subjects. Constructing such meta-models will likely not be trivial, but we’re thinking about it. Hopefully the manuscript John and I are working on will help further these ideas, as does writing blog posts like this.

“The model simulates the initial height of the tallest saplings 10 years following gap creation (potentially either advanced regeneration or gap colonizers), and grows them until they are at least 7 m in height when they are passed to FVS for continued simulation. Our approach does not aim to produce a thorough mechanistic model of regeneration dynamics, but rather is one that is sufficiently mechanistically-based to allow us to reliably predict regeneration for trees most likely to recruit to canopy positions from readily-collectable field data.”

In the model we assume that each forest gap contains space for a given number of 7m tall trees. For each of these spaces in a gap, we estimate the probability that it is in one of four states 10 years after harvest:

occupied by a 2m or taller sugar maple tree (SM)

occupied by a 2m or taller ironwood tree (IW)

occupied by a 2m or taller tree of another species (OT)

not occupied by a tree 2m or taller (i.e., empty, ET)

To estimate the probabilities of these states for each of the gap spaces, given different environmental conditions, we use regression modelling for composition data:

“The gap-level probability for each of the four gap-space states (i.e., composition probabilities) is estimated by a regression model for composition data (Aitchison, 1982 and Aitchison, 1986). Our raw composition data are a vector for each of our empirical gaps specifying the proportion of all saplings with height >2 m that were sugar maple, ironwood, or other species (i.e., SM, IW, and OT). If the total number of trees with height >2 m is denoted by t, the proportion of empty spaces (ET) equals zero if t > n, otherwise ET = (n − t)/n. These raw composition data provide information on the ratios of the components (i.e., gap-space states). The use of standard statistical methods with raw composition data can lead to spurious correlation effects, in part due to the absence of an interpretable covariance structure (Aitchison, 1986). However, transforming composition data, for example by taking logarithms of ratios (log-ratios), enables a mapping of the data onto the whole of real space and the use of standard unconstrained multivariate analyses (Aitchison and Egozcue, 2005). We transformed our composition data with a centred log-ratio transform using the ‘aComp’ scale in the ‘compositions’ package (van den Boogaart and Tolosana-Delgado, 2008) in R (R Development Core Team, 2009). These transformed data were then ready for use in a standard multivariate regression model. A centred log-ratio transform is appropriate in our case as our composition data are proportions (not amounts) and the difference between components is relative (not absolute). The ‘aComp’ transformation uses the centred log-ratio scalar product (Aitchison, 2001) and worked examples of the transformation computation can be found in Tolosana-Delgado et al. (2005).”

One of the things I’d like to highlight here is that the R script I wrote to do this modelling is available online as supplementary material to the paper. You can view the R script here and the data we ran it for here.

If you look at the R script you can see that for each gap, proportions of gap-spaces in the four states predicted by the regression model are interpreted as the probability that gap-space is in the corresponding state. With these probabilities we predict the state of each gap space by comparing a random value between 0 and 1 to the cumulative probabilities for each state estimated for the gap. Table 1 in the paper shows an example of this.

With this model setup we ran the model for scenarios of different soil conditions, deer densities, canopy openness and Ironwood basal area (the environmental factors in the model that influence regeneration). The results for these scenarios are shown in the figure below.

Hopefully this gives you an idea about how the model works. The paper has all the details of course, so check that out. If you’d like a copy of the paper(s) or have any questions just get in touch (email or @jamesmillington on twitter)

Millington, J.D.A., Walters, M.B., Matonis, M.S. and Liu, J. (2013) Filling the gap: A compositional gap regeneration model for managed northern hardwood forests Ecological Modelling 253 17–27 doi: 10.1016/j.ecolmodel.2012.12.033Regeneration of trees in canopy gaps created by timber harvest is vital for the sustainability of many managed forests. In northern hardwood forests of the Great Lakes region of North America, regeneration density and composition are highly variable because of multiple drivers that include browsing by herbivores, seed availability, and physical characteristics of forest gaps and stands. The long-term consequences of variability in regeneration for economic productivity and wildlife habitat are uncertain. To better understand and evaluate drivers and long-term consequences of regeneration variability, simulation models that combine statistical models of regeneration with established forest growth and yield models are useful. We present the structure, parameterization, testing and use of a stochastic, regression-based compositional forest gap regeneration model developed with the express purpose of being integrated with the US Forest Service forest growth and yield model ‘Forest Vegetation Simulator’ (FVS) to form an integrated simulation model. The innovative structure of our regeneration model represents only those trees regenerating in gaps with the best chance of subsequently growing into the canopy (i.e., the tallest). Using a multi-model inference (MMI) approach and field data collected from the Upper Peninsula of Michigan we find that ‘habitat type’ (a proxy for soil moisture and nutrients), deer density, canopy openness and basal area of mature ironwood (Ostrya virginiana) in the vicinity of a gap drive regeneration abundance and composition. The best model from our MMI approach indicates that where deer densities are high, ironwood appears to gain a competitive advantage over sugar maple (Acer saccharum) and that habitat type is an important predictor of overall regeneration success. Using sensitivity analyses we show that this regeneration model is sufficiently robust for use with FVS to simulate forest dynamics over long time periods (i.e., 200 years).

Millington, J.D.A., Walters, M.B., Matonis, M.S. and Liu, J. (2013) Modelling for forest management synergies and trade-offs: Northern hardwood tree regeneration, timber and deer Ecological Modelling 248 103–112 doi: 10.1016/j.ecolmodel.2012.09.019In many managed forests, tree regeneration density and composition following timber harvest are highly variable. This variability is due to multiple environmental drivers – including browsing by herbivores such as deer, seed availability and physical characteristics of forest gaps and stands – many of which can be influenced by forest management. Identifying management actions that produce regeneration abundance and composition appropriate for the long-term sustainability of multiple forest values (e.g., timber, wildlife) is a difficult task. However, this task can be aided by simulation tools that improve understanding and enable evaluation of synergies and trade-offs between management actions for different resources. We present a forest tree regeneration, growth, and harvest simulation model developed with the express purpose of assisting managers to evaluate the impacts of timber and deer management on tree regeneration and forest dynamics in northern hardwood forests over long time periods under different scenarios. The model couples regeneration and deer density sub-models developed from empirical data with the Ontario variant of the US Forest Service individual-based forest growth model, Forest Vegetation Simulator. Our error analyses show that model output is robust given uncertainty in the sub-models. We investigate scenarios for timber and deer management actions in northern hardwood stands for 200 years. Results indicate that higher levels of mature ironwood (Ostrya virginiana) removal and lower deer densities significantly increase sugar maple (Acer saccharum) regeneration success rates. Furthermore, our results show that although deer densities have an immediate and consistent negative impact on forest regeneration and timber through time, the non-removal of mature ironwood trees has cumulative negative impacts due to feedbacks on competition between ironwood and sugar maple. These results demonstrate the utility of the simulation model to managers for examining long-term impacts, synergies and trade-offs of multiple forest management actions.