Jenn has sent a couple of emails in response to last spring’s work:
September 29
Here’s some feedback on thhe Key Results (from June). More on Monday!
Silique number does not seem to be a good proxy for the number of seeds actually released (e.g., p. 153)
I’m not sure where to go with this. Seems like there could be several explanations - either the siliques opened with a lot of variability, there’s more variation in seeds/silique than we estimated, or some seeds are much more viable than others.
Both seed production and per-generation spread varies among generations – potentially from seasonality or from variation in protocol
this is not surprising given that the greenhouses don’t regulate temperature and light perfectly, and there is more light in the summer, but it can also be really hot then and sometimes plants may not have gotten quite enough water. I don’t think there was any variation in the protocol, but there could of course have been some differences (i.e. accidents) between generations
Within a generation, there is variation among runways in seed production – presumably from location effects within the greenhouse. Variation among pots within a runway is much less, and is consistent with a kind of demographic stochasticity
this surprised me. Not the demographic stochasticity, but the location effects – these could come from either their location in the growing chambers (some variation in water availability and light, and although the pots were moved around a bunch when the seedlings were small, they pretty much stayed put once they really started growing and bolting) or from their variation in the runways, and how that interacts with air currents in the greenhouse.
After accounting for generation effects, there is negative autocorrelation in per-generation spread in some of the treatments. This need further investigation–it might be about getting to the stable distribution, but it also might be that an exceptionally long-distance spread event probably has a single seed in the furthest pot, which produces fewer seeds to disperse the next generation.
this seems like the most interesting part!
I will read through the notebook entries first thing Monday and send more feedback then. I remember now that you ended the notebook with a strategy for the paper - I will start there! Maybe I can be the most helpful there. Seems good to solidify the strategy and the questions to ask before you dive back into the weeds of the analyses.
October 2
I’ve spent some more time now thinking about your notes from May 1 and June 7.
I have a few comments below, but I think it might be most efficient to just have a chat over Skype, because some of your ideas were clearer to me than others as written. This week, I’m free on Thursday from 12:30 - 2 or on Friday from 2:30 - 4:15. (or Wednesday morning between 9 - 11:45 is also possible).
What I sent is a raw “lab notebook” so not surprising that it’s hard to follow. I’d start with the “key results” below, and then look at the final entry (7 June); the latter has cross references back to the supporting analyses, if you want to look into details. The May 1 entry might also be useful.
There are quite a few empirical questions that I posed on May 1 that I didn’t yet address; since I tend to get easily lost in the weeds on data analysis I’ve decided to focus on fitting/simulating a “clean” model that can be compared with some of the patterns I’ve already identified. But if you see empirical questions that you think might be of interest you can highlight them.
I agree that it will be easy to get lost in the weeds on the data analysis in a way that isn’t really helping progress toward answering the bigger picture questions. Seems like there’s a balance to strike between being able to explain the variability we observed and also being helpful/generalizable to other systems.
To me the most interesting ones are 10 - 12 (and you’ve already addressed 10/11).
Some of the others, I have explored (i.e. height vs. siliques) and some we probably don’t have enough data for (silique number vs. seed number - it turned out to be way harder to count seed numbers than we expected so we don’t have much data on this).
Other than that, comments on the meaning/utility of the observations in the final entry would be helpful, along with thoughts on the “strategy for a paper.” Note that for the latter, we don’t need to do the “simple model of stochastic spread” as Neubert/Kot/Lewis have already shown that stochastic integro-difference models generate a linear increase in var(cumulative spread).
Comments on the paper strategy:
In terms of what others have done to quantify variability, not so much (as you note), and for example Melbourne & Hastings ended up with a ton of unexplained variation despite trying to predict it. I can send a summary later of what I took away from my reading. Other papers without evolution include a lot of work in protists by Emanual Fronhofer and Florian Altermatt (and a PhD student Renato Giametto), the yeast system (Gandhi et al 2016, PNAS, from the Gore lab), this Goldwasser et al. 1994 paper (that might have some kernel of help, but is also tangential).
The original motivating question you posed, “What are the drivers of variation in spread rate, and are they predictable?” is one that I still find interesting, although I struggled to remember what you intended by the predictable part (through time? across systems? etc.).
I think this motivates bullets 1 & 2 (in the in this paper, we will do 3 things…).
I think bullet 3: about how evolution might make spread more or less predictable is one that I think is a much bigger question that is beyond the scope of this paper. (what Tom & I proposed with the BIRS group and will pitch to CIEE, and we might write a TREE paper this fall if our pitch gets accepted where we detail all the hypotheses - there are numerous ones and certainly both some theory along with lots of numerical simulations will be necessary to answer them.)
Sounds like you’re juggling lots of things this term as well. I would lobby for writing the most interesting, but also most straightforward/simplest story (i.e. ignoring a lot of the evolution) would mean that this paper might get written sooner rather than later. And there will be plenty of time in the future to go further (and a ton of people who are interested in pursuing the evolution/variability question).
Comments on your further observations:
Number of home pot seedlings declining through time is probably because of algae build up, and presumably other pathogens/fungi/pests that got passed from one generation to the next in the scraping of the surface (despite trying to minimize this). I wondered if that also could have contributed to the decelerating trend in continuous runways, although it shouldn’t affect what’s happening at the front. There could be maternal effects that we don’t understand very well that contribute as well.
We don’t have enough repetition in seasonality to do anything much with the timing data (and this is dipping back into the weeds, but the attached file shows those dates, for whatever they’re worth. Thinning is not relevant since we dropped treatment A data.)
You note that variance seems to even out in the evolution experiment. The simple explanation is that the one or two genotypes were ‘fixed’ at the leading edge of each runway. However, given how much variation we observed with just one genotype in the other experiment, maybe this is less satisfying.
I found it odd/surprising that seedling production is independent of silique number among the solitary plants. I don’t have much intuition for how to interpret this result.