Alan Perelson’s 70th Birthday Conference: Viral Dynamics: Past, Present and Future

Sankalp and I have just returned from a weekend trip to Santa Fe for the Viral Dynamics conference in honour of Alan Perelson’s 70th birthday.

The conference itself was very high quality – excellent talks throughout from some extremely eminent people in virus research. I particularly appreciated David Ho’s opening talk and Alan Perelson’s closing keynote; David’s talk on HIV dynamics reminding me just how good Alan and Avidan Neumann’s modelling contribution was: it wasn’t about developing big complex models, or doing very fancy mathematics; it was about doing the right simple model to make the most use of the data. Alan’s talk focussed on his earlier work in theoretical immunology – very many interesting examples showing how much you can learn by thinking in mathematical/computational ways.

The best part of the conference was meeting up with people – whether old friends from the short time I spent in LANL (Alan, Jack) and my PhD days (Ruy, Sebastian) – or brilliant people I hadn’t met before with whom I had some very stimulating conversations.

What was also evident was the warmth felt by so many people towards Alan. I only spent 3 months in the lab in 1994 – in between my degree and PhD – and went back for another month in the summer of 1995 – and yet when Ruy Ribeiro sent the invitation I immediately felt that this was a meeting I couldn’t miss. Many people there had collaborated with Alan for many years. And while Alan’s contribution to science is enormous, the plaque that the organizers made for him was for friendship, collaboration and mentorship, with a network graph of his collaborative research outputs. In this, Alan is a positive example for us all.

We went with a poster:


which was Sankalp’s first conference poster presentation! I thought that this would be a good opportunity for him; although Sankalp’s model is about bacteriophage in the context of AMR, while the conference focussed on human disease viruses, the conference attendees mainly worked in mathematical models of virus dynamics. This meant that Sankalp was among people who understood what he was doing and why he was doing it, speaking the same language. Sankalp was busy – he had people speaking with him for the full 2 hours of the poster session – and we received many interesting ideas and suggestions from these conversations.

Speaking at Biolog Phenotype Microarray Conference

Today I will be presenting at the Biolog Phenotype Microarrays conference at the University of Florence. Yesterday’s meeting was very good, with many interesting talks on different applications of Biolog arrays, including use of different software (mainly ductApe and opm). A highlight was meeting one of the lead developers of opm, Lea Vaas.

My talk will combine some of Matthias’s results on fitting models to Biolog data, with a demonstration of Mike’s HiPerFit software. Matthias’s work is nearly published (just waiting for a referee to agree to the last minor edit) and Mike’s software is nearly finished (a few bugs to iron out and a few guides to write) so it is all very exciting. The live demo depends on everything working just fine! It worked last night in my hotel room…

The Swing Game: a real life model for the Evolution of Cooperation

I am currently attending the very enjoyable Modelling Biological Evolution 2015 at the University of Leicester, where I have, of course, enjoyed catching up with old friends, meeting some great new people, and hearing some inspirational talks. This has led me to revisit an idea for a model for evolution of cooperation that I came up with last year. If I am being honest, I am unlikely to have the time to analyze these ideas. So I am putting them in this blog post in the hope that someone somewhere might be interested in doing the maths/simulations. If you are interested, please be in touch! It starts with a true story from.

Last year I was in a park with my two young children (aged 3 and 1) and some friends of the 3-year-old. Our 3-year-old and another child (also 3) started to argue about who was going to push the baby swing containing the 1-year-old. I discussed the situation with the children and the other child came up with the following solution: one child pushes the swing; the child who is not pushing the swing can at any point say “swap” and then they swap; repeat until they’ve had enough or we leave the park. At first I was dubious about what whether this would work – but what happened blew me away! The other child had the first time. My daughter swiftly said “swap” so she stared her turn only shortly after the other child called “swap” again. I said to my daugher: “maybe if you let X have a long turn, he might then give you a long turn too” and this is exactly what happened.

As we left the park I realized that this might be a very interesting game theory model! It has the possibility for cooperation, defection, reward, punishment, and then I realized a lot more (as I will explain below). It is also interesting for operation in continuous time rather than discrete episodes. I am not aware of other continuous time models although I would expect that they must exist. So here is my thinking:

1. The game is played for some time T (more on that later). The children take turns to push the swing and have a pay-off that is some function of the time spent pushing the swing (again, more below). The bystander can call swap – so the “stategy” lies with the bystander that will be some function to determine when they call “swap”.

2. It is immediately apparent that a linear pay-off for swing push time t won’t work (each child sums the time spent pushing the swing) as this could lead to a strategy of calling “swap” after an infinitessimaly small time interval. This might be fixed in one of a number of ways  – two spring to mind: (i) Having a penalty associated with a “swap” since there is time lost to the game (so total possible pay-off to both players is reduced) (ii) Having a non-linear pay-off for swing time t, for example a sigmoid function (t^2/(1+t^2)) or such-like. This is probably more interesting. The key question is what constraints on pay-offs are needed so as to obtain interesting playing strategies.

3. The game could be constructed with either deterministic or stochastic strategies. Stochastic strategy is probably going to be more interesting.

4. What I would find particularly interesting is to model how the children’s knowledge of T affects the extent to which they cooperate. For example, the children might know T with absolute certainty, or T might be stochastic, with children knowing some partial information about T. Suppose, for example, T has some distribution with a certain mean and variance, and the children have this information. To what extent does knowledge of the variance impact on cooperation? This is interesting because it relates to reliability of parental information. Imagine a parent who says “you have 10 minutes left” and the child knows that this means 10 with variance 1, as opposed to a parent who says “you have 10 minutes left” and the child knows that the variance is very high (say 5): does this impact on cooperation? Similarly skew of distribution (right-skewed – so 10 minutes means at least 10 minutes vs symmetrical – so 10 minutes could mean shorter).

5. There is also the question of asymmetrical knowledge of T. This could be, for example, two children who have better or less capacity to estimate T (for example an older child playing with a younger child). Would asymmetrical knowledge lead to “cheating” strategies being admitted? Anyway, these are just some of my ideas. Over to you!

Modelling Biological Evolution 2013: Conference Highlights

Over the last couple of days I have been attending the Modelling Biological Evolution conference at the University of Leicester organized by Andrew Morozov.

For me, the most interesting theme to have emerged is work on evolutionary branching: conditions under which polymorphisms (or even speciation) might arise. These were all talked about in the context of mathematical models (ODE-type formulations based on generalized Lotka-Volterra systems). The best talk I attended was by Andrew White (Heriot Watt University). He described various system of parasite-host co-evolution, the most interesting of which demonstrated increases in diversity: a new host could emerge that was resistant to current parasites, following which a new parasite could emerge that would infect that host. He rather nicely linked that work to experimental work from Mike Brockhurst (University of York) on phage infections of bacteria showing similar patterns. The results could of course be interpreted at a speciation level, or, probably more fairly, at the level of molecular diversification (e.g. of MHC types in an immune system). What I really appreciated about this resut is that it spoke to the idea that increased diversity can result through a positive feedback mechanism: diversification leads to new niches and thus the potential for further diversification. I have thought for some time that this is the most important mechanism that drives diversification / speciation in natural systems and it was nice to see an example of the mechanism in action.

The other talk I particularly appreciated on the subject was by Claus Rueffler (University of Vienna). He spoke about a result on complexity and diversity in Doebeli and Ispolatov 2010 that also contains this feedback idea. This paper relies on a specific model to obtain its result on conditions for evolutionary branching. Rueffler demonstrated general conditions under which branching might take place that depend only upon the properties of the Hessian matrix associated with key parameters in model space. The important point is that the analysis is model-independent: it only considers the properties of the model forms needed to obtain the result.

Similar ideas were presented by Eva Kisdi (University of Helsinki). She focussed on models that include evolutionary trade-offs (e.g. between virulence and transmissibility): her point was that instead of choosing a function and analyzing its consequences, one could consider desired properties of a model (e.g. branching or limit cycles) and then use “critical function analysis” to derive conditions for possible trade-off functions that would admit the desired behaviour. Eva made the important point that many models make ad hoc choices of functions and thus lead to ad hoc results of little predictive value.

I think Eva’s point really touched on some of the weaknesses that emerged in many of the talks that I attended: there was a great deal of theory (some of which was very good), but very little interface with real biological data. I find this somewhat surprising: modelling in ecology and evolution has been around for very much longer that modelling in say molecular biology (where I currently work), and yet seems to be less mature. I think that the field would really benefit from far greater interaction between theoretical and experimental researchers. Ideally, models should be looking to generate empirically falsifiable hypotheses.

Perhaps the most entertaining talks were given by Nadav Shnerb and David Kessler (both Bar Ilan University). Nadav’s first talk was about power-law-like distributions observed in genus/species distributions. Core to his work is Stephen Hubbell’s neutral theory of biodiversity.
Nadav showed that distributions of number of species within genera could be explained by a neutral model for radiation and the genus and species level coupled with extinction. Nadav’s most important point was that if you wish to make an argument that a certain observed trait is adaptive, then you have to rule out the null hypothesis that it could arise neutrally through mutation/drift. I hope that is something we addressed with regards global regulators in gene regulatory networks in Jenkins and Stekel 2010. David spoke about biodiversity distributions also, showing that adaptive forces could explain biodiversity data (they are generally poor at this due to competitive exclusion that occurs in many models) if the fitness trait is allowed a continuous rather than discrete distribution.

Nadav’s second talk was about first names of babies. This was very interesting – especially as I have a young family (and a daughter with a very old-fashioned name). He looked at the error distribution (easily shown to be binomial-like noise proportional to square root of mean) that is superimposed on a deterministic increase and decrease in popularity of a name over a 60 year period. His thesis was that the error distribution due to external events would be proportional to mean (not root mean), and, as only 5 names in his data set (Norwegian names in ~ 20th Century) did not fit binomial noise, he ruled out external events (e.g. celebrity) as being a major driver. The problem I have with this is that he didn’t rule out external events in the deterministic part of the data (e.g. initiating a rise in popularity of a name that then follows the deterministic feedback law he proposed).

Invitation to Contribute a Talk to Modelling Biological Evolution 2013: Recent Progress, Current Challenges and Future Directions

The International Conference Modelling Biological Evolution 2013: Recent Progress, Current Challenges and Future Directions will be held at the University of Leicester on May 1-3, 2013. The topics sound very interesting, and are:

  • Evolutionary Epidemiology of Infectious Disease
  • Models of Somatic Evolution of Cancer
  • Evolutionary Population Ecology
  • Models in Behavioural Ecology and Sociobiology
  • Solving Social Dilemmas
  • Models of Evolution of Language
  • Population and Quantitative Genetics

I have been invited to contribute a talk and will give a talk with the following title and abstract:


Adaptation for protein synthesis efficiency in natural and artificial gene regulatory networks


Dorota Herman, Dafyd Jenkins, Chris Thomas and Dov Stekel


In this talk, we will summarize work on the use of mathematical and computer models to explore the evolution and adaptation of gene regulatory network architectures.

First, we will look at a natural system, the korAB operon in RK2 plasmids, which is a beautiful natural example of a negatively and cooperatively self-regulating operon. We use a biologically grounded mechanistic multi-scale stochastic model to compare four hypotheses for the action of the regulatory mechanism: increased robustness to extrinsic factors, decreased protein fluctuations, faster response-time of the operon and reduced host burden through improved efficiency of protein production. We find that the strongest impact of all elements of the regulatory architecture is on improving the efficiency of protein synthesis by reduction in the number of mRNA molecules needed to be produced, leading to a greater than ten-fold reduction in host energy required to express these plasmid proteins.

Next, we summarize results from two different artificial gene regulatory network models that are free to evolve: a fine-grained model that allows detailed molecular interactions, and a coarse-grained model that allows rapid evolution of many generations. A similar theme emerges in these models too: the control of cell energy and resources is a major driver of gene network topology and function. This is demonstrated in the fine-grained model with the emergence of biologically realistic mRNA and protein turnover rates that optimize energy usage and cell division time, and the evolution of basic repressor activities, and in the coarse-grained model by emergence of global regulators keeping all cellular systems under negative control.o


So far as I am aware, the conference organizers have extended their registration deadline, so places are still available for the next few days.

Westminster Food and Nutrition Forum Keynote Seminar

Yesterday I attended the Westminster Food and Nutrition Forum Keynote Seminar: meeting the challenges of food security: implementing the Green Food Project, innovation, biodiversity and land use. The forum was extremely interesting and well attended, and pointed to a wide range of potential research opportunities within my lab and school. In this post I will summarize the talks to the best of my notes. We will get transcripts and slides in due course, but I would rather get my thoughts into this blog in a timely fashion. Very brief summaries of the talks appear in black and I have added some follow-up thoughts, often relevant to my place of work, in blue.

The first session was chaired by Lord Cameron of Dillington, who is clearly passionate and committed to the Food Security cause. He introduced the food security agenda by stating that we could focus on national or local food security issues (different speakers did each), but wanted a global background. the main issues are:

  • Current global population is 7B people predicted to raise to 9N by 2050 but there is a deficit in food production growth relative to population growth.
  • Moreover, world GDP is set to raise by 400%, leading to likely changes in diet – less arable and more livestock results in extra draw on resources.
  • Climate change is likely to have two impacts: drought in major continents; loss of good agricultural land close to the sea level.
  • Pressure on world water supplies: 1.5M pa preventable deaths due to lack of sanitized water; unsustainable aquifer use, especially in South Asia; but only 2% of rainfall is used for food in Africa (vis 40% in SE Asia or 70% in California) leading to good opportunities in Africa.

The talks in the session followed very well from this introduction, addressing many of the issues raised in greater detail.

Michael Winter focussed on the UK agenda, drawing on the National Ecosystem Assessment (2011). His main focus was a plea for strong cross-disciplinarity between ecosystems and agriculture. He described how “ecosystem services” is the language of nature conservationists (with one set of agendas) and “food security” is the language of agriculturalists (with a different set of agendas), but actually the need for Green food and sustainable agriculture needs a broader vision that encompasses both.

Given Michael’s influence in Defra, I think that there is a good opportunity within my division (Agricultural and Environmental Sciences) and the University of Nottingham’s School of Biosciences as a whole to engage with this agenda in our research strategy.

John Ingram, who is NERC‘s food security leader, started by stating that agriculture is the largest driver of land-cover change, and with particular risks in rate of biodiversity loss, nitrogen cycle and climate change. He referred to the Feed the Future Report (2012). His main point was that the biggest impact could be through reduction of food waste. This occurs at all levels of the supply chain, but is difficult to measure because of many complicating factors. However, as an approximation, 4600 kcal of food are grown per person per day, but only 2000 kcal of food pppd  are consumed. Losses are at every level: harvest losses, animal feed (for meat/milk production), distribution losses and consumer waste. In the UK/US most losses are at the home / municipal level, whereas in the developing world, most losses are on farm. Thus he concludes that a major research priority is not in the sciences, but in social research, to identify public perceptions, attitudes etc that lead to the high level of food waste.

This last point is a clear research opportunity. What is interesting is that, with a few exceptions (see Tara Garnett and her analysis below), most GFS awareness and research activity is taking place within science departments (for example the one I work in), but we actually need people who work in sociology and policy more actively engaged in this research. The divides between these sorts of departments in most traditional universities is very large, but if we can cross these divides, then we have an opportunity for very high impact cross-disciplinary research.

Chris Fawcett from AMEC focussed his talk on global water security. Water stress impacts on 40% of the global population. The key challenge is to balance the needs for water between the competing demands of domestic, industrial and agricultural use, the latter using 70% of blue water globally. He referred to statistics on,  that 1kg of beef requires 15400 litres of water, whereas 1kg of wheat requires 1800 litres of water. From the UK’s perspective, while we have sufficient water resources for our domestic use, we are the world’s 5th largest importer of “virtual water”, with 62% of our water footprint being from imported goods.

Chris mentioned a number of technology-based solutions, including catchment water stewardship, balance distribution (transfers and storage), re-use of treated waste water, urban storm water, surface-drip irrigation and drought- and salt- tolerant crops.

We have no water expertise within AES, and maybe this is a gap both from a research and teaching perspective, given that AMEC and other such institutions are potential employers for our graduates. 

Yuelai Lu spoke for the UK-China Sustainable Agriculture Innovation Network, SAIN. He spoke about the situation in China, which has seen continuous growth in grain production and especially livestock production over the last 30 years. He stated that he did not foresee a food security risk in China over the next 20/30 years (!), following which the Chinese population size would stabilize, and saw growth in that period coming through intensification. The challenges facing China are with an ageing labour force, loss of farmland, resource use inefficiency (especially N and P), greenhouse gas emissions and “institutional constraints”. 

The next talk, from Phil Bloomer at Oxfam, provided a completely different perspective. He spoke about food security in terms of unsustainable inequality. His first point was that increased food prices has led to increased land prices, which in turn has led to an unprecedented scale of international land purchase. This has tended to be in countries with the least governance, and has led to large-scale dispossession leading to poverty and food insecurity. He stressed the need for global policy change from consultation of local people to consent of local people.

In terms of impact of climate change, he said that there was need for financial assistance.

Impact of biofuels is on food price stability and climate change, the latter because biofuels have a polluting impact due to food displacement. He believes that biofuel cut-backs are essential, including a complete phase-out of biofuels that compete with food.

He also mentioned the importance of small-holder farms. 2B people depend on small-holdings, with a labour of 500M people, mostly women. He spoke of the efficiency of small-holdings (presumably in terms of yield per hectare?) because of the high level of labour required.

The last talk in the first session was from Nick von Westenholz of the Crop Protection Association. Nick’s main point was about the importance of policy makers taking an evidence-based approach to decisions. This is particularly the case with GM, where the technologies are not even being investigated due to non-evidence-based concerns.

The second session was chaired by Barry Gardiner, MP. His emotive opening statement focussed on the mix of food, energy and water security and its impact on global justice.

James Marsden from Natural England spoke mainly about biodiversity loss. He referred to the Natural Environment White Paper (2011) and the EU target to halt biodiversity loss by 2020. He focussed on two measures: that at least 50% of SSSIs should be in favourable condition (currently 37.6%); and that farmland birds should recover, this being an important measure of ecosystem health. On the latter, he collated data from RSPB, BTO, JNCC and Defra showing that while numbers of generalist birds had remained stable, the number of specialist birds is in steep decline.

This did lead me to wonder what mathematical / computer modelling has been carried out on farm bird populations in the UK or elsewhere. This is an area where model predictions could clearly be beneficial, impacting on policy and practice. Something to investigate.

Andrea Graham from the NFU spoke briefly about NFU programmes and industry-led initiatives. Her most interesting point was the use of the term “knowledge exchange” instead of “knowledge transfer”, which I think best reflect the sorts of relationships that we as university academics with an interest in agriculture and environment would want to develop with the farming community and industry.

Daniel Crossley of the Food Ethics Council spoke briefly about the major challenges of hunger and unsustainable production methods. He stated that there was progress in shifting the discourse away from greater global productivity and towards other factors, including  demand (consumption), food waste and issues of profit as the sole motive in affordability, justice, access to foods and food fairness.

Jim Kirke from British American Tobacco has some interestingly different perspectives. He stressed the need for robust ecosystem services supported by resilient biodiversity to meet the demands of society, and emphasised that agriculture is not just about food but also other products. Specifically, he stated that this requires effective stewardship, and, somewhat controversially in my view, said that subsistence farmers do not have the resources to carry this out. He also stated that cropping and resource management depends on farmers’ livelihoods, and that this is an important factor in prioritisation. He stated that we need improvements in the way that demand volume and market prices can feed into cropping decisions in order to avoid chronic waste.

Tim Benton, who is RCUK’s GFS champion, focussed his talk on the importance of spatial scales beyond the farm. Sustainability is a global issue: the ecology of a field does not just depend on the management of the field, but on a larger scale encompassing landscape, national and global scales.

An important point he made is that for a set level of global demand, a reduction of yield in one location would lead to increased yield in another location, and so no net environmental benefit. Thus he criticised organic farming, stating that increased sustainability could be achieved either through maintaining yields while increasing environmental benefits, or by increasing yields for level environmental benefits. Reduction in yield for increased environmental benefit is not sustainable, in his view.

It may be politically unwise to disagree too strongly with RCUK’s GFS champion, but I do not agree with his last point. This analysis is predicated on sustainability given a certain level of global demand. There could be a role for reducing yield while increasing environmental benefits if this were coupled with decreased demand, for example by reducing food waste (as per John Ingram’s talk), a shift from consumption of animal-based to plant-based foods, or a concerted effort to reduce human population growth.

Tara Garnett, of the Food Climate Research Network, gave what in my view was the most impressive talk of the day. It surprised me, as a scientist, to take this view, given that Tara is carrying out social research, but actually, and importantly, her analysis demonstrated with utter clarity that GFS is as much a social issue as a scientific one, and thus that the solutions are going to be as much social as scientific. Moreover, Tara’s analysis provided a conceptual framework into which all of the previous talks could be integrated.

Tara started by emphasising that food production and consumption are at the centre of multiple societal concerns, including economics, health, environment and ethics. She then stated that there were three broad approaches to food sustainability, which could be analysed in terms of several concerns, including food and environmental sustainability, animal welfare and nutrition, as well as key stakeholders and values. She covered a great deal of material at quite a rapid rate, so my synopsis is patchy at best – although I can see that she has published this analysis here. The three approaches are:

  1. The supply-side challenge (efficiency): this is a macro-level, and the key stakeholders tend to be governments, corporations, scientists etc. The focus is on delivering more food, or greater environmental sustainability, using better technologies. Food security is met through increased supply. Animal welfare is considered from a scientific perspective. Nutritional concerns are about making ‘inevitable’ consumption more healthy.
  2. The demand-side challenge: needing more sustainable food. The key stakeholders tend to be NGOs. Much of the focus is targetted at the high impacts of meat and dairy products, and so the need to eat a more sustainable diet. Nutritional benefits of meat and dairy are often ignored. Animal welfare focusses on a more romantic view: “cows belong in fields”.
  3. The equity challenge: not so much on production and consumption, but on the inequity of power structures. The spectrum of stakeholders is broader, and the focus of food security is on socio-economic systems and small-holders. Sustainability is assumed to be an outcome of greater equity, but there is little engagement with environmental metrics or animal welfare.

People strongly aligned with one of these positions disagree with each other because they have different views on how the world works, what things might be possible as opposed to be inevitable, and what things might be desirable.

Tara’s conclusion is that each perspective alone is too simplistic, and that the challenge of GFS needs all three perspectives. Ultimately, GFS is not just a scientific or technical problem, but values matter, and we need to be open to different values.

As I said above, I particularly enjoyed Tara’s analysis, and again it highlights the importance of us scientists building appropriate research collaboration with social researchers. What is also interesting about Tara’s analysis is that each of the challenges is progressively harder to meet. With regards the supply-side challenge, we are actually very good at using science and technology to improve outcomes. With regards the demand-side challenge, this is much harder, but there are precedents of success in large-scale behavioural change. Recycling is an excellent example, where, combined with appropriate infrastructure, most people and businesses are happy to dispose of recyclable waste in more sustainable ways. The equity challenge is much the hardest of the three, and something that as a human society we have not yet met.

The last talk of the day was a brief update from Karen Morgan of Defra on implementing the Green Food Project. Karen emphasised the importance of working in partnership with key organizations.