Monday, October 28, 2013

Marxist Cribbage

This post does not require any knowledge of ecology, evolution, or science in general. It instead requires - or at least benefits from - knowledge of the card game Cribbage. If you lack such knowledge and are interested, you can check out this site. It is a truly great game.

Cribbage was my Dad's favorite card game - by far. He even wrote a wonderful short story The Unplayed Card about his alter-ego, Scruffy MacChubb, caught up in a cribbage tournament in a remote BC community. Scruffy makes it all the way to the finals and, as a stranger in the community, risks alienating the entire town if he were to win. So he throws the final hand of the final game by playing a suboptimal card that allows the town favorite, Sandy, to win the tournament instead.

The crowd dissolved in cheers and applause. Sandy clasped his hands as if in prayer. His wife rushed to his side and hugged him as if to break him in two. The small crowd pressed around him anxious to shake his hand. The native son had come through. The coveted trophy would stay where it belonged and not go to a stranger. Sandy broke away from the well-wishers and came to where Scruffy was still sitting at the table. "I want to buy you a drink," he began. "I've never met a better player. It's a tradition, the winner buys the second place player a beer. Come on. It will be an honor." Scruffy smiled at Sandy and got up from his chair. "I could sure use a cold beer right now." Sandy's fans immediately began slapping Scruffy on the back and vying for the opportunity to buy him a second cold beer. Scruffy allowed himself to be swept away toward the bar.

Of course, Scruffy instilled a love of cribbage in his sons and so, on our yearly steelhead fishing pilgrimage to our family cabin in BC, we always play cribbage. Sometimes we play the two person version and sometimes the four person version. On this last week's trip, however, there were five of us. What to do when five need to play? Improvise, which led us inevitably to the invention of Marxist Cribbage.

The rules of Marxist Cribbage are the same as regular cribbage, except for the following:
  1. Deal 6 cards to each of 4 people – the “comrades.” The person not dealt to is the person with highest score at the time (that is, the person who is leading) – the “bourgeoisie.”
  2. The comrades each give one card (face down) to the bourgeoisie (becomes his/her hand) and one card to the crib.
  3. The crib then goes to the person with the lowest score – “the commissar.”
  4. The crib is always counted last. That is, even if the commissar earlier counted his hand, he has to count his crib after all others have counted their hands.
  5. All five players play independently and separately count their scores. This is done by using multiple color pegs per lane on the crib board.
  6. When someone first exceeds 120 points (and would therefore “win”) all other players also get to count their hands (and the crib) – thus leading to the possibility of multiple possible “winners.”
  7. The bourgeoisie and the commissar on the first hand are chosen by turning over cards – in the same manner as the first dealer is determined.
The Marxist Cribbage Conclave at Corral Creek, Kispiox River
(Scot Hooker, Ross Hooker, Brad Anholt, and Art Yeates - photo by Andrew Hendry)
In our first implementation of this game - and one was enough - Marxist Cribbage led to everyone winning - and thus, I guess, everyone losing. I never had an opportunity to play Marxist Cribbage with Scruffy but I expect he would not have approved of our rule changes. Perhaps he would find encouragement, however, in the fact that it kept the five of us buying each other cold beers for the rest of the evening while the stars glittered outside and the steelhead in the river below girded themselves for the next day's battle.

Andy Hendry (aka Scruffy MacChubb)
b. Feb. 9, 1939; d. Oct. 24, 2013

Thursday, October 24, 2013

The spatial patterns of directional phenotypic selection

Alas! Unlike the previous post by Joost, I cannot say that this will be the next blockbuster Hollywood script. Just a recap of another Ecology Letters article (Siepielski et al., 2013). So mundane. I know. Anyways, on to science!

The principal underlying process driving adaptive divergence, and thus ecological speciation, is selection. Local adaptation occurs among populations, often in response to directional selection imposed by abiotic and biotic factors. Since 1983, when Lande and Arnold presented a standardized method to estimate selection, there have been thousands of studies that have estimated selection, and recent meta-analyses have looked at how selection varies temporally within populations. However, we lack a comprehensive understanding of the spatial variation in selection among populations that might drive adaptive divergence. Is there actually spatial variation in selection, or is all such observed variation actually due to sampling error? If there is ‘real’ spatial variation, how does selection vary: in its strength, its direction, or both? Is the variation enough to advance local adaptation? These questions were the motivation for our recent article, published in Ecology Letters.

Wordle of the article body. Just because. And wouldn't you know it, the largest word is selection!

My colleagues and I reviewed the literature for studies that had spatial replicates of selection estimates among at least two populations. We focused on selection on continuous phenotypic traits in un-manipulated wild populations, and found 60 studies that met our requirements. The first thing we noticed was a geographical bias in spatially replicated estimates of selection: the majority of the estimates are in temperate regions of the northern hemisphere, centred at about 40° latitude.

Figure 1 from the article. Gradients in blue, differentials in red.

Using multivariate models proposed by Morrissey and Hadfield (2012), we analyzed directional selection estimates. There is a signature of spatial variation in selection, even after correcting for sampling error. In other words, after we account for within-study sampling error, about 12% of the variation in selection we observe is due to real spatial variation in selection among populations.

So spatial variation in selection among populations is real, but what are the characteristics of this variation? Does it vary more in direction? Does it vary more in strength? Understanding these types of dynamics is important, especially when it comes to understanding adaptive divergence. Differences in the direction of selection among populations are important for two reasons: (1) differences in direction could mean divergent selection among the populations, and (2) a more rugged fitness landscape could be envisioned in this case, also important for divergent selection. On the other hand, variation in strength, but not direction, of selection could mean that populations are at various stages of becoming locally adapted, or could represent some kind of genetic constraint among populations.

So what did we find? There was variation in the direction of selection among populations, but where there were differences in direction, the selection estimates were of relatively small magnitude. It appears that more of the spatial variation observed among populations is in the magnitude, or strength, of selection, and not in the direction of selection. We posit three possible reasons for this. First, the selection estimated could be in response to shared environmental factors among populations. Second, variation in strength could be present due to different starting population phenotypic means. In other words, two populations might be subject to the same fitness function, but if their starting, mean phenotypes are different, then there will be variation in the strength of selection toward whatever local or global optimum is being approached. Lastly, gene flow could also have an effect. Gene flow can either facilitate or hamper adaption, depending on whether the gene flow is coming from populations of similar or dissimilar selective regimes; either way, it can affect the strength of selection observed in a population.

One of the things my co-authors and I really wanted to look at was the spatial structure of selection. Does selection vary in a spatially autocorrelated fashion (such as a gradient in the phenotypic optimum across space), or is it more patchy, or mosaic-like in its structure? Unfortunately, we could not do a formal analysis for three reasons. The first reason is that there was the lack of spatial replication (the mode number of population replicates was 2). Second, many studies used a small sample size, which produced excessive sampling error for such an analysis. Third, the populations were not always randomly selected populations, and were instead selected intentionally because of some kind of contrast among the populations, which would bias our analysis.

The magnitude of spatial variation in selection we found is comparable to that of temporal variation in selection within populations (Siepielski et al., 2009; Kingsolver et al., 2012; Morrissey & Hadfield, 2012). However, interpreting this comparison must be done with caution for several reasons. As mentioned above, populations are not always selected randomly, and this might affect the detection spatial variation more than the detection of temporal variation in selection. Ideally, we would have access to several studies that have multiple spatiotemporally replicated selection estimates, but not a lot of studies do that.

So, folks: that is what we need! More spatiotemporally replicated studies of selection in naturally occurring populations – particularly studies NOT near 40°N latitude. Don’t forget to report your standard errors, and if you do gamma estimates, don’t forget to double them (Stinchcombe et al., 2008)! Happy selection estimating!

The article (F1000 Prime recommended!):

Siepielski AM, Gotanda KM, Morrissey MB, Diamond SE, DiBattista JD, Carlson SM. 2013. The spatial patterns of directional phenotypic selection. Ecology Letters 16: 1382-1392, doi: 10.1111/ele.12174

Kingsolver J, Diamond S, Siepielski A, Carlson S. 2012. Synthetic analyses of phenotypic selection in natural populations: lessons, limitations and future directions. Evolutionary Ecology: 1-18.
Lande R, Arnold SJ. 1983. The measurement of selection on correlated characters. Evolution 37: 1210-1226.
Morrissey MB, Hadfield JD. 2012. Directional selection in temporally replicated studies is remarkably consistent. Evolution 66: 435-442.
Siepielski AM, DiBattista JD, Carlson SM. 2009. It's about time: the temporal dynamics of phenotypic selection in the wild. Ecology Letters 12: 1261-1276.
Stinchcombe JR, Agrawal AF, Hohenlohe PA, Arnold SJ, Blows MW. 2008. Estimating nonlinear selection gradients using quadratic regression coefficients: double or nothing? Evolution 62: 2435-2440.