Emergence in ant colonies

Go to the ant, you sluggard;
    consider its ways and be wise!
It has no commander,
    no overseer or ruler,
yet it stores its provisions in summer

and gathers its food at harvest.

    Proverbs 6:6-8

Ant colonies are amazing. It is incredible what they can achieve. I love the video below. It highlights how complex structures and functions emerge in an ant colony even though there is no individual directing the whole operation.

Ant colonies are often cited as an example of emergence, including how complexity can emerge from simple rules. Ant colonies feature in Godel, Escher, Bach by Douglas Hofstadter, Emergence: from chaos to order by John Holland, and Emergence: The Connected Lives of Ants, Brains, Cities, and Software by Steven Johnson.

Important steps towards describing and understanding a system with emergent properties include identifying how to break down the system into single components and determining how those components interact with one another.

As described in the video the colony is composed of several distinct classes (castes) of ant: soldiers, excavators, foragers, garbage collectors, and gardeners. Each ant has a very limited repertoire of methods to interact with other ants and their environment. Ants have poor hearing and sight. They communicate with a few signals involving touch, but mostly communicate by producing trails of distinct chemicals (pheromones).  Each organic molecule is identified with a specific message such as follow this trail, detection of food, presence of an enemy, or danger.

For an ant colony the components are simple and the interactions between the parts are simple. Nevertheless, complex structures such as bridges and tree houses emerge. There is no chief engineer directing the construction of these structures or a blueprint drawn up by an architect. The queen is not a dictator mandating that the colony must last for her lifetime, which covers many generations of worker ants.

Ant colonies have characteristic properties of emergent systems. The system has properties that the individual components do not. Complex structures can emerge from a system with simple components and interactions. The properties that emerge are hard to predict a priori. That is if one only knew about the properties of individual ants and how they interact, and not the properties of the colony, it would be hard to predict that they could achieve what they do.

Universality is highlighted in a nice review article, The principles of collective animal behaviour by D.J.T Sumpter. Some of the abstract is below.

I argue that the key to understanding collective behaviour lies in identifying the principles of the behavioural algorithms followed by individual animals and of how information flows between the animals. These principles, such as positive feedback, response thresholds and individual integrity, are repeatedly observed in very different animal societies. The future of collective behaviour research lies in classifying these principles, establishing the properties they produce at a group level and asking why they have evolved in so many different and distinct natural systems.

Who should get to attend elite universities in the USA?

Equitable access to good education is a desirable goal. Yet it rarely happens and debate about how to achieve it can be diluted by focusing on access to elite institutions and on "culture war" rhetoric.

This week The Economist had a leader (editorial) about admission policies for universities in the USA. Below I reproduce some of the leader, highlighting some points I found poignant.

A diversity of backgrounds in elite institutions is a desirable goal. In pursuing it, though, how much violence should be done to other liberal principles—fairness, meritocracy, the treatment of people as individuals and not avatars for their group identities? At present, the size of racial preferences is large and hard to defend. The child of two college-educated Nigerian immigrants probably has more advantages in life than the child of an Asian taxi driver or a white child born into Appalachian poverty. Such backgrounds all add to diversity. But, under the current regime, the first is heavily more favoured than the others.

Racial preferences are not, however, the most galling thing about the ultra-selective universities that anoint America’s elite. ...A startling 43% of white students admitted to Harvard enjoy some kind of non-academic admissions preference: being an athlete, the child of an alumnus, or a member of the dean’s list of special applicants (such as the offspring of powerful people or big donors). 

A cynic could argue that racial balancing works as a virtue-signalling veneer atop a grotesquely unfair system. A study published in 2017 found that most of Harvard’s undergraduates hailed from families in the top 10% of the income distribution. Princeton had more students from the top 1% than the bottom 60%. When this is the case, it seems unfair that it is often minority students—not the trust-funders—who have their credentials questioned. University presidents and administrators who preen about all their diverse classes might look at how Britain—a country of kings, queens, knights and lords—has fostered a university system that is less riven with ancestral privilege.

...Legacy admissions should be ended. Colleges claiming that alumni donations would wither without them should look to Caltech, MIT and Johns Hopkins— ....[who all] ditched the practice..

In some ways, the question of who gets into a handful of elite universities is a distraction from the deeper causes of social immobility in America. Schooling in poorer neighbourhoods was dismal even before covid-19. The long school closures demanded by teachers’ unions wiped out two decades of progress in test scores for nine-year-olds, with hard-up, black and Hispanic children worst affected. Efforts to help the needy should start before birth and be sustained throughout childhood. Nothing the Supreme Court says about the consideration of race in college admissions will affect the more basic problem, that too few Americans from poorer families are sufficiently well-nurtured or well-taught to be ready to apply to college. However the court rules, that is a debate America needs to have.

On a related note, Malcolm Gladwell has a fascinating podcast episode, Outliers, Revisited  that brings out some of the issues including, how privileged parents game the system for their children.

Did Turing really "explain" pattern formation?

 Exactly seventy years ago, Alan Turing published a seminal article, in which he proposed a simple reaction-diffusion model for pattern formation in biological systems. The basic idea is that there are two molecules (morphogens) that react with one another chemically and also diffuse through the system.

The potential relevance of the model can be seen by comparing the lower panels below. The left panel is a real fish and the right panel shows the results of a simulation. The figure above is taken from a beautiful review article published a decade ago.

Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation  Shigeru Kondo and Takashi Miura

The authors state that the model is not accepted by many experimental biologists and hope their review will lead to a greater engagement with it. Some of the reasons are related to issues in the philosophy of science and how to model complex systems. What is an explanation? What is the role of simple models for complex systems that ignore so many details?

Kondo and Miura point out the universality of the reaction-diffusion model in the sense that a similar model can be derived where the "molecules" are instead a circuit of cellular signals. Diffusion can be replaced by a relay of signals between cells. Alfred Gierer and  Hans Meinhardt in 1972 showed that all that is required is a network with "a short-range positive feedback [competing] with a long-range negative feedback."

A short video from the Sante Fe Institute also provides a helpful introduction including some simulations.

 

There is another problem with Turing's model that is succinctly described in the opening paragraph a recent PRL. In a system with two molecular species, patterns only form when there is a large difference between the diffusivity of the two molecules. However, this seems unrealistic because one expects the molecules to have comparable diffusivities.

Turing’s Diffusive Threshold in Random Reaction-Diffusion Systems 

Pierre A. Haas and Raymond E. Goldstein 

 In 1952, Turing described the pattern-forming instability that now bears his name [1]: diffusion can destabilize a fixed point of a system of reactions that is stable in well-mixed conditions. Nigh on threescore and ten years on, the contribution of Turing’s mechanism to chemical and biological morphogenesis remains debated, not least because of the diffusive threshold inherent in the mechanism: chemical species in reaction systems are expected to have roughly equal diffusivities, yet Turing instabilities cannot arise at equal diffusivities [2,3]. It remains an open problem to determine the diffusivity difference required for generic systems to undergo this instability, yet this diffusive threshold has been recognized at least since reduced models of the Belousov–Zhabotinsky reaction [4,5] only produced Turing patterns at unphysically large diffusivity differences.

I first became aware of this paper through a commentary by Changbong Hyeon, at the Journal Club for Condensed Matter. It is also helpful because it explains the simple mathematics behind the threshold value of the model parameters for pattern formation.