Thursday, 15 December 2016

Positional inheritance - draft chapter

Positional inheritance has become one of my key concepts. It's important when explaining universal Darwinism, because it is common, simple and easy to understand and visualize. However, my previous writings on the topic have been spread out over many web pages. Here are the main points, collected from my previous writings and organized. The page is low in hyperlinks and animations - since this is a draft of a book chapter on the topic. However, pictures still illustrate the main points.

Positional inheritance

We have previously seen that copying is found ubiquitously in nature, from spreading ripples to propagating cracks, from growing crystals to scattering radiation. Of course, copying, variation and selection are the basis of Darwinian evolutionary theory. The copying can take a variety of forms, but the most basic is positional inheritance.

It is common knowledge that people inherit the environment of their parents - along with their parents genes. They inherit the local climate, the local language, government and religion - along with traits coded in DNA. A number of parental traits are inherited in these examples, but one of the attributes which is always inherited is position.

It is common for organisms to inherit their parents' position with considerable precision. Not all organisms have effective dispersal strategies - so often the apple does not fall far from the tree. Rabbits tend to inherit the warren of their parents. Corals inherit their parent's reef - and so on. Much the same is true of many inorganic natural forms.


Here are some examples of inorganic positional inheritance:

  • Raindrops - split and produce offspring that inherit their parent's position.
  • Cracks - when a crack tip divides the offspring crack tips start their lives nearby.
  • Atoms - when atoms split, the offspring particles originate near to the parent atom.
  • Ripples - parent ripples give rise to child ripples near to their parents.
Because of locality in physics, any form of inheritance is also accompanied by positional inheritance. That makes positional inheritance the most widespread form of inheritance in existence. Positional inheritance applies to waves and particles of all kinds. Since waves and particles are important building blocks of the universe, this makes positional inheritance very widespread.


The products of positional inheritance often form tree-like structures. The roots and branches of plants resemble trees - and actually are phylogenetic trees of plant cells, laid down in order during development - in a combination of phylogeny and ontogeny. Similarly, lightning, propagating cracks, fractal drainage patterns, and crystalline dendrites are all associated with prominent visual trees. In each case, these are family trees, that show the path of descent. That these trees are in fact family trees can often be easily verified by filming their formation in slow motion. Videos of lightning strikes slowed down show that forks always descend from existing branches. If you look at videos of bullets hitting panes of glass you will see that propagating cracks behave in a similar manner - the cracks spread outwards in a radial pattern where each crack descends from an earlier parent crack.

Sometimes the associated phylogenetic trees are less obvious. For example, in a landslide, each moving boulder has been pushed into motion by collisions with one or more parent boulders. Though each boulder can trace its ancestry back to the first falling stone, the resulting family tree is not obvious to casual observers. It's the same with splitting raindrops, vortices and photons. Family trees are still involved, but you would need a time lapse image to see them.

Heritable fitness

One of the commonly-specified requirements for Darwinian systems is that fitness must be heritable. In other words, on average, relatively fit offspring should be ancestral to relatively fit descendants. Without this condition being met, adaptations can't get off the ground. Does positional inheritance exhibit heritable fitness? Often, fitness is heritable in systems involving positional inheritance - simply as a result of the uneven distribution of resources needed to fuel division.

For example, in diffusion-limited aggregation systems, the concentration of aggregating particles is often greater in some places than others. In electrical discharge systems, the potential gradients can be greater in some places than others. With propagating cracks, the medium can be more brittle in some places than others. These situations are all commonplace ones. In each case, the association between fit ancestors and fit descendants is due to what might be called the smoothness of nature: the tendency of natural systems to be locally fairly uniform on a small scale - the tendency for nearby places to be alike.

In short, ancestors who are in the right place at the right time tend to have descendants who are in the who are in the right place at the right time - while ancestors who are in the wrong place at the wrong time tend to have descendants who are in the who are in the wrong place at the wrong time. The reason is simple: the descendants are born near to the ancestors and so tend to share a similar environment. The result is heritable fitness.


One thing that evolving systems typically need, in order to exhibit complex adaptations, is high-fidelity copying. Excessive noise often results in inherited information getting lost - and this leads to the disintegration of complex adaptations. However, positional inheritance often has pretty high fidelity - allowing adaptations based on it to remain stable. If you think of it in terms of coordinates in the universe that are unknown to an observer, by learning the location of an object an observer gains a considerable quantity of information - that object's coordinates in three dimensional space. If the offspring is within 1 meter of the parent, then that's about 265 bits of mutual information copied with high-fidelity. Say 350 bits of spacetime. Of course in practice, few positional inheritance systems take up the whole universe, so 350 bits is an upper limit. 350 bits is peanuts compared to biological systems, but it represents a search space of considerable size - it's enough for some non-trivial optimization processes to take place.


Positional inheritance also results in adaptation - another hallmark of Darwinian evolution. Cracks adaptively seek the weakest path through matter, streams adaptively trace out the boundaries of their associated drainage basins and turbulence selectively forms where there is the most energy to feed it.

Some cases which are easy to understand can be found in the organic realm. A tree growing partly underneath a bridge is a useful example. Where the branches are under the bridge they don't grow so well, due to lack of light. The parts of the tree that are not under the bridge grow more vigorously. The result is an adaptive fit between the tree and the bridge. This adaptation is not caused by to changes in DNA. It can happen even if every cell in the tree is genetically identical. With a tree under a bridge the adaptive fit between the tree and its environment is caused by differential reproductive success of the cells of the tree - their different rates of growth, reproduction and death. However the important evolving variable is not stored chemically the tree's cells - rather it is the position of the cells themselves which affects their fitness.

If it is acknowledged that the goodness of fit between the tree and the bridge is an adaptation, then by the same logic we ought to count a number of inorganic systems as exhibiting adaptations too - since they display essentially the same dynamics. Crystal dendrites growing near a heat source adapts to grow around the hot area. Rivers and streams adapt to avoid rocky outcrops, cracks propagate around reinforced areas - and so on.

Multiple inheritance channels

Since the modern evolutionary synthesis traditional evolutionary theory has specialized in studying the evolution of nucleic acid-based creatures. A splinter group has rebelled against this orthodoxy, promoting dual inheritance theory - the idea that there are two main information highways in biology - one which transmits inherited information via cells and the other which transmits inherited information down the generations using brains and social learning. However, two inheritance channels is just not enough. Information can also be transmitted down the generations using multiple other channels. Velocity, time, chemical composition and electrical charge are among the many other variables that can be inherited.

Temporal inheritance merits a mention here. Positional inheritance only covers the three dimensions of space. However since Einstein's era, science has understood that space and time are interwoven, and that it often makes sense to talk about spacetime. Spatio-temporal inheritance is a bit of a mouthful, though. Also, it makes reasonable practical sense to talk about positional inheritance and temporal inheritance separately.

Including temporal inheritance and velocity inheritance - which are both also common - bumps up the information carrying capacity of many simple physical systems, making their evolutionary dynamics more interesting.

Universal inheritance

Positional inheritance makes inheritance ubiquitous in the universe. Far from being confined to biology, inheritance happens whenever starlight hits dust - one of the most common interactions in the universe. This is part of the justification for using the term "Universal" in "Universal Darwinism". A number of other writers on the topic have expanded Darwinism to culture, but left the theory confined to biology - leaving chemistry and physics out of the domain of Darwinism. Others have embraced Darwinism in physics - but only applied it to quantum theory, observation selection or the possibility that our entire visible universe might have ancestor universes that existed before the big bang. These applications of Darwinism are interesting, but still narrow, making "Universal Darwinism" not very "universal". Here, Darwinian evolutionary theory is expanded to most dissipative structures - making its application domain much larger and making the theory correspondingly more significant.


Positional inheritance doesn't lead to adaptations on the scale seen in biological evolution. Various problems and limitations reduce its scope for generating adaptations. Many inorganic systems exhibiting positional inheritance lack important properties found in the organic domain.

One such property is an unlimited number of generations. Living organisms today can trace their lineage back four billion years. By contrast, many positional inheritance systems last for tens, hundreds or thousands of generations before going extinct. Electrical discharges or propagating cracks and splitting photons are all examples of positional inheritance systems which tend to have definite origins and finite lifespans. I some cases, the finite lifespan is a product of the lack of a growth phase. In biology, organisms typically divide and then grow before dividing again. Not all positional inheritance systems have this growth phase. Some divide, divide and divide again. Rocks are usually like this and so are photons. By contrast electrical discharges and drainage basins do have a growth phase. Without a growth phase, unlimited inheritance is obviously impossible. Even with a growth phase, inorganic systems often have a limited temporal extent. Lightning strikes feature a growth phase, but it is fueled by a finite potential difference, and once the potential gradient diminishes, the lightning's pathway disappears.

Another limitation involves the quantity of material inherited. Living organisms can transmit megabytes of information to their descendants. However positional inheritance just doesn't support such large quantities of information. 10 - 50 bits seems like a more reasonable figure for many positional inheritance systems. You can still communicate using 10-50 bits - but the bandwidth limit restricts what can be said.


Peter Godfrey-Smith has a section in Darwinian Populations and Natural Selection denigrating the significance of positional inheritance. He writes (on page 55):

Parent and offspring often correlate with respect to their location. It is possible to inherit a high-fitness location; one tree can inherit the sunny side of the hill from another. But the significance of this inherited variation is limited. A population can near-literally 'explore' a physical space, if location is heritable and is linked with fitness. It may move along gradients of environmental quality it may climb hills, or settle around water. But to the extent that reproductive success is being determined by location per se it is not being determined by the intrinsic features that individuals have. If extrinsic features are most of what matters to realized fitness — if intrinsic character is not very important - then other than this physical wandering, not much can happen.

What can happen is that adaptations can develop. Lightning strikes can find the shortest path to the ground, propagating cracks can locate weaknesses in materials and drainage patterns can develop structures that efficiently drain basins. The idea that concepts like 'fitness' and 'adaptation' apply to these kinds of simple inorganic systems is a big deal for physics - and a big deal for Darwinism.

Godfrey-Smith attempts to draw a distinction between "intrinsic" and "extrinsic" traits - and then claims that this distinction affects the "Darwinian character" of processes - with extrinsic traits not being very "Darwinian". However, most traditional evolutionary theory has no use for such a distinction - all it cares about is whether traits are inherited. If you look at axiomatic expressions of Darwinian evolution, "intrinsic" and "extrinsic" inheritance don't get mentioned. That's because this is a distinction that doesn't make much difference: it is irrelevant to most evolutionary theory. Inheritance of traits is what matters - not whether those traits are inherited via "intrinsic" or "extrinsic" mechanisms.

Peter says "the significance of this inherited variation is limited". It seems to me that the significance of this inherited variation is huge. It it wasn't for positional inheritance, we would all have been born in the vacuum of space and died instantly. It may be only "physical wandering" that means that we were born on the surface of a planet - rather than in interstellar space - but it makes the difference between life and death for all of us. Location is actually a very important property that affects fitness. Evolutionary theory is mostly agnostic about how information is passed down the generations - so we can use its existing tools to study positional inheritance.


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