In biology, the assumption that physical variation entirely results from selection began to be questioned in the 1960s, as molecular biology started to obtain empirical data that could be compared to the mathematical predictions of population genetics. In 1968, geneticist Motoo Kimura predicted that the vast majority of evolutionary changes at the molecular level are caused not by selection, but by random drift of selectively neutral mutants. Even in the absence of selection, evolutionary change will occur simply as a result of chance, and Kimura reasoned that this could be analyzed with tools from probability theory.
In genetics, the neutral theory was hotly debated for decades, but Kimura’s work eventually led to a dramatic reversal in the way selection is viewed: geneticists now infer selection only when it can be shown that the assumption of neutrality has been violated. The success of the neutral theory triggered a shift in perspective, from the fitness of individuals, to the population-level consequences of both drift and selection.
But is the neutral theory relevant above the molecular level? Theoretical ecologists began to recognize neutral patterns in tree communities in the 1990s, and in most societies, the distribution of baby names is a surprisingly good fit to neutral expectations. Neutral patterns, it turns out, are everywhere (Lansing and Cox 2011).
In genetics, the neutral theory was hotly debated for decades, but Kimura’s work eventually led to a dramatic reversal in the way selection is viewed: geneticists now infer selection only when it can be shown that the assumption of neutrality has been violated. The success of the neutral theory triggered a shift in perspective, from the fitness of individuals, to the population-level consequences of both drift and selection.
But is the neutral theory relevant above the molecular level? Theoretical ecologists began to recognize neutral patterns in tree communities in the 1990s, and in most societies, the distribution of baby names is a surprisingly good fit to neutral expectations. Neutral patterns, it turns out, are everywhere (Lansing and Cox 2011).
Lansing JS, Cox MP. 2011. The domain of the replicators: Selection, neutrality, and cultural evolution. Current Anthropology 52:105-25.
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To explore this idea further, consider the following simulation of neutral genetic diversity.
Here, we combine mutation events and random sampling to re-create the standard neutral model from genetics. Note that random sampling represents the mating process – some parents have more offspring than others just by chance, so the frequencies of the DNA sequences that people carry (their 'haplotype') fluctuates over time. In the simulation above, haplotype traces are colored red if they survive to the present.
This model has two parameters, the mutation rate $\mu$, which determines the rate at which new haplotypes are generated through mutation ('innovation'), and the population size N, which dictates the speed of genetic drift. Drift occurs faster in smaller populations, while a hypothetical population of infinite size would have no drift at all.
In this simulation μ = 0.01 and N = 2000, so that the diversity parameter θ = 4Nμ = 40. To estimate θ from the data, we can use the maximum likelihood estimator of the number of haplotypes k
\[ E(k) \approx \sum\nolimits_{i = 0}^{n-1} {\frac{\theta}{{\theta + i}}} \]
The aim is to find a value of θ that causes the maximum likelihood value of kML to match the observed k (Ewens 1972). Here, n is the number of chromosomes sampled, such that n is twice the population size (i.e., n = 2N) when modeling nuclear chromosomes in a human population. This is because each human carries two copies of each chromosome; one from their mother and one from their father. A larger k implies a larger θ; that is, a faster generation of haplotypes (higher μ) or a slower random loss of haplotypes through drift (higher N).
Explore for yourself how different values of the mutation rate μ and population size N produce characteristic distributions of DNA haplotypes.
This model has two parameters, the mutation rate $\mu$, which determines the rate at which new haplotypes are generated through mutation ('innovation'), and the population size N, which dictates the speed of genetic drift. Drift occurs faster in smaller populations, while a hypothetical population of infinite size would have no drift at all.
In this simulation μ = 0.01 and N = 2000, so that the diversity parameter θ = 4Nμ = 40. To estimate θ from the data, we can use the maximum likelihood estimator of the number of haplotypes k
\[ E(k) \approx \sum\nolimits_{i = 0}^{n-1} {\frac{\theta}{{\theta + i}}} \]
The aim is to find a value of θ that causes the maximum likelihood value of kML to match the observed k (Ewens 1972). Here, n is the number of chromosomes sampled, such that n is twice the population size (i.e., n = 2N) when modeling nuclear chromosomes in a human population. This is because each human carries two copies of each chromosome; one from their mother and one from their father. A larger k implies a larger θ; that is, a faster generation of haplotypes (higher μ) or a slower random loss of haplotypes through drift (higher N).
Explore for yourself how different values of the mutation rate μ and population size N produce characteristic distributions of DNA haplotypes.
Importantly, this way of thinking proves useful far beyond genetics. In the population genetic simulations above, the two key parameters were called 'mutation rate' and 'population size'. However, these parameters ultimately describe
To get an intuitive grasp of this, explore the datasets from very different research fields: simulated neutral data ('Simulated'), real genetic haplotypes from the village of Kateri in western Timor ('Timor'), baby names from the USA in 2015 ('Baby Names'), and tree species in a tropical forest in Singapore ('Tree Species'). Or upload your own data ('Custom Data')! Change the innovation (μ) and drift (N) parameters, and see how the expected neutral distribution changes.
- a constant rate of adding diversity, and
- the intensity of random fluctuations in the frequency of types.
To get an intuitive grasp of this, explore the datasets from very different research fields: simulated neutral data ('Simulated'), real genetic haplotypes from the village of Kateri in western Timor ('Timor'), baby names from the USA in 2015 ('Baby Names'), and tree species in a tropical forest in Singapore ('Tree Species'). Or upload your own data ('Custom Data')! Change the innovation (μ) and drift (N) parameters, and see how the expected neutral distribution changes.
References:
Lansing JS, Cox MP. 2011. The domain of the replicators: Selection, neutrality, and cultural evolution. Current Anthropology 52:105-25.
Kimura M. 1968. Evolutionary rate at the molecular level. Nature 217:624-6.
Lansing JS, Cox MP. 2011. The domain of the replicators: Selection, neutrality, and cultural evolution. Current Anthropology 52:105-25.
Kimura M. 1968. Evolutionary rate at the molecular level. Nature 217:624-6.