An Introduction To Natural Selection

August 5, 2015March 6, 2018kevinbinz Leave a comment

Part Of: Demystifying Life sequence
Followup To: Population Genetics
Content Summary: 1400 words, 14 min read

How Natural Selection Works

Consider the following process:

Organisms pass along traits to their offspring.
Organisms vary. These random but small variations trickle through the generations.
Occasionally, the offspring of some individual will vary in a way that gives them an advantage.
On average, such individuals will survive and reproduce more successfully.

This is how favorable variations come to accumulate in populations.

Let’s plug in a concrete example. Consider a population of grizzly bears that has recently migrated to the Arctic.

Occasionally, the offspring of some grizzly bear will have a fur color mutation that renders their fur white.
This descendent will on average survive and reproduce more successfully.

Over time, we would expect increasing numbers of such bears to possess white fur.

Biological Fitness Is Height

The above process is straightforward enough, but it lacks a rigorous mathematical basis. In the 1940s, the Modern Evolutionary Synthesis enriched natural selection by connecting it to population genetics, and its metaphor of Gene-Space. Recall what we mean by such a landscape:

A Genotype Is A Location.
Organisms Are Unmoving Points
Birth Is Point Creation, Death Is Point Erasure
Genome Differences Are Distances

Onto this topography, we identified the following features:

A Species Is A Cluster Of Points
Species Are Vehicles
Genetic Drift is Random Travel.

In order to understand how natural selection enriches this metaphor, we must define “advantage”. Let biological fitness refer to how how many fertile offspring an individual organism leaves behind. An elephant with eight grandchildren is more fit than her neighbor with two grandchildren.

Every organism achieves one particular level of biological fitness. Fitness denotes how well-suited an organism is to its environment. Being a measure of organism-environment harmony, we can view fitness as defined for every genotype. Since we can define some number for every point in gene-space, we have license to introduce the following identification:

Biological Fitness Is Height

Here is one possible fitness landscape (image credit Bjørn Østman).

We can imagine millions of alien worlds, each with its own fitness landscape. What is the contours of Earth’s?

Let me gesture at three facts of our fitness landscape, to be elaborated next time:

The total volume of fitness is constrained by the sun. This is hinted at by the ecological notion of carrying capacity.
Fitness volume can be forcibly taken from one area of the landscape to another. This is the meaning of predation.
Since most mutations are harmless, the landscape is flat in most directions. Most non-neutral mutations are negative, but some are positive (example).

Natural Selection As Mountain Climbing

A species is a cluster of points. Biological fitness is height. What happens when a species resides on a slope?

The organisms uphill will produce comparatively more copies of themselves than those downhill. Child points that would have been evenly distributed now move preferentially uphill. Child points continue appearing more frequently uphill. This is locomotion: a slithering, amoeba-like process of genotype improvement.

We have thus arrived at a new identification:

Natural Selection Is Uphill Locomotion

As you can see, natural selection explains how species gradually become better suited to their environment. It is a non-random process: genetic movement is in a single direction.

Consider: ancestral species of the camel family originated in the American Southwest millions of years ago, where they evolved a number of adaptations to wind-blown deserts and other unfavorable environments, including a long neck and long legs. Numerous other special designs emerged in the course of time: double rows of protective eyelashes, hairy ear openings, the ability to close the nostrils, a keen sense of sight and smell, humps for storing fat, a protective coat of long and coarse hair (different from the soft undercoat known as “camel hair”), and remarkable abilities to take in water (up to 100 liters at a time) and do without it (up to 17 days).

Moles, on the other hand, evolved for burrowing in the earth in search of earthworms and other food sources inaccessible to most animals. A number of specialized adaptations evolved, but often in directions opposite to those of the camel: round bodies, short legs, a flat pointed head, broad claws on the forefeet for digging. In addition, most moles are blind and hard of hearing.

The mechanism behind these adaptations is selection, because each results in an increase in fitness, with one exception. Loss of sight and hearing in moles is not an example of natural selection, but of genetic drift: blindness wouldn’t confer any advantages underground, but arguably neither would eyesight.

Microbiologists in my audience might recognize a strong analogy with bacterial locomotion. Most bacteria have two modes of movement: directed movement (chemotaxis) when its chemical sensors detect food, and a random walk when no such signal is present. This corresponds with natural selection and genetic drift, respectively.

Consequences Of Optimization Algorithms

Computer scientists in my audience might note a strong analogy to gradient descent, a kind of algorithm. In fact, there is a precise sense in which natural selection is an optimization algorithm. In fact, computer scientists have used this insight to design powerful evolutionary algorithms that spawn not one program, but thousands of programs, rewarding those with a comparative advantage. Evolutionary algorithms have proven an extremely fertile discipline in problem spaces with high dimensionality. Consider, for example, recent advances in evolvable hardware:

As predicted, the principle of natural selection could successfully produce specialized circuits using a fraction of the resources a human would have required. And no one had the foggiest notion how it worked. Dr. Thompson peered inside his perfect offspring to gain insight into its methods, but what he found inside was baffling. The plucky chip was utilizing only thirty-seven of its one hundred logic gates, and most of them were arranged in a curious collection of feedback loops. Five individual logic cells were functionally disconnected from the rest— with no pathways that would allow them to influence the output— yet when the researcher disabled any one of them the chip lost its ability to discriminate the tones…

It seems that evolution had not merely selected the best code for the task, it had also advocated those programs which took advantage of the electromagnetic quirks of that specific microchip environment. The five separate logic cells were clearly crucial to the chip’s operation, but they were interacting with the main circuitry through some unorthodox method— most likely via the subtle magnetic fields that are created when electrons flow through circuitry, an effect known as magnetic flux. There was also evidence that the circuit was not relying solely on the transistors’ absolute ON and OFF positions like a typical chip; it was capitalizing upon analogue shades of gray along with the digital black and white.

In gradient descent, there is a distinction between global optima and local optima. Despite the existence of an objectively superior solution, the algorithm cannot get there due to its fixation with local ascent.

This distinction also features strongly in nature. Consider again our example of camels and moles:

Given such a stunning variety of specialized differences between the camel and the mole, it is curious that the structure of their necks remains basically the same. Surely the camel could do with more vertebrae and flex in foraging through the coarse and thorny plants that compose its standard fare, whereas moles could just as surely do with fewer vertebrae and less flex. What is almost as sure, however, is that there is substantial cost in restructuring the neck’s nerve network to conform to a greater or fewer number of vertebrae, particularly in rerouting spinal nerves which innervate different aspects of the body.

Here we see natural selection as a “tinkerer”; unable to completely throw away old solutions, but instead perpetually laboring to improve its current designs.

Takeaways

In the landscape of all possible genomes, we can encode comparative advantages as differences in height.
Well-adapted organisms are better at replicating their genes (in other words, none of your ancestors were childless).
Viewed in the lens of population genetics, natural selection becomes a kind of uphill locomotion.
When view computationally, natural selection reveals itself to be an optimization algorithm.
Natural solution can outmatch human intelligence, but it is also a “tinkerer”; unable to start from scratch.

An Introduction To Population Genetics

August 2, 2015March 23, 2017kevinbinz Leave a comment

Part Of: Demystifying Life sequence
Content Summary: 1200 words, 12 min read

Central Thesis Of Molecular Biology

In every cell of your body, there exist molecules called deoxyribonucleic acid. Such cells come in four flavors and (due to their atomic shape) tend to pair up and create long strings. These strings become very long, over two inches when held end-to-end (but of course, they fold up dramatically so each can comfortably inhabit a single cell). Since your cells have about 46 inches worth (six billion molecules), each cell contains twenty-three unique strings. They look like this:

Let us refer to these strings as chromosomes, and to all of them collectively as the human genome. Finally, since typing “deoxyribonucleic acid” is fairly onerous, we will use the acronym DNA.

In 1956, Francis Crick presented his Central Thesis Of Molecular Biology, which describes how the causal chain DNA → RNA → amino acids → protein ultimately motivates every trait of every living organism. A gene is a sequence of DNA that encodes a protein. A genotype (some animal’s unique DNA) explains phenotype (that animal’s unique traits). Genotype-phenotype maps (GP-maps) turn out to be very important in what follows.

Duplication vs. Mutation

Every time a cell duplicates itself (mitosis), its DNA is copied into the new cell. If every cell contains exactly the same code, how can they be different? The basic explanation of cellular differentiation involves feedback loops in the genetic causal chain (collectively named the Gene Regulatory Network). When a lung cell is duplicated, for example, it inherits not just the entire genome, but also proteins for activating lung genes and deactivating other code.

Germ cells are created by a different process entirely. Instead of genome duplication (mitosis), germ cells inherit what is essentially half a genome, in a process known as meiosis. Here’s how these two processes work:

Recall that deoxyribonucleic acid is a collection of atoms. Replicating such a fragile object is imperfect. There are many kinds of ways the process can go wrong; for example:

Replacement Mutation (e.g., AGTC → AATC)
Duplication Mutation (e.g., AGTC → AGGTC)
Insertion Mutation (e.g., AGTC → AGATC)

How many mutations do you have? While you can always get your DNA sequenced to find out, the answer for most people is about sixty.

The Landscape Of Gene-Space

Consider all animals whose genome is three molecules long. How many genetically unique kinds of these animals are there? Recall there are four kinds of DNA: cytosine (C), guanine (G), adenine (A), or thymine (T). We can use the following formula:

$|Permutations| = |Possibilities|^{|Slots|}$

Here we have 3^4 = 81 possible genotypes in this particular gene-space. To visualize this, imagine a 4-sided Rubik’s Cube: each dimension is a slot, each cube a particular genotype in the space.

But humans have approximately three billion base pairs; the size of a realistic gene-space is almost incomprehensibly large (4^3,000,000,000), far exceeding the number of atoms in the universe. Reasoning about 3D cubes is easy, reasoning about 3,000,000,000-D hypercubes is a bit harder. So we employ dimension reduction to aid comprehension. If you laid all 4^3,000,000,000 numbers out on a two dimensional matrix, each cell would be so tiny that the surface would appear continuous. We have arrived at our first metaphor identification:

A Genotype Is A Location

We can summarize our discussion of mitosis, meiosis, and mutation as follows:

An Organism Is A Stationary Point
Birth Is Point Creation, Death Is Point Erasure.

Finally, let us explore the concept of genetic distance. From our toy gene-space, let me take seven nodes and draw lines indicating valid replacement mutations between them.

The key observation is that distances vary. Many nodes are connected via one mutation, but the minimum distance from top (ATG) to bottom (CCC) is three mutations. In other words:

Varying Genome Differences Are Varying Distances

Our gene-space landscape, then, looks something like this:

Species Are Clusters

What is a species? After all, there is no encoding of the word “jaguar” in the jaguar genome. Rather, members of a species share more genetic similarities to one another than other organisms. In terms of our metaphor:

A Species Is A Cluster Of Points

In the above landscape, we might have two species. But there are many ways to cluster data. Consider these competing definitions:

Which clustering approach is correct? It depends on the scale of our axes:

If we chose Granular but are too “zoomed in”, we have accidentally defined four new species of Shih Tzu.
If we chose Course but are too “zoomed out”, we have accidentally defined Mammal as its own species.

The point is that scale matters, and we should define species on a scale that makes good biological sense. The most popular scale is that defined by successful interbreeding (i.e., produce fertile offspring). For greater distances (large genetic dissimilarity), such interbreeding is impossible. We therefore constrain the size of our specie clusters by maximum interbreeding distance.

The approach just outlined is the one in use today. However, any man-made criteria for categorizing reality has its stretch points. For example, consider ring species.

Consider the Larus gulls’ populations in the above image. These gulls habitats form a ring around the North Pole, not normally crossed by individual gulls. The European herring gull {6} can hybridize with the American herring gull {5}, which can hybridize with the East Siberian herring gull {4} which can hybridize with Heuglin’s gull {3}, which can hybridize with the Siberian lesser black-backed gull {2}, which can hybridize with the lesser black-backed gulls {1}. However, the lesser black-backed gulls {1} and herring gulls {6} are sufficiently different that they do not normally hybridize.

Genetic Drift Is Random Travel

Landscapes without movement aren’t very interesting. With our brand-new concept as Species As Clusters, let’s see if we can make sense of travel.

Consider the phenomenon of population bottleneck. Many factors may contribute to population reduction (e.g., novel predators). Often, the survivors are just lucky. Descendants of the survivors tend to be more similar to them than the average genome of the original species. By this process, bottlenecks induces change in the species as a whole:

Why wouldn’t such movement cancel itself out in the long run? The reason why resides in the size of gene-space. For our genome is length two, mutations cancelling each other out would be a fairly common occurence. Would cancelling out increase or decrease on a genome of length 1,000? Surely less. How much less (a forteriori!) the case for genomes with three billion molecules. By the extreme dimensionality of gene-space, then, we are witness to non-cancellative genetic movement!

Genetic Drift Is (Random) Travel.

Importantly, it is not the individuals that travel (modify their genomes), but the species as a whole.

Species Are Vehicles.

Viewing the species itself as actor, rather than the individual, is an important paradigm shift of population genetics.

Takeaways

In this post, I introduced the following metaphor:

A Genotype Is A Location.
Organisms Are Unmoving Points
Birth Is Point Creation, Death Is Point Erasure
Genome Differences Are Distances

We then strengthened our metaphor with the following considerations:

A Species Is A Cluster Of Points
Species Are Vehicles
Genetic Drift is (Random) Travel.

We are left with the image of specie vehicles clumsily moving around gene-space. But genetic drift is not the only mechanism by which species navigate gene-space. In our next post, we explore a more sophisticated property of living things.

Fewer Lacunae

Distilled, Integrative Research

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An Introduction To Natural Selection

An Introduction To Population Genetics