# European Society for Evolutionary Biology congress, Groningen, 2017

The European Society for Evolutionary Biology meeting this year took place August 20–25 in Groningen, Netherlands. As usual, the meeting was great, with lots of good talks and posters. I was also happy to meet colleagues, including people from Linköping who I’ve missed a lot since moving.

Here are some of my subjective highlights:

There were several interesting talks in the recombination symposium, spanning from theory to molecular biology and from within-population variation to phylogenetic distances. For example: Irene Tiemann-Boege talked about recombination hotspot evolution from the molecular perspective with mutation bias and GC-biased gene conversion (Arbeithuber & al 2015), while Franciso Úbeda de Torres presented a population genetic model model of recombination hotspots. I would need to pore over the paper to understand what was going on and if the model solves the hotspot paradox (as the title said), and how it is different from his previous model (Úbeda & Wilkins 2011).

There were also talks about young sex chromosomes. Alison Wright talked about recombination suppression on the evolving guppy sex chromosomes (Wright & al 2017), and Bengt Hansson about the autosome–sex chromosome fusion in Sylvioidea birds (Pala & al 2012).

Piter Bijma gave two (!) talks on social genetic effects. That is when your trait value depends not just on your genotype, but on the genotype on others around you, a situation that is probably not at all uncommon. After all, animals often live in groups, and plants have to stay put where they are. One can model this, which leads to a slightly whacky quantitative genetics where heritable variance can be greater than the trait variance, and where the individual and social effects can cancel each other out and prevent response to selection.

I first heard about this at ICQG in Edinburgh a few years ago (if memory serves, it was Bruce Walsh presenting Bijma’s slides?), but have only made a couple of fairly idle and unsuccessful attempts to understand it since. I got the feeling that social genetic effects should have some bearing on debates about kin selection versus multilevel selection, but I’m not sure how it all fits together. It is nice that it comes with a way to estimate effects (given that we know which individuals are in groups together and their relatedness), and there are some compelling case studies (Wade & al 2010). On the other hand, separating social genetic effects from other social effects must be tricky; for example, early social environment effects can look like indirect genetic effects (Canario, Lundeheim & Bijma 2017).

Philipp Gienapp talked about using realised relatedness (i.e. genomic relationships a.k.a. throw all the markers into the model and let partial pooling sort them out) to estimate quantitative genetic parameters in the wild. There is a lot of relevant information in the animal breeding and human genetics literature, but applying these things in the wild comes with challenges that deserves some new research to sort things out. Evolutionary genetics, similar to human genetics, is more interested in parameter estimation than prediction of phenotypes or breeding values. On the other hand, human genetics methods often work on GWAS summary statistics. In this way, evolutionary genetics is probably more similar to breeding. Also, the relatedness structure of the the populations may matter. Evolution happens in all kinds of populations, large and small, structured and well-mixed. Therefore, evolutionary geneticists may work with populations that are different from those in breeding and human genetics.

For example, someone asked about estimating genetic correlations with genomic relationships. There are certainly animal breeding and human genetics papers about realised relatedness and genetic correlation (Jia & Jannik 2012, Visscher & al 2014 etc), because of course, breeders need to deal a lot with correlated traits and human geneticists really like finding genetic correlations between different GWAS traits.

Speaking of population structure, Fst scans are still all the rage. There was a lot of discussion about trying to find regions of the genome that stand out as more differentiated in closely related populations (”genomic islands of speciation/divergence/differentiation”), and as less differentiated in mostly separated populations (introgression, possibly adaptive). But it’s not just Fst outliers. It’s encouraging to see different kinds of quantitative and population genomic methods applied in the same systems. On the hybrid and introgression side of things, Leslie Turner (Turner & Harr 2014) and Jun Kitano (Ravinet & al 2017) gave interesting talks on mice and sticklebacks, respectively. Danièle Filiaut showed an super impressive integrative GWAS and selection mapping study of local adaptation in Swedish Arabidopsis thaliana (Kedaffrec & al 2016).

Susan Johnston spoke about recombination mapping in Soay sheep and Rum deer (Johnston & al 2016, 2017). Given how few large long term genetic studies like this there are, it’s marvelous to be see the same kind of analysis in two parallel systems. Jason Munshi-South gave what seemed like a fascinating talk about rodent evolution in New York City (Harris & Munshi-South 2017). Unfortunately, too many other people thought so too, and I mostly failed to eavesdrop form the corridor.

Finally, Nina Wedell gave a wonderful presidential address about Evolution in the 21th century. ”Because I can. I’m the president now.” Yes!

The talk was about threats to evolutionary biology, examples of it’s usefulness and a series of calls to action. I liked the part about celebrating science much more than the common call to explain science to people. You know, like you hear at seminars and the march for science: We need to ”get out there” (where?) and ”explain what we’re doing” (to whom?). Because if it is true that science and scientists are being questioned, then scientists should speak in a way that works even if they’re not starting by default from a position of authority. Scientists need not just explain the science, but justify why the science is worth listening to in the first place.

”As your current president, I encourage you to celebrate evolution!”

I think this is precisely right, and it made me so happy. Of course, it leaves questions like ”What does that mean?”, ”How do we do it?”, but as a two word slogan, I think it is perfect.

Celebration aligns with sound rhetorical strategy in two ways. First, explanation is fine when someone asks for it, or is otherwise already disposed to listen to an explanation. But otherwise, it is more important to awake interest and a positive state of mind before laying out the facts. (I can’t claim to be any kind of rhetorics expert. But see Rhetoric: for Herennius, Book I, V-VII for ancient wisdom on the topic.) By the way, I’m sure this is what people who are good at science communication actually do. Second, celebration means concentrating on the excitement and wonder, and the good things science can do. In that way, it prevents the trap of listing all the bad things that will happen if Trumpists, creationists and anti-vaccine activists get their way.

Nina Wedell also gave examples of the usefulness of evolution: biomimicry, directed evolution of enzymes, the power of evolutionary algorithms, plant and animal breeding, and prevention of resistance to herbicides and antibiotics. These are all good, worthy things, but also quite a limited subset of evolutionary biology? Maybe this idea is that evolutionary biology should be a basic science supporting applications like these. In line with that, she brought up how serendipitous useful things can come from studying strange diverse organisms and figuring out how they do things. The example in talk was the CRISPR–Cas system. Similar stories apply to a other proteins used as biomedical and biotechnology tools, such as Taq polymerase and Green fluorescent protein.

I have to question a remark about reproducibility, though. The list of threats included ”critique of the scientific method” and concerns over reproducibility, as if this was something that came from outside of science. I may have misunderstood. It was a very brief comment. But if problems with reproducibility are a threat to science, and I think they can be, then it’s not just a problem of image but a problem with how scientists perform, analyse, and report their science.

Evolutionary biology hasn’t been in the reproducibility crisis news the same way as psychology or behavioural genetics, but I don’t know if that is because of better quality, or just that no one has looked that carefully for the problems. There are certainly contradictory results here too, and the same overly flexible data analysis and selective reporting practices that cause problems elsewhere must be common in evolution too. I can think of some reasons why evolutionary biology may be better off. Parts of the field default to analysing data with multilevel or mixed models. Mixed models are not perfect, but they help with some multiple testing problems by fitting and partially pooling a lot of coefficients in the same model. Also, studies that use classical model organisms may be able to get a lot of replication, low variance, and large sample sizes in a way that is impossible for example with human experiments.

So I don’t know if there is a desperate need for large initiatives for replication of key results, preregistration of studies, and improvement of data analysis practice in evolution; there may or there may not. But wouldn’t it still be wonderful if we had them?

Bingo! I don’t have a ton of photos from Groningen, but here is my conference bingo card. Note what conspicuously isn’t filled in: the poster sessions took place in nice big room, and were not that loud. In retrospect, I probably didn’t go to enough of the non-genetic inheritance talks, and I should’ve put Fisher 1930 instead of 1918.

Annonser

# EBM 2016, Marseille

In September, I went to the 20th Evolutionary Biology Meeting in Marseille. This is a very nice little meeting. I listened to a lot of talks, had some very good conversations, met some people, and presented our effort to map domestication traits in the chicken with quantitative trait locus mapping and gene expression (Johnsson & al 2015, 2016, and some unpublished stuff).

Time for a little conference report. Late, but this time less than a year from the actual conference. Here are some of my highlights:

Richard Cordaux on pill bugs, Wolbachia and sex manipulation — I did not know that Wolbachia, the intracellular parasite superstar of arthropods, had feminization of hosts in its repertoire (Cordaux & al 2004). Not only that, but in some populations of pill bugs, a large chunk of the genome of the feminizing Wolbachia has inserted into the pill bug genome, thus forming a new W chromosome (Leclercq & al 2016, published since the conference). He also told me how this is an example of the importance of preserving genetic resources — the lines of pill bugs have been maintained for a long time, and now they’re able to return to them with genomics tools and continue old lines of research. I think that is seriously cool.

Olaya Rendueles Garcia on positive frequency-dependent selection maintaining diversity in social bacterium Myxococcus xanthus (Rendueles, Amherd & Velicer 2015) — In my opinion, this was the best talk of the conference. It had everything: an interesting phenomenon, a compelling study system, good visuals and presentation. In short: M. xanthus of the same genotype tend to cooperate, inhabit their own little turfs in the soil, and exclude other genotypes. So it seems positive frequency-dependent selection maintains diversity in this case — diversity across patches, that is.

A very nice thing about this kind of meetings is that one gets a look into the amazing diversity of organisms. Or as someone put it: the complete and utter mess. In this department, I was particularly struck by … Sally Leys — sponges; Marie-Claude Marsolier-Kergoat — bison; Richard Dorrell — stramenopile chloroplasts.

I am by no means a transposable elements person. In fact, one might believe I was actively avoiding transposable elements by my choice of study species. But transposable elements are really quite interesting, and seem quite important to genome evolution, both to neutrally evolving and occasionally adaptive sequences. This meeting had a good transposon session, with several interesting talks.

Anton Crombach presented models the gap gene network in Drosophila melanogaster and Megaselia abdita, with some evolutionary perspectives (Crombach & al 2016). A couple of years ago, Marjoram, Zubair & Nuzhdin used the gap gene network as their example model to illustrate the suggestion to combine systems biology models with genetic mapping. I very much doubt (though I may be wrong; it happens a lot) that there is much meaningful variation within populations in the gap gene network. A between-species analysis seems much more fruitful, and leads to the interesting result where the outcome, in terms of gap gene expression along the embryo, is pretty similar but the way that the system gets there is quite different.

If you’ve had a beer with me and talked about the future of quantitative genetics, you’re pretty likely to have heard me talk about how in the bright future, we will not just map variation in phenotypes, but in the parameters of dynamical models. (I also think that the mapping will take place through fully Bayesian hierarchical models where the same posterior can be variously summarized for doing genomic prediction or for mapping the major quantitative trait genes, interactions etc. Of course, setting up and running whole-genome long read sequencing will be as convenient and cheap as an overnight PCR. And generally, there will be pie in the sky etc.) At any rate, what Anton Crombach showed was an example of combining systems biology modelling with variation (between clades). I thought it was exciting.

It was fun to hear Didier Raoult, one of the discoverers of giant viruses, speak. He was somewhat of a quotation machine.

”One of the major problems in biology is that people believe what they’ve learned.”

(About viruses being alive or not) ”People ask: are they alive, are they alive? I don’t care, and they don’t care either”

Very entertaining, and quite fascinating stuff about giant viruses.

If there are any readers out there who worry about social media ruining science by spilling the beans about unpublished results presented at meetings, do not worry. There were a few more cool unpublished things. Conference participants, you probably don’t know who you are, but I eagerly await your papers.

I think this will be the last evolution-themed conference for me in a while. The EBM definitely has a different range of themes than the others I’ve been to: ESEB, or rather: the subset of ESEB I see choosing my adventure through the multiple-session programme, and the Swedish evolution meetings. There was more molecular evolution, more microorganisms and even some orgin of life research.

# A year ago in Lund: the panel discussion at Evolution in Sweden 2016

This meeting took place on the 13th and 14th of January 2016 in Lund. It feels a bit odd to write about it now, but my blog is clearly in a state of anachronistic anarchy as well as ett upphöjt tillstånd av språklig förvirring, so that’s okay. It was a nice meeting, spanning quite a lot of things, from mosasaurs to retroviruses. It ended with a panel discussion of sorts that made me want to see more panel discussions at meetings.

The panel consisted of Anna-Liisa Laine, Sergey Gavrilets, Per Lundberg, Niklas Wahlberg, and Charlie Cornwallis, and a lot of people joined in with comments. I don’t know how the participants were chosen (Anna-Liisa Laine and Sergey Gavrilets were the invited speakers, so they seem like obvious choices), or how they were briefed; Per Lundberg served as a moderator and asked the other participants about their predictions about the future of the field (if memory serves me right).

I thought some of the points were interesting. One of Sergey Gavrilets’ three anticipated future developments was links between different levels of organisation; he mentioned systems biology and community ecology in the same breath. This sounded interesting to me, who not so secretly dreams of the day when systems biology, quantitative genetics, and populations genetics can all be brought to bear on the same phenotypes. (The other two directions of research he brought up were cliodynamics and human evolution.) He himself had, earlier in his talk, provided an example where a model of human behaviour shows the possibility of something interesting — that a kind of cooperation or drive for equality can be favoured without anything like kin or group selection. That is, in some circumstances it pays to protect the weak, and thus make sure that they bullies do not get too much ahead. He said something to the effect that now is the time to apply evolutionary biology to humans. I would disagree with that. On the one hand, if you are interested in studying humans, any time is the time. On the other hand, if the claim is that now, evolutionary biology is mature and solid, so one can go out and apply it to help other disciplines to sort out their problems … I think that would be overly optimistic.

A lot of the discussion was about Mats Björklund‘s talk about predicting evolution, or failing to do so. Unfortunately, I think he had already left, and this was the one talk of the conference that I missed (due to dull practical circumstances stemming from a misplaced wallet), so this part of the discussion mostly passed me by.

A commonplace that recurred a few times was jokes about sequencing … this or that will not be solved by sequencing thousands of genomes, or by big data — you know the kind. This is true, of course; massively parallel sequencing is good when you want to 1) make a new reference genome sequence; 2) get lots and lots of genetic markers or 3) quantify sequences in some library. That certainly doesn’t cover all of evolutionary biology, but it is still quite useful. Every time this came up part of me felt like putting my hand up to declare that I do in fact think that sequencing thousands of individuals is a good idea. But I didn’t, so I write it here where even fewer people will read it.

This is (according to my notes) what the whiteboard said at the end of the session:

”It’s complicated …”
”We need more data …”
”Predictions are difficult/impossible”
”We need more models”

Eventually we’ll get there (where?)
Revise assumptions, models, theories, methods, what to measure

Nothing in evolutionary biology makes sense except in the light of ecology phylogeny disease

Everything in evolution makes sense in the light of mangled Dobzhansky quotes.

(Seriously, I get why pastiches of this particular quote are so common: It’s a very good turn of phrase, and one can easily substitute the scientific field and the concept one thinks is particularly important. Nothing in behavioural ecology makes sense except in the light of Zahavi’s handicap principle etc. It is a fun internal joke, but at the same time sounds properly authoritative. Michael Lynch’s version sometimes seems to be quoted in the latter way.)

# Paper: ”Feralisation targets different genomic loci to domestication in the chicken”

It is out: Feralisation targets different genomic loci to domestication in the chicken. This is the second of our papers on the Kauai feral and admixed chicken population, and came out a few days ago.

The Kauai chicken population is kind of famous: you can find them for instance on Flickr, or on YouTube. We’ve previously looked at their plumage, listened to the roosters’ crowings, and sequenced mitochondrial DNA to investigate their origins. Based on this, we concur with the common view that the chickens of Kauai probably are a mixture of feral birds of domestic origin and wild Junglefowl. The Kauai chickens look and sound like a mix of wild and domestic, and we found mitochondrial DNA of two haplogroups, one of which (called D) is typical in ancient chicken DNA from Pacific islands (Gering et al 2015).

In this paper, we looked at the rest of the genome of the same chickens — you didn’t think we sequenced the whole thing just to look at the mitochondrion plus a subset of markers, did you? We turn to population genomics, and a family of methods called selective sweep mapping, to search for regions of their genome that show signs of being affected by natural selection. This lets us: 1) draw pretty rainbow plots such as  this one …

(Figure 1a from the paper in question, Johnsson & al 2016. cc:by The chromosomes have been laid out on the horizontal axis with different colours, and split into windows of 40 kb. Each dot represents the heterozygosity of that windows. For all the details, see the paper.)

… 2) highlight a regions of the genome that may have been selected during feralisation on Kauai (these are the icicles in the graph, highligthed by arrows); 3) conclude that the regions that look like they’ve been selected in feralisation overlap very little with the ones that look like they’ve been selected in chicken domestication. Hence the title.

That was the main result, but of course we also look at what genes are highlighted. Mostly we have no idea how they may contribute to feralisation, but a couple of regions overlap with those that we’ve previously found in genetic mapping of comb size and egg laying in our wild-by-domestic intercross. We also compare the potentially selected regions to domestic chicken sequences.

Last year, Ewen Callaway visited Dominic Wright, Eben Gering and Rie Henriksen on the last fieldtrip to Kauai. The article, When chickens go wild, was published in Nature News in January, and it explains a lot of the ideas nicely. This paper was submitted by then, so the samples they gathered on that trip do not feature in it. But, spoiler alert: there is more to come. (I don’t know what role I personally will play, but that is less important.)

As you may have guessed if you looked at the author list, this was a collaboration between quite a lot of people in Linköping, Michigan, London, and Victoria. Thanks to all involved! This was great fun, and for those of you who like this sort of thing, I hope the paper will be an interesting read.

Literature

M. Johnsson, E. Gering, P. Willis, S. Lopez, L. Van Dorp, G. Hellenthal, R. Henriksen, U. Friberg & D. Wright. (2016) Feralisation targets different genomic loci to domestication in the chicken. Nature Communications. doi:10.1038/ncomms12950

# Toying with models: The Game of Life with selection

Conway’s Game of life is probably the most famous cellular automaton, consisting of a grid of cells developing according simple rules. Today, we’re going to add mutation and selection to the game, and let patterns evolve.

The fate of a cell depends on the number cells that live in the of neighbouring positions. A cell with fewer than two neighbours die from starvation. A cell with more than three neighbours die from overpopulation. If a position is empty and has three neighbours, it will be filled by a cell. These rules lead to some interesting patterns, such as still lives that never change, oscillators that alternate between states, patterns that eventually die out but take long time to do so, patterns that keep generating new cells, and so forth.

When I played with the Game of life when I was a child, I liked one pattern called ”virus”, that looked a bit like this. On its own, a grid of four-by-four blocks is a still life, but add one cell (the virus), and the whole pattern breaks. This is a version on a 30 x 30 cell board. It unfolds rather slowly, but in the end, a glider collides with a block, and you are left with some oscillators.

There are probably other interesting ways that evolution could be added to the game of life. We will take a hierarchical approach where the game is taken to describe development, and the unit of selection is the pattern. Each generation, we will create a variable population of patterns, allow them to develop and pick the fittest. So, here the term ”development” refers to what happens to a pattern when applying the rules of life, and the term ”evolution” refers to how the population of patterns change over the generations. This differ slightly from Game of life terminology, where ”evolution” and ”generation” usually refer to the development of a pattern, but it is consistent with how biologists use the words: development takes place during the life of an organism, and evolution happens over the generations as organisms reproduce and pass on their genes to offspring. I don’t think there’s any deep analogy here, but we can think of the initial state of the board as the heritable material that is being passed on and occasionally mutated. We let the pattern develop, and at some point, we apply selection.

First, we need an implementation of the game of life in R. We will represent the board as a matrix of ones (live cells) and zeroes (empty positions). Here is function develops the board one tick in time. After dealing with the corners and edges, it’s very short, but also slow as molasses. The next function does this for a given number of ticks.

## Develop one tick. Return new board matrix.
develop <- function(board_matrix) {
padded <- rbind(matrix(0, nrow = 1, ncol = ncol(board_matrix) + 2),
cbind(matrix(0, ncol = 1, nrow = nrow(board_matrix)),
board_matrix,
matrix(0, ncol = 1, nrow = nrow(board_matrix))),
matrix(0, nrow = 1, ncol = ncol(board_matrix) + 2))
for (i in 2:(nrow(padded) - 1)) {
for (j in 2:(ncol(padded) - 1)) {
if (neighbours < 2 | neighbours > 3) {
new_board[i, j] <- 0
}
if (neighbours == 3) {
new_board[i, j] <- 1
}
}
}
}

## Develop a board a given number of ticks.
tick <- function(board_matrix, ticks) {
if (ticks > 0) {
for (i in 1:ticks) {
board_matrix <- develop(board_matrix)
}
}
board_matrix
}


We introduce random mutations to the board. We will use a mutation rate of 0.0011 per cell, which gives us a mean of a bout one mutation for a 30 x 30 board.

## Mutate a board
mutate <- function(board_matrix, mutation_rate) {
mutated <- as.vector(board_matrix)
outcomes <- rbinom(n = length(mutated), size = 1, prob = mutation_rate)
for (i in 1:length(outcomes)) {
if (outcomes[i] == 1)
mutated[i] <- ifelse(mutated[i] == 0, 1, 0)
}
matrix(mutated, ncol = ncol(board_matrix), nrow = nrow(board_matrix))
}


I was interested in the virus pattern, so I decided to apply a simple directional selection scheme for number of cells at tick 80, which is a while after the virus pattern has stabilized itself into oscillators. We will count the number of cells at tick 80 and call that ”fitness”, even if it actually isn’t (it is a trait that affects fitness by virtue of the fact that we select on it). We will allow the top half of the population to produce two offspring each, thus keeping the population size constant at 100 individuals.

## Calculates the fitness of an individual at a given time
get_fitness <- function(board_matrix, time) {
board_matrix %>% tick(time) %>% sum
}

## Develop a generation and calculate fitness
grow <- function(generation) {
generation$fitness <- sapply(generation$board, get_fitness, time = 80)
generation
}

## Select a generation based on fitness, and create the next generation,
next_generation <- function(generation) {
keep <- order(generation$fitness, decreasing = TRUE)[1:50] new_generation <- list(board = vector(mode = "list", length = 100), fitness = numeric(100)) ix <- rep(keep, each = 2) for (i in 1:100) new_generation$board[[i]] <- generation$board[[ix[i]]] new_generation$board <- lapply(new_generation$board, mutate, mutation_rate = mu) new_generation } ## Evolve a board, with mutation and selection for a number of generation. evolve <- function(board, n_gen = 10) { generations <- vector(mode = "list", length = n_gen) generations[[1]] <- list(board = vector(mode = "list", length = 100), fitness = numeric(100)) for (i in 1:100) generations[[1]]$board[[i]] <- board
generations[[1]]$board <- lapply(generations[[1]]$board, mutate, mutation_rate = mu)

for (i in 1:(n_gen - 1)) {
generations[[i]] <- grow(generations[[i]])
generations[[i + 1]] <- next_generation(generations[[i]])
}
generations[[n_gen]] <- grow(generations[[n_gen]])
generations
}


Let me now tell you that I was almost completely wrong about what happens with this pattern once you apply selection. I thought that the initial pattern of nine stable blocks (36 cells) was pretty good, and that it would be preserved for long, and that virus-like patterns (like the first animation above) would mostly have degenerated around 80. As this plot of the evolution of the number of cells in one replicate shows, I grossly underestimated this pattern. The y-axis is number of cells at time 80, and the x-axis individuals, the vertical lines separating generations. Already by generation five, most individuals do better than 36 cells in this case:

As one example, here is the starting position and the state at time 80 for a couple of individuals from generation 10 of one of my replicates:

Here is how the average cell number at time 80 evolves in five replicates. Clearly, things are still going on at generation 10, not only in the replicate shown above.

Here is the same plot for the virus pattern I showed above, i.e. the blocks but with one single added cell, fixed in the starting population. Prior genetic architecture matters. Even if the virus pattern has fewer cells than the blocks pattern at time 80, it is apparently a better starting point to quickly evolve more cells:

And finally, out of curiosity, what happens if we start with an empty 30 x 30 board?

Not much. The simple still life block evolves a lot. But in my replicate three, this creature emerged. ”Life, uh, finds a way.”

Unfortunately, many of the selected patterns extended to the edges of the board, making them play not precisely the game of life, but the game of life with edge effects. I’d like to use a much bigger board and see how far patterns extend. It would also be fun to follow them longer. To do that, I would need to implement a more efficient way to update the board (this is very possible, but I was lazy). It would also be fun to select for something more complex, with multiple fitness components, potentially in conflict, e.g. favouring patterns that grow large at a later time while being as small as possible at an earlier time.

Code is on github, including functions to display and animate boards with the animation package and ImageMagick, and code for the plots. Again, the blocks_selection.R script is slow, so leave it running and go do something else.

# Toying with models: The Luria–Delbrück fluctuation test

I hope that Genetics will continue running expository papers about their old classics, like this one by Philip Meneely about Luria & Delbrück (1943). Luria & Delbrück performed an experiment on bacteriophage resistance in Escherichia coli, growing bacterial cultures, exposing them to a phage, and then plating and counting the survivors, who have become resistant to the phage. They considered two hypotheses: either resistance occurs adaptively, in response to the phage, or it occurs by mutation some time during the growth of the culture but before the phages are added. They find the latter to be the case, and this is an example of how mutations happen irrespective of their effects of fitness, in a sense at random. Their analysis is based on a model of bacterial growth and mutation, and the aim of this exercise is to explore this model by simulating some data.

First, we assume that mutation happens with a fixed mutation rate $\mu = 2 \cdot 10^{-8}$, which is quite close to their estimated value, and that the mutation can’t reverse. We also assume that the bacteria grow by doubling each generation up to 30 generations. We start a culture from a single susceptible bacterium, and let it grow for a number of generations before the phage is added. (We’re going to use discrete generations, while Luria & Delbrück use a continuous function.) Then:

$n_{susceptible,i+1}= 2 (n_{susceptible,i} - n_{mutants,i})$

$n_{resistant,i+1} = 2 (n_{resistant,i} + n_{mutants,i})$

That is, every generation i, the mutants that occur move from the susceptible to the resistant category. The number of mutants that happen among the susceptible is binomially distributed:

$n_{mutants,i} \sim Binomial(n_{susceptible,i}, \mu)$.

This is an R function to simulate a culture:

culture <- function(generations, mu) {
n_susceptible <- numeric(generations)
n_resistant <- numeric(generations)
n_mutants <- numeric(generations)
n_susceptible[1] <- 1
for (i in 1:(generations - 1)) {
n_mutants[i] <- rbinom(n = 1, size = n_susceptible[i], prob = mu)
n_susceptible[i + 1] &lt;- 2 * (n_susceptible[i] - n_mutants[i])
n_resistant[i + 1] &lt;- 2 * (n_resistant[i] + n_mutants[i])
}
data.frame(generation = 1:generations,
n_susceptible,
n_resistant,
n_mutants)
}
cultures <- replicate(1000, culture(30, 2e-8), simplify = FALSE)


We run a few replicate cultures and plot the number of resistant bacteria. This graph shows the point pretty well: Because of random mutation and exponential growth, the cultures where mutations happen to arise relatively early will give rise to a lot more resistant bacteria than the ones were the first mutations are late. Therefore, there will be a lot of variation between the cultures because of their different histories.

combined <- Reduce(function (x, y) rbind(x, y), cultures)
combined$culture <- rep(1:1000, each = 30) resistant_plot <- qplot(x = generation, y = n_resistant, group = culture, data = combined, geom = "line", alpha = I(1/10), size = I(1)) + theme_bw()  We compare this to what happens under the alternative hypothesis where resistance arises as a consequence of introduction of the phage with some resistance rate (this is not the same as the mutation rate above, even though we’re using the same value). Then the number of resistant cells in a culture will be: $n_{acquired} \sim Binomial(2^{29}, \mu_{aquried})$. resistant <- unlist(lapply(cultures, function(x) max(x$n_resistant)))

acquired_resistant <- rbinom(n = 1000, size = 2^29, 2e-8)

resistant_combined <- rbind(transform(data.frame(resistant = acquired_resistant), model = "acquired"),
transform(data.frame(resistant = resistant), model = "mutation"))

resistant_histograms <- qplot(x = resistant, data = resistant_combined,bins = 10) +
facet_wrap(~ model, scale = "free_x")


Here are two histograms side by side to compare the cases. The important thing is the shape. If the acquired resistance hypothesis holds, the number of resistant bacteria in replicate cultures follows a Poisson distribution, because it arises when one counts the number of binomially distributed events that occur in a given number of trials. The interesting thing about the Poisson distribution in this case is that its mean is equal to the variance. However, under the mutation model (as we’ve already illustrated), there is a lot of variation between cultures. These fluctuations make the variance much larger than the mean, which is also what Luria and Delbrück found in their data. Therefore, the results are inconsistent with acquired mutation, and hence the experiment is called the Luria–Delbrück fluctuation test.

mean(resistant)
var(resistant)
mean(acquired_resistant)
var(acquired_resistant)


Literature

Luria, S. E., & Delbrück, M. (1943). Mutations of bacteria from virus sensitivity to virus resistance. Genetics, 28(6), 491.

Meneely, P. M. (2016). Pick Your Poisson: An Educational Primer for Luria and Delbrück’s Classic Paper. Genetics, 202(2), 371-375.

# Gruppselektion fungerar, men är det viktigt?

Det här kommer bara vara roligt för dem som redan bryr sig om gruppselektion, men de är förvånansvärt många. Av någon anledning är gruppselektion väldigt provocerande. Ordet ”selektion” är en omskrivning för naturligt urval. Naturligt urval händer när vissa individer i en population har egenskaper som gör dem bättre på att överleva och fortplanta sig än andra. Om egenskaperna ifråga är ärftliga gör det att populationens egenskaper ändras över generationerna. Detta är evolution genom naturligt urval. De genetiska varianter som får individer att klara sig bättre ökar i frekvens. Men tänk om populationen består av grupper av individer som lever särskilt nära varandra. Kan det finnas egenskaper hos en grupp som gör den framgångsrik och som inte kan förklaras av selektion på individer? Ja, det fullt möjligt. Frågan är hur viktigt det är i naturen.

Organismer gör vanligtvis inte saker för populationens, artens eller gruppens skull. De gör saker för sig själva och sin avkomma. Men det finns många situationer där det är lönsamt, alltså förknippat med större reproduktiv framgång, att samarbeta, hjälpa andra och bete sig altruistiskt. Det är ganska tydligt varför det kan vara fördelaktigt för en individ att hjälpa sina ungar. De bär ju på hälften av ens genetiska material! Vi tänker oss en art där ungarna behöver omvårdnad medan de är små. Där kan en genetisk variant som ökar föräldrabeteendet sprida sig, eftersom den ger bäraren fler överlevande ungar, där i medeltal hälften i av dem kommer bära på samma variant. Samma resonemang fungerar för mer avlägsna släktingar, bara i mindre grad, eftersom sannolikheten att vi delar genetiska varianter blir mindre ju längre från varandra i släktträdet vi befinner oss. Detta kallas släktskapsselektion (engelska: kin selection), att förbättra sin reproduktiva förmåga indirekt genom släktingar. Tyvärr är det ett ganska uselt namn, eftersom det är ett namn på en typ av strategier, inte en egen form av selektion. Ett annat namn för samma sak är inclusive fitness, men det är typ omöjligt att översätta till något vettigt.

Det finns en lång lista med möjliga sätt som altruism kan löna sig i längden (se t.ex. West, Griffin & Gardner 2006). Det kan handla om att hjälpa sina släktingar, som ovan, eller att byta tjänster och gentjänster, eller min favorit: grönt skägg-altruism. Det är en situation där vi tänker oss en genetisk variant som har två olika effekter. Å ena sidan får den individen att bete sig altruistiskt mot individer som har ett visst kännetecken, hypotesens ”gröna skägg”. Dessutom får den individen själv att odla ett grönt skägg, alltså uttrycka samma signal. På så sätt kan den sprida sig genom att bärarna känner igen och hjälper varandra.

Så sociala interaktioner och altruism är inga stora mysterier som helt saknar förklaringar. Men att det inte verkar finnas ett skriande teoretiskt behov av gruppselektion betyder inte att effekter på gruppnivå inte finns. Låt oss därför ta ett exempel där selektion på gruppnivå utan tvivel fungerar och påverkar egenskaper. Naturligtvis kommer exemplet från artificiell selektion, inte naturligt urval, och det handlar om höns. En första version av experimentet ifråga beskrivs av William Muir (1996). Höns är inte riktigt anpassade för ett liv i industriell uppfödning. Ett vanligt problematiskt beteende är att hönsen hackar varandra, i värsta fall till döds. Det här experimentet gick ut på att försöka avla dem för att klara sig bättre i gruppburar med flera höns — utan att klippa i deras näbbar, vilket knappast löser problemet för hönsen men hindrar symptomen … Näbbtrimning är förbjudet bland annat i Sverige. Muir avlade höns på överlevnad i gruppburar, där invånarna i en bur valdes eller valdes bort tillsammans som en grupp. I generation 2 var dödligheten 70%. Jag upprepar: på ett år dog 70% av hönsen. I generation 6 var dödligheten 9% procent, vilket är samma dödlighet som kontrolldjur som hölls ensamma.

En stor del av dödligheten förklaras av hur mycket individen blir hackad. Det kan såklart finnas genetiska varianter som skyddar offer mot fjäderhackning, men det viktigaste för individens överlevnad är inte hur mycket den själv hackar utan hur mycket de andra hackar. Det här fenomenet, när en individs egenskaper påverkas av vilka genetiska varianter som finns hos dem hen interagerar med, kan beskrivas med indirekta genetiska effekter. Indirekta genetiska effekter är en mekanism för hur gruppselektion kan fungera. Okej, men vad hade hänt med vanlig avel på individuell nivå? I ett liknande experiment, med höns i gruppburar, tittade författarna (Bijma & co 2007) på direkta och indirekta genetiska effekter på överlevnad. Jag har skrivit om heritabilitet förut, ett mått på hur stor del av variationen i en egenskap som beror på genetisk variation. Den kan skattas med en statistisk modell (se t.ex. Kruuk 2004) där en lägger samman mätningar och släktträd från ett antal individer och uppskattar hur stor del av egenskapen som går i släkten. Bijma & co använde en utökad version av samma modell som också tar hänsyn till effekten av andra gruppmedlemmar och deras släktträd. Det ger dels en vanlig direkt genetisk varianskomponent, den som används till heritabilitet, och en total varians som räknar med påverkan från de andra gruppmedlemmarna. I det här fallet var den totala genetiska variansen för överlevnad ungefär tre gånger så stor som den direkta genetiska variansen. Det intressanta med genetisk varians i avelssammanhang är att den visar hur snabbt en population kommer påverkas av selektion. I den här populationen bör alltså gruppselektion vara betydligt effektivare än individuell selektion i att minska dödligheten. I princip är det möjligt att ha en direkt och indirekt genetisk effekt i motsatt riktning, där selektion på individ och grupp skulle ge motsatta resultat.

Så långt hönshuset. Kan något liknande hända i naturen? Nyligen kom det en artikel (Pruitt & Goodnight 2014) som hävdar att de sett lokal anpassning på gruppnivå hos spindlar av arten Anelosimus studiosus. Spindlarna lever i kolonier där individerna kan klassificeras i två olika beteendetyper: lugna och aggressiva spindlar. Beroende på hur mycket resurser det finns i omgivningarna har naturliga kolonier olika sammansättning. Så författarna samlade in spindlar från olika ställen, födde upp dem i laboratoriet, testade deras beteende och satte ut dem igen i konstruerade kolonier med olika gruppsammansättning. Sedan kom de tillbaka med jämna mellanrum för att se hur bra experimentkolonierna klarade sig. Kort och gott löpte kolonierna större risk att dö ut om deras sammansättning inte matchade sammansättningen hos naturliga kolonier på den platsen. Det verkar som att på vissa platser är det bra att ha många aggressiva spindlar i en koloni, på andra färre, och om en koloni har för många eller för få kommer den klara sig sämre. I rika omgivningar med mycket att äta verkar det fungera bättre att ha många aggressiva individer. I fattigare omgivningar är det bättre med många lugna.

(A. studiosus av Joe Lapp, på Flickr. cc:by 2.0)

Beteendetyperna, ”lugn” och ”aggressiv” verkar i det här fallet vara till största del bestämda av genetiska varianter. Så frågan är: Vilka interaktioner mellan individer inom kolonin är det som gör att en koloni får en viss sammansättning? Någonting verkar det vara i alla fall, för författarna prövade också att flytta kolonier mellan rik och fattig miljö. Och det ser ut som att kolonier behåller sin karaktäristiska sammansättning över generationerna. Spindlar som kommer från en fattig miljö fortsätter hålla en låg andel aggressiva individer i sina kolonier, även om det vore bättre för dem att ha fler. De verkar vara lokalt anpassade till en resursfattig miljö, där en låg andel aggressiva spindlar hade fungerat bättre.

Oftast det såklart så att de en lever närmast ofta också är de en är närmast släkt med. Så om släktskapsselektion och gruppselektion händer samtidigt kommer det vara svårt eller omöjligt att skilja dem åt. Att jag har svårt att komma på hur en alternativ förklaring med släktsskapsselektion skulle se ut i fallet spindlarna kan bara vara min bristande fantasi. Det är populärt att påstå något i stil med ”gruppselektion och släktskapsselektion är samma sak” av matematiska skäl. Men bevisen för att de bara är beskrivningar av samma process verkar inte vara entydiga. van Veelen m.fl. (2012) ger ett motexempel på en modell där de inte ger samma resultat. Jag kan inte påstå att jag förstår den teoretiska litteraturen på det här området, men att modeller av gruppselektion och av släktskapsselektion är bevisat matematiskt ekvivalenta verkar vara för mycket sagt.

Litteratur

West, S. A., Griffin, A. S., & Gardner, A. (2007). Social semantics: altruism, cooperation, mutualism, strong reciprocity and group selection. Journal of evolutionary biology, 20(2), 415-432.
Bijma, P., Muir, W. M., Ellen, E. D., Wolf, J. B., Van Arendonk, J. A. (2007). Multilevel selection 2: estimating the genetic parameters determining inheritance and response to selection. Genetics, 175(1), 289-299.
Kruuk, L. E. (2004). Estimating genetic parameters in natural populations using the ‘animal model’. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 359(1446), 873-890.
Nature.