Category Archives: Climate Emergency

On Ecological Models and the Coronavirus

We are caught up now in a coronavirus pandemic with an unknown end point. There is a great deal now available about COVID-19, and I want to concentrate on the models of this pandemic that currently fill our media channels. In particular I want to use the current situation to reflect on the role of mathematical models in helping to solve ecological problems and make predictions of future trends. To oversimplify greatly, the scientific world is aligned along an axis from those supporting simple models to those tied up in complex multifactor models. To make this specific, the simple epidemic model approach provides us with a coronavirus model that has three classes of actors – susceptible, infected, and recovered individuals, and one key parameter, the relative infection rate of one person to another. If you as an infected person pass on the disease to more than one additional person, the pandemic will grow. If you pass the disease on to less than one person (on average), the pandemic will collapse. Social distancing will flip us into the favourable state of declining infections. There is a similar sort of model in ecology for predator-prey interactions, called the Lotka-Volterra model, in which one predator eating one prey species will change the population size of both depending on the rate of killing of the predator and the rate of reproduction of the prey.

So far so good. We can all have an intuitive understanding of such simple models, but of course the critics rise up in horror with the cry that “the devil is in the details”. And indeed this is also a universal truth. All humans are not equally affected by COVID-19. Older people do poorly, young children appear to be little bothered by the virus. All prey individuals in nature are also not equally susceptible to being caught by a predator. Young prey may not run as fast as adults, poorly fed prey in winter may run more slowly than well fed animals. The consequences of this ‘inequality’ is what leads to the need for an increasing investment in scientific research. We can pretend the world is simple and the virus will just “go away”, and a simple view of predation that “larger animals eat smaller animals” could fail to recognize that a small predator might drive a dinosaur species extinct if the small predator eats only the eggs of the prey and avoids the big adults. The world is complicated, and that is what makes it both interesting to many and infuriating to some who demand simplicity.

One of the purposes of a mathematical model is to allow predictions of coming events, and we hear much of this with the COVID-19 models currently in circulation. A simple principle is “all models are wrong’ but this must be matched with the corollary that in general “the simpler the model the more likely it is to provide poor forecasts. But there is a corollary that might be called the “Carl Walters’ Law” that there is some optimal level of complexity for a good result, and too much complexity is also a recipe for poor projections. The difficulty is that we can often only find this optimal point after the fact, so that we learn by doing. This does not sit well with politicians and business-people who demand “PRECISE PRECISION PROMPTLY!” 

These uncertainties reflect on to our current decision making in the coronavirus pandemic, in issues to fight climate change, and in the conservation of threatened species and ecosystems. Our models, our scientific understanding, and our decisions are never perfect or complete, and as we see so clearly with COVID-19 the science in particular can be pushed but cannot be rushed, even when money is not limiting. The combination of planning, judgement and knowledge that we call wisdom may come more slowly than we wish. Meanwhile there are many details that need investigation.  

Adam, D. (2020) Modelling the Pandemic: The simulations driving the world’s response to COVID-19. Nature, 580, 316-318. Doi: 10.1038/d41586-020-01003-6 

Neher, R.A., Dyrdak, R., Druelle, V., Hodcroft, E.B. & Albert, J. (2020) Potential impact of seasonal forcing on a SARS-CoV-2 pandemic. Swiss Medical Weekly 150, w20224. Doi: 10.4414/smw.2020.20224.

Xu, B., Cai, J., He, D., Chowell, G. & Xu, B. (2020) Mechanistic modelling of multiple waves in an influenza epidemic or pandemic. Journal of Theoretical Biology, 486, 110070. Doi: 10.1016/j.jtbi.2019.110070.

On the Rules of Civilization in 2020

We are all citizens of the Earth, so we will start with the single assumption that we wish to protect the Earth for our children and grandchildren, If you do no agree with this assumption we hope you will find life on Mars to be more congenial. If you are content with life on Earth, please observe these rules.

  1. Listen to Greta, in English or Swedish.
  2. For further guidance join 350.org. https://350.org/about/   
  3. If you think the present climate crisis is a minor problem, please read David Wallace-Wells’ book (2019). 
  4. If you are an old person (>45 years) go to (9) below. If you are a young person, keep reading.
  5. The world is a mess and it is not your fault. Do not give up. Become active. Vote. Go to political meetings and ask questions.
  6. Ask about policies at the local, regional, and national level. How is this policy – this war, this new freeway, this new oil pipeline – helping to solve the Earth’s climate crisis.
  7. Do not take business-as-usual for an answer to your questions. Challenge the system to do better.
  8. Work to make voting compulsory. That would begin to ensure democracy. Cut the voting age to 16. Work for proportional representation. You must design a fool-proof world. We have failed to do so.
  9. If you are an older person and at least 45 years old, realize that half or more of your life is over. You have time now to atone for your environmental sins of the past and to work hard to protect the Earth for the young people. Read Stiglitz (2012) or Reich (2018).
  10. Support strong legislation. For many policies we old people should not have a vote. At best to be nice to the elderly, perhaps our vote should count in the reverse proportion of age/100, so a 50 year old would have ½ a vote, and a 75 year old would have ¼ a vote relative to the young people who will inherit the planet.  
  11. Stop supporting the electoral parties who have made the environment a mess. Demand real sustainability, not nonsense policies.
  12. Encourage taxes on wealth. No matter what you may think, you cannot take it with you. Believe it or not, there are countries on Earth with good policies for people and for the environment. Mimic the good. Shame the bad.
  13. If you wish to be radical, vote for policies that provide the highest salaries and lowest taxes to nurses, doctors, teachers, and social workers, and the lowest salaries and highest taxes to CEOs, politicians, lawyers, economists, and TV personalities.
  14. Work for equality in the world, and remember that you as an individual are important, but you are not the most important person in the world. We already know who that is.

Reich, R. (2018). Saving Capitalism: For the Many, Not the Few. 219 pp. ISBN: 978-0-385-35057-0)

Stiglitz, J.E. (2012) ‘The Price of Inequality.’ W.W. Norton and Company: New York. 560 pp. ISBN: 978-0-393-34506-3

Wallace-Wells, David (2019) ‘The Uninhabitable Earth: Life After Warming ‘ Tim Duggan Books: New York. 304 pp. ISBN: 978-0-525-57670-9.