F Rosa Rubicondior: How Evolution Works - Choas, Catastrophe and Tipping Points

Tuesday 26 March 2024

How Evolution Works - Choas, Catastrophe and Tipping Points

Hyphal mycelium.
credit: Maxim Ohairwe.
Researchers Discover Evolutionary “Tipping Point” in Fungi

An interesting paper has just been published which illustrates how chaos theory and catastrophe theory are related and explain the appearance of 'punctuated equilibrium' in the fossil record. It concerns the small environmental change that can trigger a large phenotypic change in the growth and shape of fungal hyphae.

One of the more annoying things to emerge in evolutionary biology during the last 30 years or so is the idea that 'Punctuated Evolution' (PE) somehow either falsifies or replaces Darwinian evolution as the explanation for biodiversity. Of course, it does neither. The term was invented by Stephen J Gould and Niles Eldredge, to explain the appearance of sudden change in the geological column, where species appear to remain unchanged for prolonged periods of time, then change, in what, with the compression of time in the geological column, looks like instantaneously.

Sadly, the term quickly became entangled with both American nationalism and creationism; the latter because it appears to refute the person whom creationists think is the arch prophet of the 'evil' of evolution - Charles Darwin, the leading figure in creationist demonology - as though the entire body of evolutionary biology hangs on the authority of one 19th century biologist; the former because it appears to have replaced one of the most famous scientific theories with one 'discovered' by Americans, so asserting American pre-eminence in science.
Tell me about 'Punctuated Equilibrium'; who popularized the idea and the arguments for and against it. Punctuated equilibrium is a theory in evolutionary biology that suggests that the tempo of evolution is not constant but rather characterized by periods of relatively rapid change (punctuation) interspersed with prolonged periods of stability (equilibrium). This concept was popularized by paleontologists Niles Eldredge and Stephen Jay Gould in their 1972 paper "Punctuated Equilibria: An Alternative to Phyletic Gradualism."

Arguments for punctuated equilibrium include:
  1. Fossil Record: Eldredge and Gould argued that the fossil record often shows long periods of stasis, where species exhibit little morphological change over millions of years, followed by relatively rapid bursts of evolutionary change when new species appear.
  2. Lack of Transitional Forms: They also pointed out that the fossil record frequently lacks the transitional forms predicted by gradualism, which suggests that evolution may occur in more rapid bursts.
  3. Genetic Mechanisms: Some genetic models also support the idea of punctuated equilibrium, suggesting that small populations undergoing rapid change due to factors like genetic drift and founder effects can lead to rapid speciation.
Arguments against punctuated equilibrium include:
  1. Lack of Evidence: Critics argue that punctuated equilibrium is based more on interpretation of the fossil record rather than direct evidence from genetic or ecological studies.
  2. Sampling Bias: Some scientists suggest that the apparent gaps in the fossil record may be due to incomplete sampling rather than actual periods of stasis.
  3. Mechanistic Explanation: Critics also question the mechanisms underlying punctuated equilibrium, arguing that it may be difficult to explain how rapid evolutionary change occurs in the absence of significant environmental pressures or genetic changes.
Overall, punctuated equilibrium remains a subject of debate within evolutionary biology, with proponents arguing that it provides a more accurate description of patterns of evolution observed in the fossil record, while critics suggest that it may overemphasize the importance of long periods of stasis and rapid bursts of change.
The main argument against PE is that it isn't necessary because it seeks to explain something that doesn't need explaining. It is based on the false assumption that the environmental drivers of evolution change at a constant rate, like the ticking of a clock. In reality, it is the environment which has prolonged periods of equilibrium followed by short bursts of rapid change. PE should apply to the environment, not the organisms within it. Species merely reflect and record the environment's pace of change.

So, the question then is why is the environment subject to the sort of change that triggers rapid change?

And here is where chaos and catastrophe theories offer an explanation - the proverbial flapping of a butterfly's wing on a Pacific island causing a hurricane in the Himalayas:
Tell me about 'Catastrophe Theory' with some examples, please. Catastrophe theory is a branch of mathematics that studies how slight changes in certain parameters can lead to sudden and dramatic changes in the behavior of a system. It was pioneered by the French mathematician René Thom in the 1960s.

The central idea of catastrophe theory is that gradual changes in one or more independent variables can trigger abrupt, discontinuous changes in the behavior or appearance of a system. These abrupt changes are referred to as "catastrophes." The theory provides a framework for understanding and predicting these sudden transitions.

One of the most famous examples of catastrophe theory is the "cusp catastrophe." In this model, a system's behavior is represented by a surface with a cusp-shaped fold. As one or more control parameters change, the system can move smoothly along the surface until it reaches a critical point, at which it suddenly jumps from one branch of the surface to another. This abrupt change is the catastrophe.

A classic application of catastrophe theory is in the study of animal behavior, particularly aggression. For example, consider the behavior of two animals engaged in a conflict. As the level of aggression or intimidation from one animal increases, the other animal may initially respond calmly. However, once a certain threshold is crossed, the response may suddenly escalate into a full-blown fight, leading to a dramatic change in the interaction between the animals. This sudden transition corresponds to a catastrophe in the mathematical model.

Another example comes from physics, particularly in the study of phase transitions. For instance, consider the transition of a substance from a liquid to a gas as temperature increases. Initially, as temperature rises, the substance may behave predictably, gradually transitioning from liquid to gas. However, at a certain critical temperature, the transition becomes abrupt, leading to the sudden formation of bubbles and rapid vaporization. This phase transition can be modeled using catastrophe theory, where small changes in temperature result in a catastrophic change in the state of the substance.

Overall, catastrophe theory provides a powerful framework for understanding sudden and unexpected changes in a wide range of systems, from physical and biological systems to social and economic phenomena.

Now tell me about Chaos Theory and how it related to Catastrophe Theory.

Chaos theory is another branch of mathematics and physics that deals with the behavior of dynamical systems that are highly sensitive to initial conditions. It studies systems that appear to be random and unpredictable but actually follow deterministic laws. Chaos theory emerged as a distinct field of study in the late 20th century, with contributions from mathematicians such as Edward Lorenz, who famously discovered the phenomenon of deterministic chaos through his work on weather forecasting.

Unlike catastrophe theory, which focuses on sudden and discontinuous changes in the behavior of systems, chaos theory deals with systems that exhibit complex, non-linear behavior over time. These systems are often characterized by their sensitivity to initial conditions, meaning that tiny differences in the starting state of the system can lead to vastly different outcomes over time. This phenomenon is commonly referred to as the "butterfly effect," where a small change in one part of a system can have large effects elsewhere.

Despite their differences, chaos theory and catastrophe theory are related in several ways:
  1. Non-linear dynamics: Both chaos theory and catastrophe theory deal with systems that exhibit non-linear behavior. In chaos theory, this non-linearity often leads to complex and unpredictable behavior, while in catastrophe theory, it can lead to sudden transitions between different states of the system.
  2. Sensitivity to parameters: Both chaos theory and catastrophe theory involve the study of systems that are sensitive to changes in certain parameters. In chaos theory, small changes in initial conditions can lead to vastly different outcomes, while in catastrophe theory, small changes in control parameters can lead to abrupt changes in the behavior of the system.
  3. Applications: While chaos theory and catastrophe theory have different focuses, they are both used to study complex systems in various fields, including physics, biology, ecology, economics, and sociology. Both theories provide valuable insights into the behavior of these systems and can help researchers understand and predict their dynamics.
In summary, chaos theory and catastrophe theory are related branches of mathematics and physics that study complex and non-linear systems. While chaos theory focuses on the unpredictable behavior of deterministic systems, catastrophe theory focuses on sudden and discontinuous changes in the behavior of systems. Despite their differences, both theories provide valuable tools for understanding the dynamics of complex systems in the natural and social sciences.
So, what we have is an environment which is subject to chaos in which small changes result in 'catastrophic' changes in which the environment appears to flip into a new state. A different set of environmental selectors then come into play, driving rapid change in the species in that environment, or extinction. The result, in the fossil record can then look like a period of stasis followed by disequilibrium and rapid change but the underlying mechanism, as far as the evolution of the species is concerned is still natural selection acting on inherited variance. There is no need to propose a different process because existing processes explain it.

An example of how this works was the subject of the paper I mentioned earlier, where small environmental change is the 'tipping point' which drives a phenotypic change in the hyphae of a fungus. This was shown by a team of researchers led by Assistant Professor, Enrique Rojas, of the Department of Biology, New York University, New York, NY, USA. The team have published their findings in an open access paper in Cell Reports. It is explained in a New York University Press release:
Scientists have found a “tipping point” in the evolution of fungi that throttles their growth and sculpts their shapes. The findings, published in the journal Cell Reports, demonstrate how slight changes in environmental factors can lead to huge changes in evolutionary outcomes.

Fungi are nature’s great composters. They wait within the forest floor to feed on fallen trees and autumn leaves, releasing essential nutrients from these plants back into the Earth.

Although fungi often bring to mind mushroom caps, fungi also have underground “roots” called mycelia. Mycelia are made up of thousands of interconnected, microscopic, finger-like cells called hyphae that grow into vast networks. Hyphae worm their way through the soil by growing from their tips. To do so, they inflate themselves, similar to the long balloons used to make balloon animals.
Hyphae of the fungus Allomyces arbuscula growing as part of a mycelium.
Credit: Maxim Ohairwe.
Their elongated forms allow hyphae to locate and consume nutrients within the soil. But not all hyphae are the same shape: some have rounded tips, while others are pointed. The hyphae of water molds—fungus-like pathogens that cause blight in crops—are particularly pointy.

A major challenge in biology is to identify the specific evolutionary factors that determine the shape—or form—of a given organism,” said Enrique Rojas, assistant professor of biology at New York University and the study’s senior author.

Assistant Professor, Enrique Rojas, senior author
Department of Biology,
New York University, New York, NY, USA.
To understand the reasons for different shapes of hyphae, Rojas and his colleagues combined theory and experiments to investigate fungi and water molds from across nature. They first employed physics-based models of inflationary tip growth to determine all possible shapes of hyphae. Surprisingly, the shapes of actual hyphae found in nature assumed only a small subset of the possible shapes.
An Achlya bisexualis hypha growing.
Credit: Maxim Ohairwe.
The researchers hypothesized that the limited shapes observed in nature reflected “survival of the fittest,” and that the many possible shapes not observed in real fungi were, for some reason, weaker evolutionary rejects. To explore this idea, they examined the growth rate of hyphae with different shapes to create a fitness landscape for hyphae.

“Our eureka moment was when we realized that the shapes of hyphae were intimately connected to their ability to grow fast,” said Maxim Ohairwe, a PhD student in NYU’s Department of Biology and the lead author of the study.

A fitness landscape is like a topographic map that visualizes the evolution of an organism: every species wanders through its fitness landscape by testing whether or not random mutations in its genes increase its growth rate, or fitness. A species only stops its restless wandering when a new mutation decreases its fitness—that is, when it is at a fitness peak.
The fitness landscape of hyphae showing that natural shapes are constrained by a tipping point.

Credit: Maxim Ohairwe.
However, Rojas’s team found that fitness landscapes can be much more rich than a system of peaks and valleys. In fact, they found that the fitness landscape for hyphae contained an overhanging cliff, or tipping point, and that this acts as a barrier to evolution, strongly limiting the shapes of fungal hyphae. Accordingly, they predicted that hyphae with shapes near the brink of the tipping point would be particularly vulnerable to small environmental, chemical, or genetic changes.

The researchers tested their prediction by treating fungi near the tipping point with small amounts of chemicals that affected hyphal growth. They used one chemical that reduces pressure within the hyphae and another derived from a sea sponge that blocks the hypha’s ability to deliver cellular components to the tip of the cell. Both treatments caused the same dramatic effect: the hyphae elongated much more slowly and with a strange nub shape not found in nature.
An Achlya bisexualis hypha that was treated with a chemical that blocks subcellular transport. The treatment caused the hypha to elongate much more slowly and with a strange nub shape not found in nature.

Credit: Maxim Ohairwe.

Our findings explain hyphal shape diversity in an enormous, diverse, and important group of species. More broadly, they also demonstrate an important new evolutionary principle: that fitness landscapes can have instabilities, or tipping points, that impose strict constraints on complex traits, like biological form.

Assistant Professor, Enrique Rojas.
The researchers believe that their results have critical implications for our understanding of many ecological and evolutionary systems. For example, those species whose evolution is subject to a tipping point may be the most vulnerable to the gradual increase in temperature caused by climate change. Their findings could also aid in the development of new antimicrobials against disease-causing fungi by identifying vulnerabilities in their growth associated with an evolutionary tipping point.

In addition to Rojas and Ohairwe, Branka Živanović of the University of Belgrade was a study coauthor.
Technical detail appears in the team's open access paper in Cell Reports:
Graphical abstract
  • Diverse tip-growing cells grow by inflating themselves with turgor pressure
  • There is an intrinsic mechanical instability in the mechanism of inflationary growth
  • The instability leads to a bifurcation of the fitness landscape of tip growth
  • The bifurcation strictly constrains observable cell shapes from across nature

Cellular morphology affects many aspects of cellular and organismal physiology. This makes it challenging to dissect the evolutionary basis for specific morphologies since various cellular functions may exert competing selective pressures on this trait, and the influence of these pressures will depend on the specific mechanisms of morphogenesis. In this light, we combined experiment and theory to investigate the complex basis for morphological diversity among tip-growing cells from across the tree of life. We discovered that an instability in the widespread mechanism of “inflationary” tip growth leads directly to a bifurcation in the common fitness landscape of tip-growing cells, which imposes a strict global constraint on their morphologies. This result rationalizes the morphology of an enormous diversity of important fungal, plant, protistan, and bacterial systems. More broadly, our study elucidates the principle that strong evolutionary constraints on complex traits, like biological form, may emerge from emergent instabilities within developmental systems.


It is often taken for granted that cellular morphology is functional,1 and yet in relatively few cases has the function or the selective advantage of this trait been explicitly demonstrated.2,3 The comma shape of Vibrio cholerae cells, for one example, aids the “corkscrewing” of this bacterial pathogen into the host epithelium. In another case, the highly variable crescent morphology of fish keratocytes emerges from the cytoskeletal dynamics that drive their motility, leading to a correlation between morphology and motility rate.4 However, while there are many other examples of correlations between morphology and cell state, type, or function,5,6,7 these correlations do not necessarily mean that morphology serves a specific function.

On the contrary, morphology typically affects many critical functions that cells perform. For example, during fungal, plant, and animal development, cellular morphology influences the assembly of the cytoskeleton,8,9,10,11,12 which governs myriad sub-cellular processes. Similarly, neuronal morphology affects action-potential propagation,13 neuronal connectivity,14 and signal integration.15 Therefore, in general, morphology is likely to be subject to many competing evolutionary pressures, whose effects will also be constrained by the mechanisms of cellular morphogenesis. Given this complexity, a major challenge in biology is to identify and quantitatively weigh the multiple evolutionary and developmental factors that determine cellular morphology for a given system.

Tip-growing cells (Figure 1) provide an instructive example of the complex morphology-function question. These cells are found in a polyphyletic group of species that encompasses nearly all fungi, many important protistan pathogens, pollen tubes and root hairs in plants, as well as the phylum of bacteria that produces our best antibiotics. On one hand, it is clear that the filamentous morphology of tip-growing cells is intimately tied to their common function, which is to locate and consume nutrients (or deliver the gamete in the case of pollen tubes). On the other hand, the apical morphology of tip-growing cells is variable (Figures 1A and S1A), and it is completely unknown whether specific morphologies contribute to cellular function(s) or if this variation simply reflects non-adaptive variation in the underlying mechanisms of morphogenesis. This question is particularly compelling for tip-growing cells since they arose many times via convergent evolution.
Figure 1 Tip-growing cells are found in diverse taxa.
Evolutionary developmental biology was conceived to address similar questions in animal systems, but the classic concepts and tools from this field have rarely been applied to single-cell morphology. A central tenet of evolutionary developmental biology is that in order to understand morphological diversity across species, it is critical to understand the mechanistic variation in their developmental programs. A valuable method that emerged from this field was the “theoretical morphospace,”16 a comparative strategy commonly used to interpret constraints on organismal morphology.17,18 In this light, our goal was to dissect the complex basis for the morphology of tip-growing cells by combining a mechanistic investigation of their morphogenesis with a top-down analysis of their morphological variation across taxa.

The morphology of tip-growing cells is defined by the geometry of the polysaccharide cell wall (Figure 1C). Because cell-wall geometry is determined by the apical cell-wall expansion that also leads to cell growth, morphogenesis and growth are the same process for these cells. In most cases, tip growth is self-similar such that apical morphology is approximately constant (Figures 1B and 2A ). Therefore, the coordinated steady-state synthesis, metabolism, and physical expansion of the apical cell wall are key processes underlying tip-growth morphogenesis.
Figure 2 Tip-growing cells exhibit limited morphological variation
Tip-growing cells restrict cell-wall synthesis to the cell apex via localized exocytosis of cell-wall polysaccharides (Figure 1C),19,20 which is dependent on the actin cytoskeleton in eukaryotic systems.21,22,23 The coordination of exocytosis with cell-wall expansion typically relies on a spatial gradient of cell-wall biochemistry whereby the nascent, expanding cell wall is biochemically distinct from the mature, non-expanding wall (Figure 1C).24,25,26 For example, during pollen-tube growth, enzymes that prevent cell-wall cross-linking are packaged into the same exocytic vesicles that contain wall polysaccharides,27 ensuring that the nascent cell wall is mechanically soft.24 Pollen-tube growth, in turn, depends on the irreversible stretching of the soft apical cell wall by the turgor pressure within the cell (Figure 1C).28 As for pollen tubes, the growth of fission yeast and the mating projections of budding yeast (examples of transient tip growth) are also akin to controlled “inflation” of the cell by turgor pressure.26,29

Theoretical studies have demonstrated that inflationary tip growth can, in principle, explain a range of apical morphologies, from round to highly tapered (Figure 1A).30,31,32 However, this mechanism was not interrogated experimentally in non-plant species, which are precisely those that exhibit non-round apical morphologies. Similarly, the cellular basis for morphological variability that was proposed by previous theories was not tested. According to one theory, generation of non-round apical morphologies required a large spatial gradient in cell-wall thickness, which is not observed experimentally.33 Therefore, it is unknown (1) if diverse tip-growing systems use inflationary growth, (2) whether inflationary growth can generate natural morphologies in a manner consistent with underlying cell biology, and (3) whether tip-growing cells from across nature assume all morphologies realizable by inflationary growth.

By addressing these questions, we identified strong mechanistic and evolutionary constraints on the morphological diversity of tip-growing cells from across nature. Through precise mechanical characterization of cell-wall expansion in three divergent tip-growing systems—a protist, a fungus, and a plant—we first confirmed that each of them drives tip growth via inflation. We then systematically generalized previous theoretical models of inflationary growth30,31 to account for our data, which allowed us to describe the entire morphospace of tip-growing cells on mechanistic grounds. Surprisingly, we found that morphologies from across nature populated a relatively small region of this morphospace. Further analysis revealed that an emergent cusp bifurcation34 in the morphospace separated fast-growing natural morphologies from slow-growing hypothetical morphologies. We therefore interpret the morphospace as a fitness landscape and conclude that natural selection for fast growth imposes a strong constraint on the morphology of diverse tip-growing cells. Collectively, our results explain the morphological variation of an enormous diversity of important cellular systems. They also explicitly demonstrate a simple but important evolutionary principle: that emergent instabilities in developmental systems can impose strong constraints on complex traits, like biological form.
This paper shows how the appearance of 'punctuated equilibrium' can be explained by a 'tipping point' response to a small environmental change in a system subject to chaos and on the cusp of 'catastrophe', exactly as catastrophe theory predicts. The underlying mechanism of evolution was and remains, Darwinian natural selection in which the selectors are subject to 'catastrophic' change. 'Punctuated equilibrium' is what happens to the environment; the fossil record is simply a record of that change written into the geological column.

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