One of the things that I enjoy most about the science I do is collaborating with both field biologists who know their systems inside out, and theoreticians who’s specialist expertise is abstraction and equations. One thing I have learned from these collaborations is that every field or laboratory system exhibits some oddities. The Trinidadian guppy system is the latest, wonderful, system I have begun collaborating on, and it exhibits numerous quirks. One of my favourites is what we affectionately term ‘zombie males’. Because females store sperm, males can sire offspring after death. Such behavior is, of course, not particularly unusual, but this is the first time I have had to ponder whether it is necessary to incorporate such a life history ‘quirk’ in models, and if so, how. These system-specific oddities make me take issue with a quote from a theoretician colleague. It goes something like this: ‘reality is just a special case, and not a particularly interesting one’. Reality is, in fact, very interesting. However, the oddities of each system do generate certain challenges for the modeler. Should they always be incorporated into models?
There is often a certain misunderstanding between field biologists and theoreticians. Part of this arises from the contrasting skill sets they need. The theoretician makes their name through abstraction and identifying general patterns. We know the name Verhulst because his logistic equation allowed ecologists to grasp how density-dependence very simply captured limits to population growth. Lotka and Volterra too have earned their rightful place in the history books of ecology, with their abstract predator-prey and competition equations. This is, in part, because of their insight that species coexistence requires stronger intraspecific competition than interspecific competition. This is about as close as ecologists will ever get to a universal law. It does not mean that the dynamics of all interacting species can be perfectly modeled with the Lotka-Volterra competition equations, but their insight is general. We still have much to learn about species interactions, but Lotka-Volterra’s important insight is here to stay.
The field biologist makes their name in a different way. They don’t rely as heavily on abstraction. Rather they rely on very careful observation and the accurate recording of what they see. Success comes from being able to make careful observations, or conduct elegant experiments, to tease apart specific aspects of their system. For example, the painstaking observational work of Jane Goodall and colleagues on chimpanzees has revealed the remarkable world of our closest living relatives.
Clearly ecology needs both careful field observers, and modelers who can use abstraction to simplify the world. Some of the very greatest biologists of all have done both. Darwin is the prime example.
Sadly I was never blessed with either good fieldwork skills or mathematical abilities. My fieldwork skills are so bad I once went to the wrong island, completely failing to make it to the field site. Shortly after starting my first post-doc working on red deer on Rum, I made my first trip to the field to show off the fieldwork credentials that had helped me get the job. I got to the port of Mallaig on the West coast of Scotland and jumped on the boat to Rum. Except it wasn’t the boat to Rum, it went to Skye instead. I had to phone my new bosses and explain that they’d employed an idiot. Things didn’t get much better in the field. I spent the first day conducting a focal watch on a female that was due to give birth. Except I watched the wrong deer, and missed the key action I was supposed to monitor. After that, my time in the field during that post-doc was primarily spent on St. Kilda helping provide logistics for catching sheep. My primary responsibility was to carry netting and poles around the island.
My first sortie into using maths in ecology was little better. As a good friend and colleagues never ceases to remind me, an integral projection model involves an integral sign. I know that now, but the first time I wrote down an integral projection model, I left that key bit out. Fortunately my modeling skills have improved since then, but I still struggle to transfer my mathematical intuition into a notation that anyone other than I can follow.
In spite of these mathematical and field skill handicaps, I have managed to carve out a niche for myself. I was forced to inhabit the ground between pure theory and field observation. I think I now speak the language of both types of researchers reasonably well, and I have some ideas of the motivations, and frustrations, of both. However, I can still not be classified as one or another, which is why when I’m asked what I do, I often say that ‘I tell theoreticians I’m an empiricist and empiricists that I’m a theoretician, and I hope the two never meet’.
The one thing that I did do was to spend about fifteen years thinking about little else other than how to link ecology and evolution. What I really mean by this is I wanted to understand whether, and how, the fields of population ecology, quantitative genetics, life history evolution and population genetics could be linked. I really enjoyed this challenge, and it meant I read widely, both theory and empiricism. Many readers may have scoffed at the idea of spending fifteen years thinking about one topic, but I really did. I got a little obsessed, and this obsession and the long hours of working on the problem, probably contributed to the break up of my first marriage. When I was thinking about this problem, I’d even quite enjoy waking up in the middle night and lying awake for a couple of hours exploring ideas. There were lots of dead ends of course, but once I realized that very many statistics of interest to life history theorists, population ecologists, quantitative geneticists and population geneticists could all be calculated from integral projection models – and therefore linkages between them explored – I felt I could finally relax a little. Until blog writing became my new obsession that is.
Once I had published my great insight I sat back and waited for the plaudits. I am eternally grateful to the Zoological Society of London, the British Ecological Society and the Oikos society, all who awarded me prizes for aspects of this work. Thank you. But I also received criticisms from some field biologists and some theoreticians. The empirical criticisms were along the lines of why didn’t I include whatever wasn’t in the model, in the model. Why did some models not include: social structure, age structure, genetic structure, males, density-dependence, environmental stochasticity, ice-cream sales in Madrid, house prices in Toulouse or the scoring record of Fernando Torres. With my beloved collaborators, I spent a little while extending models to show how some of these things could be included, although Fernando Torres’ performance in front of goal seems to explain little of anything. But that led to criticism from the theoreticians: your models are too complex to be useful. Surely here is about the right place to quote the following that is attributable to Einstein: ‘Everything should be made as simple as possible, but no simpler’. And this, finally, takes me to the crux of this blog.
In the approach I used to show how statistics of interest to researchers in different fields are linked, I simply needed to track the dynamics of a distribution of a phenotypic character. The model did not need to include age-structure, or sex-structure, or genetic structure, or density-dependence, or environmental stochasticity, or random drift. The model did need four functions describing survival, reproduction, development and inheritance. The model I developed was sufficient to do the job I wanted it to do. Adding anything further into the model would have complicated it, presumably making an already fairly impenetrable paper even less accessible. This does not mean that factors not included in the model are unimportant in determining the dynamics of the population the model was parameterised for. It simply means they were not needed to illustrate the point I wished to make. This is something that is sometimes lost on non-modellers. A model exploring factors influencing the dynamics of sex ratio variation, for example, does not necessarily need to include environmental stochasticity, even if environmental stochasticity is present in the system being caricatured with the model. Its inclusion would complicate the model, but would not impact general conclusions.
My good friend, collaborator and fellow editor of Journal of Animal Ecology, Jean-Michel Gaillard, shares a similar view, but we differ a little in our desires concerning model complexity. We have recently been having an interesting discussion about the inclusion of age-structure into a model. Jean-Michel believes that age-structure should, in general, be included in all models of ungulate populations because demographic rates vary with age in all ungulate species so far studied. You can see his Blog on this topic on this site next week. I believe that unless there is a strong justification for its inclusion, age-structure should be left out of models. My understanding of Jean-Michel’s argument is that because we know age-structure variation in demographic rates is ubiquitous, it should therefore be incorporated into models. But we know that environmental stochasticity, density-dependence, sex-differences, and inbreeding are also ubiquitous across all studies of ungulates. So is age-structure different from these? Shouldn’t these factors and processes all be included too? I agree with Jean-Michel that age variation in demographic rates is ubiquitous in ungulates, and in many other groups too. But I disagree that this means age-structure needs to be incorporated into all models. I believe that if we were to adopt a philosophy that all factors known to be important in a group of animals must be included in all models of those species, we would never make any general progress. Abstraction is a necessity of any modelling exercise. Lotka, Volterra and Vehaulst would never have written down their models without such abstraction.
So why would I rather leave age-structure out of models if it is not necessary to make a point? Age-structure can be included in the types of model I have spent the last few years or my life playing with. But the way it has been incorporated substantially inflates the number of parameters in the model, thus complicating it considerably. This means analysing the model – even using purely numerical perturbations – becomes much harder. As the number of parameters increases, it becomes harder to understand why the model gives the answers it does. This does not mean that age-structure – or any other process – should never be included in models. Instead a decision needs to be made at the outset of a modelling exercise as to which factors and processes are absolutely necessary, and which can be ignored. For some questions models will need to be complicated, but for others, not. Arguing that something is ubiquitous is not a valid justification for its inclusion in a model.
Jean-Michel and I agree that there are many reasons why people construct models. Sometimes they want an accurate representation of a particular system they are studying. They may not care whether they understand why or how the model mimics the system well, just that it does. I’d certainly settle for a model of the stock market that works like this! At the other end of the spectrum, someone might wish to construct a model that gives an approximate idea of how a system in an unstudied state might behave – for example, under what circumstances might climate change destabilize species interactions? In this case, understanding how climate influences competitive interactions between species within a model will presumably be crucial. Before starting to model, it is critical to work out why you are building a model, and how you will analyse it. There is no point in modelling just because you can. All models should be useful, but this does not mean they need to mimic the real world perfectly. I’d hate to have a complex model I don’t understand, along with the real world that continues to flummox me.
One of the most exciting innovations in ecology and evolution in recent years has been the rate of increase in integration of field data and models. The integration has benefited both theoreticians and field biologists. There is a still some tension between some theoreticians and some field biologists, but this tension should evaporate as more theoreticians collaborate with empiricists and vice versa. Theoreticians need to remember that many field biologists will have a detailed understanding of their system, and will want some explanation of why a specific process or factor does not need to be included in a model, and empiricists should remember that abstraction is central to the endeavour of modelling. Don’t expect a collaborating theoretician to want to include everything you have observed in their model.
Meanwhile, though, what to do about all those peculiarities of each and every system? Those wonders of the natural world? Those zombie fish? If I model the dynamics of only the female component of the guppy population, I can ignore the zombie males. If I model the ESS life history strategy in predator-free and predator-rich environments, I can probably ignore them too. If I want to model short-term evolutionary change, or the evolution of mate choice, perhaps I can’t. Who knows, zombie fish may do so well because females guppies might like to mate with older males who’s lives are coming to end. Bugger. Perhaps I need age-structure in the guppy model after all.
But in the short-term, given the look I’ve just got from my wife, I suspect it is time to take a break from blogging. Don’t say I didn’t learn anything from those 15 obsessive years.
Senior Editor, Journal of Animal Ecology