When did we first ‘Rock the Mic’? A meeting of my two favourite interests over at the New York Times: Linguistics and Hip Hop. Ben Zimmer writes:

In “Rapper’s Delight,” the M.C. Big Bank Hank raps, “I’m gonna rock the mic till you can’t resist,” using what was then a novel sense of rock, defined by the O.E.D. as “to handle effectively and impressively; to use or wield effectively, esp. with style or self-assurance.” To be sure, singers in the prerap era often used rock as a transitive verb, whether it was Bill Haley promising, “We’re gonna rock this joint tonight,” or the bluesman Arthur “Big Boy” Crudup more suggestively wailing, “Rock me, mama.” But the M.C.’s of early hip-hop took the verb in a new direction, transforming the microphone (abbreviated in rap circles as mic, not mike) into an emblem of stylish display. Later elaborations on the theme would allow clothes and other accessories to serve as the objects of rock, as when Kanye West boasted in a 2008 issue of Spin magazine, “I rock a bespoke suit and I go to Harold’s for fried chicken.”

It’d be nice to see more stuff on linguistics and hip hop, and, having said that, I might write a bit on the subject. In fact, I would go as far as to say that hip hop is part of reason why I fell into linguistics: the eloquent word play encouraged, and perhaps moulded, my fascination with language. To demonstrate why, here’s a track by Maryland rapper, Edan, who certainly knows how to rock the mic:

Edan — One Man Arsenal

Life without language. Neuroanthropology provides yet another great read. This time it’s on the topic of life without language — something that’s always crept into my thoughts, yet seems impossible to imagine (as I’m already so embedded within a language-using society). The post goes on to discuss Susan Schaller and the case of a profoundly deaf Mexican immigrant who did not learn sign language:

The man she would call, ‘Ildefonso,’ had figured out how to survive, in part by simply copying those around him, but he had no idea what language was. Schaller found that he observed people’s lips and mouth moving, unaware that they were making sound, unaware that there was sound, trying to figure out what was happening from the movements of the mouths. She felt that he was frustrated because he thought everyone else could figure things out from looking at each others’ moving mouths.

One problem for Schaller’s efforts was that Ildefonso’s survival strategy, imitation, actually got in the way of him learning how to sign because it short-circuited the possibility of conversation. As she puts, Ildefonso acted as if he had a kind of visual echolalia (we sometimes call it ‘echopraxia’), simply copying the actions he saw

One Man’s Take on the Facts of the Matter. Babel’s Dawn takes a look at Tecumseh Fitch’s book, The Evolution of Language, and concisely explains a clear departure between two camps in evolutionary linguistics:

One clear difference between the scenarios is in the role of the individual in relation to language. Language is somehow built into the brain in Chomsky’s thought-first scenario, while it is learned from others in the topics-first approach. Empiricists, like Morten Christiansen and Nicholas Chater, see language as ‘out there’ to be learned while nativists, like Fitch and Chomsky, say there is an internal, I-language, and the language out there is merely the sum of all those little I-languages. How to settle the dispute? Look for factual evidence.

Noam Chomsky is one of the most hysterically abused figures in the world today. Even his critics have to concede that his work inventing the field of linguistics — and so beginning to decode the structure of how language is formed in the human brain — makes him one of the most important intellectuals alive.

I agree that Chomsky is an important intellectual figure, and his massive contributions to linguistics are well-documented, but he did not invent the field. Some might say reinvented… Although, I’m not sure how favourably history will view Chomsky’s shadow having loomed over linguistics for such a long time. My own opinion, for what it’s worth, is that he’s largely been a positive influence, even if I find myself disagreeing with a lot of his major ideas.

The limitations of geological periods, imposed by physical science, cannot, of course, disprove the hypothesis of transmutation of species; but it does seem sufficient to disprove the doctrine that transmutation has taken place through ‘descent with modification by natural selection’. — Lord Kelvin (Of Geological Dynamics, 1869).

It might seem odd that I start a post about evolution with a quote claiming natural selection is inadequate to account for the transmutation of species. It is, though, highly relevant to what I’m going to discuss in the post, and strikes at the heart of why it’s fundamental for us to understand the theory of evolution by natural selection. See, in 1869, Lord Kelvin’s position was fairly reasonable, and, as you’d expect for a man of such high scientific standing, the available evidence in physics did seem to conflict with Darwin’s theory. The Sun was one particularly salient point of contention: to get the diversity of species we see on Earth, evolution needs a long time to work (on the order of hundreds of millions, if not billions of years), yet according to 19th-century physics the Sun could only have been burning for 40-million years.

We now know the Sun is powered by nuclear reactions, allowing for times far-longer than originally conceived by older models. The lesson of the story, and why I included it in the opening, is perhaps best captured with a single word: change. Change is, in fact, all around us, and, despite providing a tenuous opening to a blog post, it is very crucial to the world around us — from the melting of ice to the creation and rejection of ideas. As you shall come to see, change is fundamental to evolution, not only through the mechanisms in which it acts, but also in its conception as an idea. An idea stretching back long before Charles Darwin was even conceived.

From the Antihero of evolution to the Great Chain of Being

Tracing the early ideas for naturalistic explanations of the world takes us as far back as early antiquity. The earliest recorded material belongs to ancient Greek philosophers, with the likes of Anaximander (c. 610–546 BC) and Empedocles (c. 490–430 BC) suggesting non-supernatural explanations for the origin of living things. Though, arguably, it was the philosophy of Plato (c. 428–348 BC) and Aristotle (384–322 BC) that came to dominate the age with two fundamental ideas: essentialism and scala naturæ.

First developed by Plato, who Ernst Mayr would later refer to as the great antihero of evolutionism, essentialism is the idea of observed objects in the real world being merely reflections of a limited number of essences: the attributes that fundamentally underpin what an object or substance is. The important point being that essences do not change. Instead, they are fixed, with any variation being the product of poorly translated reflections (a good way to think of this is to imagine a house of mirrors where one person represents the constant, unchanging essence and each individual mirror representing the variations of that essence).

More relevant to evolution is the second idea, scala naturæ, put forth by Aristotle who, partly based on his own emphasis of observing the natural world, derived a linear sequence of organisms from least to most complex:

Unlike the picture above, Aristotle’s conception of the Great Chain of Being had humans as the pinnacle of creation, with plants occupying the lowest level. This teleological view of nature would later provide a profound influence on medieval philosophers, such as Augustine, who merged such views of nature with religion. Under this view, man was relegated to fourth on the chain (behind God, Angels and Demons), with Aristotle’s discussion on the specific adaptations of organisms later being fundamental to St. Thomas Aquinas’ argument from design: that the order and specified design observed in the living world provides evidence of an intelligent designer. There were plenty of other viable explanations at the time, from the speculations of Taoist philosophers, where species developed differing attributes in response to differing environments, to that of the Muslim Biologist, al-Jahiz, who speculated on the struggle for existence.

Nevertheless, it was the idea of an unchanging and eternal world, and Christianity’s later introduction of an early creation, which held sway long-enough to serve as criticisms against Darwin’s theory. Even in the 15th Century, when the Renaissance started spreading the early foundations of modern science, biology was still seen to belong in the domain of natural theologians and their belief that individual adaptations of organisms held some insight into God’s immaculate design. However, progress was far from stagnant. In the 18th Century, the Great Chain was about to unfurl, largely thanks to Carolus Linnaeus‘ Systema Naturae, which established biological nomenclature through the grouping of species within genera and orders.

Life’s Ancestry and an Older Earth

Under the mantra of God created, Linneaus organized, Linnaeus convincingly argued for a more naturalistic classification of animals, and, for the first time, placed humans together with other primates. Another fascinating aspect of Systema Naturae is its development from the first edition (1735), consisting of a modest eleven pages, to the massive three-thousand pages in the thirteenth and final edition (1767). At the dawn of the 19th Century, the Linnean method had become the standard form of biological classification, with life consisting of three kingdoms: Regnum Animale (animals), Regnum Vegetabile (Vegetable) and Regnum Lapideum (minerals). Furthermore, he also derived a classification based on 5 levels (all of which are still used today): Kingdom, class, order, genus and species.

As things were beginning to slowly develop in biology, geology was shifting into a far more dramatic pace with the discovery that sedimentary rocks were the product of ancient oceans. At the centre of this debate was an idea, made popular by Archbishop James Ussher’s dating of biblical chronology, of the Earth being relatively young: created at around 4004 B.C. The conflict, then, concerned two different theories for the thickness of sediment observed. On the one hand were the catastrophists, where sediment layers are the product of a large-scale catastrophe, and on the other were the uniformitarians, who posited a much longer period of time than allowed by the Bible.

With new methods for dating rock strata, and the discovery of creatures no longer alive today, such as Buckland’s Megalosaurus, meant the new geology was giving us our first glimpses of the history of life. In particular, it showed a trend where different groups appeared at successive stages through time — first came fish, then reptiles, with mammals being the most recent. For much of this period the dominant consensus was that of catastrophe — with the likes of Georges Cuvier arguing, on the basis of comparative anatomy, for a rigidity in species as opposed to evolutionary transformation. It was probably not until the publication of Charles Lyell‘s Principles of Geology did the consensus begin to shift towards uniformitarianism.

Lyell’s view was that observable geological processes, like erosion and volcanic activity, could, given enough time, drastically shape the landscape. For instance, Lyell shows how a long series of eruptions, built up over a period of time, had built up Mount Etna in Sicily. The importance of Principles to modern Geology cannot be understated, but, for the purposes of this essay, our interest lies in how this book would come to greatly influence a young Charles Darwin, who saw analogous processes in biology: that, like the changing rocks, life developed through incremental changes over a long period of time. However, another part of Lyell’s view, James Hutton‘s steady-stateism, meant he would largely remain in opposition to any future evolutionary theories, including the man we are now going to turn to: Jean- Baptiste de Lamarck (see picture below).

The First Evolutionary Theory

Social and economic progress in 18th Century Europe meant ideas about biological change were no longer deemed too outlandish to be considered. Pierre de Maupertuis suggested several ways in which dark-skinned humans came to be, whilst Linnaeus emphasized evolutionary transformations within genera, and Immanuel Kant speculated, on the basis of similarities between organisms, that they may have originated from a single, ancestral source. However, it was the French naturalist, Lamarck, who truly put forward the first comprehensive evolutionary theory, with the publication of Philosophie Zoologique in 1809.

Unlike some of his predecessors, Lamarck’s did not see species as being these fixed and immutable creations. Instead, he asserted that species changed progressively along a linear Chain of Being; much of which was based on the continuous gradation he saw in fossil mollusks. He is perhaps most famously remembered for subscribing to certain claims about inheritance. At its most basic, the theory stated that organisms inherited characteristics they acquired over their lifetime. Couched in current terminology: changes in your phenotype are passed onto the next generation.

These ideas are quite different to what Charles Darwin would eventually propose, but the important point to take away is that Lamarck, and many others during this period, are starting to seriously think about evolution. Much of the reason for this rests in the steady accumulation of evidence, and, looking at the larger perspective, a greater appreciation of the sciences.

In the next post, I will finally get on to discussion Darwin’s theory of evolution… After having touched upon two important precursors: Adam Smith and Thomas Malthus.

Reference: Barton et al (2007). Evolution. Cold Spring Harbor Laboratory Press: Cold Spring Harbor, New York.

A strong dose of regulation will keep the health food industry regular. Interesting article by Martin Robbins (of Lay Scientist) over at the Guardian. I’m not normally one for regulation: I think it’s often a backwards way of looking at an issue. And I’m definitely against our ridiculous zeal for legislation-only solutions. But I do think in the case of the health food industry regulation and legislation are fantastically effective. To bring it back to the post above: McKeith has literally made millions through the exploitation of a weakly controlled industry. Ultimately, though, I do think we need to also consider the other effective weapon against these erroneous claims: education. After all, those who know, know not to buy.

I Write Like… H.P. Lovecraft, apparently. It probably explains the lack of comments on my posts: people are scared shitless. It’s okay, I’m not a venomous wordsmith, just a former linguistics student searching for a new university to call home. See, not so scary now… Click the link if you fancy wasting a minute or so of your time.

The Price of Altruism. I always remember first learning about the Price equation at university, and the sad story of its progenitor, George Price, who committed suicide in 1975. Over a Gene Expression, Razib Khan has written a fantastic, in-depth review of Oren Harman’s book, The Price of Altruism. There are too many snippets of information to pick out for a summary, but here’s an ironically amusing section:

The “hawk” and “dove” morphs made famous by Richard Dawkins in The Selfish Gene go back to Maynard Smith’s work, but the terms themselves were of Price’s invention according to Harman. If I read Harman’s chronology correctly Price was already a fervent Christian by this time, having left atheism in the same period as he launched his career as an evolutionary biologist, and there is some hint that the term “dove” may have been influenced by his particular religious leanings. This possibility seems all the more amusing in light of Dawkins’ later career as an atheist polemicist.

Matt Ridley: When Ideas Have Sex. Love him for his biology, or loathe him for his economics, you can’t help but nod in agreement with Matt Ridley’s TED talk. I think he over emphasizes this apparent trend of good times to come. He clearly hasn’t read Taleb’s Black Swan (and probably isn’t all too interested given his risk-taking strategies at Northern Rock). But his stuff on trade and cultural evolution is fairly rock solid from my perspective.

Such questions are asked in a paper by Reali & Griffiths (2009) that also takes some steps to remedying the situation, by defining a neutral model at the level of linguistic variants. Specifically, they apply this neutral model to three linguistic phenomena: the s-shaped curve of language change; the distribution of word frequencies; and, the relationship between word frequencies and extinction rates. But before getting into these three phenomena, a quick overview of the model is needed (for reasons you’ll see later on):

Defining a model of language evolution that is neutral at the level of linguistic variants requires an account of learning that is explicit about the inductive biases of learners–those factors that make some variants easier to learn than others–so that it is clear that these biases do not favour particular variants. We model learning as statistical inference, with learners using Bayes’ rule to combine the clues provided by a set of utterances with inductive biases expressed through a prior distribution over languages. We define a neutral model by using a prior that assigns equal probability to different variants of a linguistic form. While it is neutral at the level of variants, this approach allows for the possibility that learners have more general expectations about the structure of a language–such as the amount of probabilistic variation in the language, and the tendency for new variants to arise–that can result in forces analogous to directed mutation at the level of entire languages.

So, if this is the case, we can instead appeal to high-level inductive biases as explanatory mechanisms for the structure of languages, without necessarily appealing to selective forces at the level of linguistic variants. By combining the Iterated Learning Model (ILM) with Bayesian learners, the authors arrive at two surprising conclusions: (1) the model is equivalent to the Wright-Fisher model of allele transmission; and, (2) the model is able to reproduce basic regularities in the structure and evolution of languages without the need for the selection or directed mutation of linguistic variants. To reach this equivalence with the Wright-Fisher model linguistic variants are treated as different alleles of a gene, with the Markov chain produced by Iterated Learning matching the model of genetic drift. Essentially, they are proposing the results from population genetics can help define the dynamics and stationary distribution of the Markov chain: this will give a good indication of what kind languages will emerge.

By using Bayesian learners, the authors are able to explicitly relate language change to individual inductive biases: by manipulating the parameters of the prior and seeing the consequences produced via Iterated Learning. Also, their mathematical formulation allows them to generalize the biological-linguistic equivalence to the case of an unbounded number of variants:

Following an argument similar to that for the finite case, iterated learning with Bayesian learners considering distributions over an unbounded vocabulary can be show to be equivalent to the Wright-Fisher model for infinitely many alleles (see the electronic supplementary material for a detailed proof).

Just to reiterate:

• Their model is neutral in regards to both selection and directed mutation at the level of linguistic variants, assuming a symmetric mutation between competing variants.
• The goal is to provide a null hypothesis to evaluate certain claims about the importance of selective pressures, which are often used to explain the “statistical regularities found in the form and evolution of languages”.
• The authors also note that the model “allows for a kind of directed mutation at the level of entire languages, with expectations about the amount of probabilistic variation in a language shaping the structure of that language over time. These expectations play a role analogous to setting the mutation rate in the Wright-Fisher model.”

Frequency effects in lexical replacement rates

As you’ve probably guessed, the authors find that their null model can account for three linguistic phenomena previously mentioned. I’m going to focus on lexical replacement rates because it’s what I’m most familiar with. Anyway, two recent studies show how the frequency of use predicts: (1) the rates at which verbs change from irregular to regular forms (Lieberman et al., 2007); and, (2) the word replacement rates in Indo-European languages (Pagel et al., 2007). So, if a word is used frequently, then it is replaced much more slowly than a less frequently used one. For instance, Pagel et al found that over a 10,000 year time scale, some words show a minimal amount of cognate replacement (zero to one) for words used frequently, while less-frequently used words might have up to nine cognate replacements. Furthermore, certain classes of words evolve at different rates, with prepositions and conjunctions changing more quickly than pronouns and numbers. When plotted, this shows an inverse relationship between the frequency of use and replacement rates.

One suggestion is that some form of linguistic, frequency-dependent, purifying selection is a central factor in determining the slow rate of evolution in highly expressed words. However, as Reali & Griffiths show, their neutral model alone is sufficient to account for the frequency effect:

In the infinite case, mutation occurs only to new variants, thus, all variants are eventually lost from the population. A new cognate is represented by a new variant. Replacement happens when the variant corresponding to the old cognate becomes extinct. The case of verb regularization is modelled by assuming that irregular and regular verbs coexist as two variants among other words in the vocabulary. Extinction of the irregular verb happens when the regular form replaces completely the irregular one.

Importantly, their analytic results and simulations indicate the replacement rate follows an inverse power-law relationship with frequency (see figure below):

Now, for me, I think this paper is quite important for the field of language evolution: all too often we assume some sort of purifying selection is shaping the trajectory of language. However, one of the apparent problems with their model is the use of a single chain of Bayesian learners. Recent studies (see Ferdinand & Zuidema, 2009) show that the outcome of iterated learning is sensitive to more factors than are explicitly encoded in the prior, including population size. This is true even when a small modification is made: e.g. expanding the population size to two individuals at each generation. I’m not entirely sure whether or not this has a profound impact on the current results, but it does stress the need for more work on developing null models for language evolution. As the authors themselves note:

While this analysis of one of the most basic aspects of language–the frequencies of different variants–emphasizes the connections between biological and cultural evolution, it also illustrates that the models developed in population genetics cover only one small part of the process of cultural evolution. We anticipate that developing neutral models that apply to the transmission of more richly structured aspects of language will require a deeper understanding of the mechanisms of cultural transmission–in this case, language learning.

Citation: Reali, F., & Griffiths, T. (2009). Words as alleles: connecting language evolution with Bayesian learners to models of genetic drift Proceedings of the Royal Society B: Biological Sciences, 277 (1680), 429-436 DOI: 10.1098/rspb.2009.1513

N.B. You can currently download this article, and the whole backlog of Royal Society articles, for free until the end of July.

We’re not running the bhopal piece, and we’re passing on the Maldive shark ban (a bit late now… Too bad it got caught up in prod week… ). As for Bhopal, it’s a cautionary call on our part as we’re in the midst of advertising negotiations with Dow (who have been inspired by Seed’s photography in their own brand campaigns). RE: the payment, as you’re on a scheduled direct-payment, the bhopal fee covers the Kerry/Carbon trading news piece fee that was outstanding. Let me know if that’s clear.

It’s a great article that’s not only revealing about Seed, but the underlying motivations of the journalism industry in general. I never thought I’d find myself linking to Chomsky’s politics, yet, given the nature of this article, maybe it’s time I dug out my copy of Manufacturing Consent.

Scientific Certainty Argumentation Methods (SCAMs): Science and the politics of doubt. H/T: Ben Goldacre. A good paper looking at what happens when science and politics mix, and how the two have different expectations of what science is. Here’s the abstract:

At least since the time of Popper, scientists have understood that science provides falsification, but not “proof.” In the world of environmental and technological controversies, however, many observers continue to call precisely for “proof,” often under the guise of “scientific certainty.” Closer examination of real-world disputes suggests that such calls may reflect not just a fundamental misunderstanding of the nature of science, but a clever and surprisingly effective political-economic tactic—”Scientific Certainty” Argumentation Methods, or SCAMs. Given that most scientific findings are inherently probabilistic and ambiguous, if agencies can be prevented from imposing any regulations until they are unambiguously “justified,” most regulations can be defeated or postponed, often for decades, allowing profitable but potentially risky activities to continue unabated. An exploratory examination of previously documented controversies suggests that SCAMs are more widespread than has been recognized in the past, and that they deserve greater attention in the future.

The secret history of X and Z. An excellent article from Ed Yong on Chromosome evolution in humans and birds. Key paragraph:

Why the similarities? It’s possible that both X and Z evolved from autosomes with features that made them more likely to become sex chromosomes. Perhaps, for example, their genes were already sparsely distributed. But Bellott ruled out this idea. He compared X to its closest counterpart in chicken, and Z to its equivalents in humans – none of these relatives had any structural features that made them stand out among other autosomes. There’s nothing that singles them out as ideal candidates for the role of sex chromosome.

You are not authorized to see these pictures of the oil spill, citizen… Do not look. Washington’s Blog has some fairly harrowing photos of the recent gulf oil spill and the damage it’s doing to wildlife. Here’s one example:

By the end of this post, you’ll hopefully be able to understand the above is not just a bunch of jibberish. Now before we get into the nitty gritty of the subject, I think a clarification of my assumptions is in order:

1. That you’ll have a basic understanding of evolutionary biology. If not, then may I suggest Evolution as a very good, and highly comprehensive, introductory text. Failing that, you can always pop over to the wikipedia page.
2. Although these posts will refer to evolutionary biology, my background is in linguistics and socio-cultural evolution — and as such, I will tend to default to the position of explaining these latter areas.
3. It might sound insulting, but you’ll also need a basic understanding of math. You’ll be surprised by the number of people who, despite being very bright, lack even an elementary grasp of the fundamentals. A good place to start is with Kahn Academy’s wonderful online resource: http://www.khanacademy.org/.
4. Having said that, I’m not really expecting anything beyond algebra level math, and I’ll do my best to try and clarify any confusions in the comments section. Also, I’m hardly a math guru, so I welcome anyone with a solid background in math to provide any hints, tips or suggestions, and, in the event I’m plain wrong, point out any mistakes.

Viability Selection

One of the best places to start is a form of natural selection which population geneticists refer to as viability selection: the probability of an individual surviving until adulthood, where it can then reproduce. To get an idea of where viability selection is as a component of natural selection I’ve taken the following diagram from wikipedia:

For the basics of any evolutionary model, the minimum requirements are:

1. The number of individuals and how they are socially organised in the Population.
2. A set of Heritable Variants.
3. The events influencing the survival and spread of heritable variants across a Life Cycle

The goal of our model, then, is to mathematically describe how events in the life cycle change the distribution of heritable variants in the population over one time period. What we want to be looking at is selection for survival. Models are generally abstractions, or simplifications, of events taking place in the natural world. A good way to narrow your focus is to make a list of assumptions. In this case, there are a few assumptions we need to highlight:

• There is a population of n individuals, with n being large enough to avoid sampling variation;
• Individuals within this population are haploid — so no sex or recombination (sorry, guys!).
• There are only two genotypes: Genotype A and Genotype B;
• Everyone is born at the same time, and every reproduces at the same time — that is, their life cycle is in lock step;

Now, we are going to have n zygotes exist at a particular time t. Under this scenario, there is no difference in the type of zygotes who are able to survive into adults, with A types being no more likely to survive than B types. Those that survive then go onto to reproduce, creating a population of zygotes at a time t + 1. In moving through time, a useful ability to have is keeping track of the frequencies of different genotypes within a population. Normally, these frequencies are between 1 and 0, which simply tells us what fraction of the population is of a certain type. This is an example of what we call state variables: A set of variables describing the state of a dynamical system, with the quantities in our case being enough to determine its future behaviour. Applied to our two types, A and B, then the frequency of A, p_A, tells us the portion of the population of type A. In population genetic models, the tendency is for the number of state variables to be one less than the number of alternative alleles. As we only have two types, it is relatively simple to work out the proportion that is type B: you simply subtract the total proportion by the frequency of A (1 — p_A).

Given the simplicity of this model, only one evolutionary force is taking place: individuals with some genotypes are more likely to survive than others. To look at the consequences of survival across a period of time, we need to look at the genotypes at time t and at time t + 1. So, if p is the frequency of the A genotype in the population at time t, then we can express it as the following:

Here, n is the number of individuals within the population. So the number of A zygotes is equal to np. As such, the number of B zygotes is n(1 — p). With a single number, p, we are now able to keep track of the differential evolution of types A and B. The value of p is flexible in the sense that in the next stage of the life cycle p might change. To provide a representation of our state variable in its next stage we use p’ (p prime).

But what happens when these zygotes mature?

Well, some will survive into adulthood, so we need to look at probabilities of both A type and B type zygotes: V(A) and V(B). For example, when V(A) = 0.5, we know that the probability of an A type zygote will survive into adulthood is 50%. Conversely, we also know that V(B) = 0.5. Next, we need to work out the number of adults with genotype A, which is simply:

number of A adults = number of individuals in a population * the frequency of the A genotype in the population at time t * V(A).

number of A adults = npV(A).

The number of B adults is then n(1 — p)V(B). Next, I want to find the frequency of genotype A among adults at p’ :

The left over adults will now mate and subsequently reproduce. As they are reproducing asexually, the adults produce z zygotes, regardless of genotype. Now we want to find the frequency of genotype A at t + 1:

As you can see: reproduction does not change the frequencies of A and B genotypes. So you can write the following recursive expression for the frequency of genotype A after one generation:

As this expression is a recursion, we can modify it to calculate the frequency of genotype A in in subsequent generations by substituting the previous generation into the recursion. Whilst repeating the equation for each generation is fine, there is, however, another method McElreath & Boyd refer to: a difference equation. To derive a difference equation for the above recursion, then you simply do the following (taken from McElreath & Boyd, 2007, pg. 15):

For your own reference, , is the change in frequency of A from time t to time t + 1, and if we use the expression, then we get the following:

So, we’re back at the start, and you should now have some understanding of what the above equation means in regards to how natural selection changes genotype frequencies. To help clarify, the equation can be broken up into two parts:

1. p(1 — p) is simply the variance in genotypes in the population: when there is no variation (p = 1 or 0), natural selection will be unable to change genotype frequencies. You see, natural selection needs variation with which to work, so when variance is maximized (p = 0.5) natural selection is at its strongest.
2. The second part of the equation, , is the proportional increase or decrease of genotype A to genotype B. As long as there is some variation in genotypes, and assuming one genotype is more fit than the other, then the frequency of one of the genotypes will increase each generation. Conversely, the frequency of the other genotype will decrease at each generation.

Reference: McElreath & Boyd (2007). Mathematical Models of Social Evolution: A guide for the perplexed. University of Chicago Press. Amazon link.

N.B. All examples and equations are adapted from Chapter 1 of the aforementioned book as it’s one of the best introductory texts I’ve read. I strongly suggest that, if you’re interested, you’ll click on the above Amazon link and buy the book.

The Human Penis Bone. From WEIRD to just weird. Scicurious reviews a very old journal article from 1913, which tells of a guy who actually grew a penis bone. Now, many mammals do have penis bones, but human males generally lack this ossified aid. However, if you’re curious about how to get one, then all you have to do is simply wear a particular type of corset (see below) and, here’s a downside for those of you planning on ditching the Viagra, get syphilis. As Scicurious explains:

The syphilis, combined with the constant irritation of the corset, had apparently caused a build up of desposits, which eventually ossified and turned in to bone. REAL BONE, with marrow and holes in it and everything! [...] So the moral of this story is: if you’re a guy, and you’re vain about your appearance, get a flat front corset. You don’t want to be sitting down in something pointy.

Wild cat found mimicking monkey calls. Some clever vocal mimicry from a margay. ScienceDaily reports:

Researchers first recorded the incident in 2005 when a group of eight pied tamarins were feeding in a ficus tree. They then observed a margay emitting calls similar to those made by tamarin babies. This attracted the attention of a tamarin “sentinel,” which climbed down from the tree to investigate the sounds coming from a tangle of vines called lianas. While the sentinel monkey started vocalizing to warn the rest of the group of the strange calls, the monkeys were clearly confounded by these familiar vocalizations, choosing to investigate rather than flee. Four other tamarins climbed down to assess the nature of the calls. At that moment, a margay emerged from the foliage walking down the trunk of a tree in a squirrel-like fashion, jumping down and then moving towards the monkeys. Realizing the ruse, the sentinel screamed an alarm and sent the other tamarins fleeing.

Nongenetic selection and evolution: flies use bacteria to adapt to parasitic worms. Jerry Coyne has a fascinating post about nongenetic evolution occurring in a mushroom-eating fruit fly Drosophila neotestacea. But how is it nongenetic? Well, as Jerry explains:

A new paper by John Jaenike and his colleagues in Science, however, shows a form of biological evolution by natural selection that isn’t based on changes in genes. It’s based on changes in the presence of symbiotic bacteria that protect a species from parasites [...] Some flies also carry another organism: the bacterial symbiont Spiroplasma, which is found in many insects.  In D. neotestacea, however, the presence of Spiroplasma protects the fly from the sterilizing effects of nematodes.  While flies with worms and no Spiroplasma are virtually sterile, the presence of the bacteria confers almost normal fertility on worm-ridden flies.  It’s not yet clear how this works, but worms in flies with Spiroplasma are much smaller than those without the bacteria. Presumably the bacteria does something to the worms (or to the flies) that makes the worms grow much more slowly.

New developments in AI. An in-depth article on artificial intelligence over at .CSV. I’m only half-way through the article, but I thought it was worth mention as, the first half at least, is pretty good. H/T: Mind Hacks.

Many English Speakers cannot understand basic grammar. Apparently, “Research into grammar by academics at Northumbria University suggests that a significant proportion of native English speakers are unable to understand some basic sentences”. Language Log and John Hawks have both picked up on the story. Once the paper is released I’ll probably write an in-depth post at GNXP.

Birth Months of World Cup Players. A short, but interesting, post over at GNXP debunking the relevance of your birth month in regards to sporting achievement. I never thought there was any controversy over the issue… But it turns out I was wrong.

Mathematical Formula Predicts Clear Favorite for FIFA World Cup. Keeping with the football theme, and apparently this formula predicts a Spanish victory. The psychic Octopus appears to think so too. I disagree. Go Netherlands!

How many Zombies do you know? Applied Statistics links to yet another Zombie-inspired study.

Dr Evan Harris. Not a link to a particular article, but it’s just nice to see Dr Evan Harris back writing his blog after being defeated in the recent UK elections.

PepsiCo has been expelled. For those of you who don’t know what this headline’s about, don’t worry, it was all just a very bad dream.