Climate change as a biological accelerator

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Or, how leafout is like driving to grandma’s house. Or, how a 90 minute fake data simulation solved a problem my lab had spent over 3000 hours on. Or, why did almost none of my co-authors like my sentence about how ‘climate change steps on the biological accelerator’?

Or… wait for it — crows are black because crows are black.

This post is by Lizzie and it’s about a paper I wrote with Andrew, Jonathan Auerbach, Cat Chamberlain, Dan Buonaiuto, Ailene Ettinger and Ignacio Morales-Castilla on one explanation for why biological responses to temperature are declining in recent decades. If you’re most interested in the paper, I suggest you just read the paper as it’s much shorter than this post (1100 versus 2100 words). This post travels through the paper’s origins (including fake data simulation!) and its trip through the friendly and peer review process, with a quick overview of the paper’s findings too.

About six years ago, a paper was published called `Declining global warming effects on the phenology of spring leaf unfolding,’ which led to lots of excitement in my tiny field of plant phenology (for North American readers: phenology is the timing of recurring life history events, such as leafout, flowering, when birds lay eggs etc.).

The paper showed that what we call a `temperature sensitivity’ (change in days per degree of temperature, as measured by linear regression) was getting smaller in magnitude recently. For example, if back in the 1980s birch tree leafout would advance 5 days per 1 degree of temperature increase, today it might be just 4 days per degree. If the trend continued, someday trees’ leafout would stand still in time perhaps, or maybe reverse and start leafing out *later* in warmer years.

I was at a meeting in Turkey reading through the supplement trying to figure what could be up with the paper. I am always worried about time-series analyses, and especially using the data they did (PEP 725) which varies in quantity and location over time. But I didn’t find anything obvious and when I talked to my colleague, Mark Schwartz, he knocked out a few additional hypotheses I had.

The biological hypothesis for this effect was obvious to everyone in the field, and laid out in the paper: temperate plants’ leafout generally responds strongly to spring temperatures and that has been the dominant controller on leafout. But, underneath the hood, plants also cue to daylength and winter cool temperatures (`chilling’); someday, if spring warming comes so early that the days are really short, or if chilling gets too low, then plants will wait a little until they leafout. And this will lead to a smaller (in magnitude) temperature sensitivity. Functionally, the biology currently suggests that with short days or low chilling plants will require more spring warming to leafout; this higher required spring warming is the most proximate delay of leafout, with chilling or daylength causing the higher threshold.

This was all well known from experiments. For decades (centuries probably), biologists have been taking dormant tree branches in the winter and putting them in little boxes where we can set light and temperature to different amounts to test and re-test this model. It’s effectively a fancy version of bringing in pussy willows to your warm house in the spring, except imagine you put some in the window, some in a cool corner, some in a warm corner etc..

At about this time, I was actually starting a meta-analysis of such experiments to estimate the effects across species of spring warming, winter cool and daylength, and about four years later was scratching my head when the results didn’t jive with the declining sensitivity paradigm in the field. And at this point a good number of high profile papers had documented this effects (here’s just a couple from PNAS, and  Nature Climate Change). Working with some excellent folks in my lab (four of the co-authors listed) we’d been taking the model from our meta-analysis and checking what it predicted for regions seeing declining sensitivities, and we could not match predictions of `declining sensitivities’ unless we warmed up the world 4C or higher (it’s warmed about 1 to 2 C in Europe). Staring again at the underlying observational data I realized that a 1 degree warmer day when it’s cool is not the same as a 1 degree warmer day when it’s warmer.

Makes total sense, right?

No, it probably doesn’t and that’s about where I was for a bit. I quickly wrote up simulations that showed my hunch could be correct, but I struggled to explain what was going on. I spent a while calling it a ‘non-stationarity in the unit of day’ issue.

And around then, in pre-Covid times, I swung through New York in a land where people used to hang out in the their offices, grad students in stats even used to offer in-person open sit-down-here-next-to-me-and-tell-me-your-statistical-troubles stats advice hours. I spent a while explaining my model to Andrew as simply as I could, explaining what is often called the ‘bucket model’ of leafout: plants need a certain amount of spring warming to fill the bucket, when the bucket is full, the plant leafs out. With climate change, days are a little warmer, so they fill the bucket more each day — so if you use a metric, such as temperature sensitivity, with day in the denominator, then it has to go down as the world warms even though plants require the same thermal sum to leaf out (are you getting my ‘non-stationarity in the unit of day’ yet?). The whole thing works without ever invoking daylength or winter temperatures (chilling). I was wobbling through this explanation — I had a couple cobbled together graphs about the underlying effect of temperature on plant development, and then the ‘bucket model’ and then connecting back to the linear regression, all of which I was dragging Andrew through in the lounge of the stats department.

When he left to get something in his office I wandered over to open office hours (also in the lounge of the stats department) to chat with Jonathan Auerbach, who is great fun to work with, and started dragging him through my problem. Andrew returned and we started de novo coding my simulation code (of course much nicer, since Jonathan wrote it). However, while I generally pegged my simulation code to a smaller (more realistic) range, Jonathan wrote up his to cover a big range of temperatures — 5 to 30 C.

As the simulated data showed up on the screen both Andrew and Jonathan had the eureka moment — “any process observed or measured as the time until reaching a threshold is inversely proportional to the speed at which that threshold is approached.”

Getting to leafout is just like driving grandma’s house, as Andrew explained it. In this case, day of leafout is akin to how long it takes to get to grandma’s house, and temperature is akin to average speed: the relationship is inherently non-linear so comparing the effect of 1 degree warming at different points along the speed (temperature) axis will give different slopes. We all know that if you drive at 50 miles per hour, driving 5 miles per hour (10%) faster will have far less of an effect on your arrival time than if you were driving at 10 miles hour and drove 5 miles (50%) faster.

But somehow I, and most everyone in my field, did not see this connection.

Instead we felt intuitively (and damn strongly if you ask me) that the slope should be constant. If you ask people about the underlying model, they will mention it’s a threshold process, so we all seemed to agree on that, but also felt strongly that using a linear model was fine. We also have a strong intuition about what should happen to the slope of a linear regression if you raise that threshold (the way short days or low winter chill should) — it should go down in magnitude. But all these intuitions are just plain wrong. I fell victim to them like everyone else.

What’s been interesting to me is how hard it’s been to get people to question that intuition. In our paper we don’t say this is definitely the cause of declining sensitivities, as we don’t know. We do state that it’s a simple explanation for it, based on the biological model we all claimed to agree on. And we did suggest a pretty simple correction to try — just log your data before you run your linear regression (and we showed that logged data did not show any sign of a declining sensitivity). But we still got a lot of fascinating responses when sending the paper out to review. While some jumped on board, at least half did not, and many of them seemed to jump up and down beside the boat demanding we all stay with them on the land.

I was surprised how much folks dug in. Here’s some of the most common responses:

  1. Mainly I found people came up with new models we should try that would show the declining sensitivity: these included trying a shifting window to `find’ the best temperature window (aka, highest correlation), decreasing winter chill that drives a higher spring warming threshold. We’ve basically done all of these and only recreated declining sensitivities with extreme effects of daylength. The rest of the models don’t produce it (even though I get that we all feel they should). And even then the log estimates picked up the change more clearly than a linear model.
  2. Many folks did not like that we suggested a log transformation (one reviewer wrote, “why this particular data transformation was used is not apparent. There are many other data transformations that could have been used as alternatives, and these could be explored for how they would affect the results”) even though the log is the natural transform of an inverse, which we wrote. I never fully got a good explanation for this. It seems a weird response to me coming from biologists. But it seemed often to go with ideas for a new model (my previous point).
  3. Multiple reviewers said that we only did the analysis for two of the original seven tree species in Fu et al. 2015 paper and thus our analysis was uncompelling. (True! I was too lazy to fit the type of thoughtful model I would want for the uneven data for all seven species, so we just did the two with the most even data where we could hold the data constant over time and space; we tested it with another species when asked and it too showed that the declining sensitivity result went away).
  4. Lots of folks looked at the supplement and said the model we proposed was too confusing, even though it’s just the math of a simple bucket model I am otherwise told is very simple.

I tried to show people how simple the model was, sending along code:

data <- data.frame(leaf_date = numeric(0),
                   cum_temp  = numeric(0),
                   mean_temp = numeric(0),
                   threshold = numeric(0),
                   delta     = numeric(0))
threshold <- 1000 # thermal sum for leafout
for(delta in c(5, 10, 15, 20)) { # this is warming added on
    for(sim in 1:1000) {
	temp <- delta * (1:100) + rnorm(100, 0, 50)
	leaf_date <- which.min(cumsum(temp) < threshold)
	cum_temp <- sum(temp[1:leaf_date])
	mean_temp <- mean(temp[1:leaf_date])
        data <- rbind(data, data.frame(leaf_date, cum_temp, mean_temp, threshold, delta))
    } 
}

Once someone understood it, then they often would go to point 1 — they no longer thought that leafout happened after a certain thermal sum (if even they agreed strongly with that in an earlier email). It was fascinating!

I think though that my favorite reply was this one: “This MS provides a simple explanation for the observed non-linearity in biological temperature sensitivity… The MS develops a model to prove this point and it is very nicely written. Nevertheless, I found this somewhat uncompelling, because that the explanation appears to be the same as the observation (e.g. crows are black, because crows are black).”

There were also reviewers who wanted to skip over the issue we were discussing and find interesting new biology in the results. At PNAS one reviewer was adamant that we talk in depth about differences we had not deemed very different (slope of -0.17 versus -0.20, both with large uncertainty intervals).

I am happy to say the paper is finally published, and the last reviewer pointed us to this fascinating paper dating back several years, before Fu et al. 2015: “On the uncertainty of phenological responses to climate change, and implications for a terrestrial biosphere model,” which shows a MODEL that produces the declining sensitivity problem, and the reviewer asked, “If the model structure and parameters are fixed in time (suggesting the biology is also fixed), how can the temperature sensitivity change (which would imply that the biology ISN’T fixed)? Is the temperature sensitivity metric itself flawed?”

I’d like to thank Faith Jones for the artwork, my friend and colleague Caroline Tucker, for alerting me the paper was out (I wrote this post a little while ago), which she figured out via Twitter (thanks to this Tweet, thanks also to Alexa Fredston for the tweet). And I’d like to thank They Might be Giants for the paper’s theme song.

27 thoughts on “Climate change as a biological accelerator”

      • What is the proposed mechanism for the “thermal sum”? Is the plant responding to the temperature of the groundwater? It seems like the plant would use something with higher heat capacity than the air, which would allow accumulation of energy over time.

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        • This is a better question for a plant physiologist, but I think mainly just that temperature controls photosynthesis (and below that something about ATP maybe?), and some minimum temperature to get water circulating around a plant. Air temperature does seem to matter, but I think there’s still a healthy debate about that in conjunction with soil temperature (and perhaps bud temperature).

        • 40+ years ago I worked in plant physiology, so I’m out of date, but generally it is the local temperature that controls the rate of physiological processes such as photosynthesis. Up in the branches, air temperature and solar radiation will be the main controls. However, especially for deciduous plants, saps rises from the roots to support leafout (think sugar maples), so soil temperature can matter, as well.

        • I bet it is something simple like the temperature of the groundwater, soil, sap, or internal temperature of the plant rising above a threshold. Something with high heat capacity gradually rising in temperature during spring and then decreasing from fall to winter.

          As Lloyd Nosnibor says below air temperature is probably not the best proxy, since it can vary so wildly over the course of the day.

        • Actually, the thermal sum has more to do with the hypothesis that plant growth (and therefore the timing of developmental stages) is proportional to accumulated energy. Summing daily temperatures is a canonical proxy measurement for the amount of energy accumulated

        • The underlying hypothesis is that plant growth is proportional to accumulated energy. Therefore accumulating daily temperatures serves as a proxy for total energy, to predict the timing of plant development stages.

          I imagine there are probably other / better proxy measurements available, such as W/m^2/day

  2. Is it not just…1 degree is a smaller % of 65% average temp than it is of a 60% average temp, and then would result in less of a physiological change in the plant in response?l when the average temp is 65%?

    Is the grandma’s house example any different then that? I assume that it isn’t but just wanted to check.

    So then what happens to the change in physiology if you adjust the temperature change accordingly, and compare physiological changes with equivalent (increments of) changes in % of average temp?

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  3. Interesting! Correct me if I’m wrong, but to me it sounds a lot like Weber-Fechner law. I’ll probably butcher it in my attempt at paraphrasing here, but it goes something like this: “for a stimulus to keep being perceived as noticeably different, the differences need to stay constant on a relative (i.e. log) scale, rather than absolute scale.” Anyway here’s the link: https://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law

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    • That’s great! I wish I had known (then I would have added it to the paper). Without actually looking at the wikipedia page, I think it works. Basically calendar time is sort of ‘absolute’ and biological time is relative. (Does perhaps mean the Weber-Fechner law explains why us human biologists got confused on this in first place?)

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      • I don’t suppose that “leafoff” is a biological process of interest? Here in Auckland New Zealand we are a couple of weeks away from the start of spring and yet one of our apple trees still has plenty of green leaves from last summer.

        I always preferred “autumn” to “fall” – perhaps now I have some evidence to support it!

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  6. Isn’t there an additional issue to do with measurement scale, i.e. using centigrade as described, you have an arbitrary zero, so even calculating the “percentage change” in temperature would be misleading. In that sense it is not like driving to grandmother. Going from 5 to 10mph is equivalent to going from 50 to 100mph, you get there twice as fast. But 10C is not ‘twice’ 5C.

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      • Thanks Matt! I was going to say similar (this meaningful zero is part of why biologists use C).

        And also that there are definitely additional issues depending on where you are on the temperature axis; our paper provides a quick and likely imperfect fix to a complicated problem, because plants are complicated. The reality of the underlying temperature response curves of plants is non-linear — if you imagine rate of response on the y and mean temperature on the x, as best we know most plants grow much slower close to zero until some almost linear long stretch up until an optimum (20-40C) until they crash hard above the optimum (proteins denature, bad stuff goes down in the cells). We don’t know that curve well enough for most plants, but it’s definitely part of the story.

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        • I think some of the push back on using zero is coming from people who don’t spend their time doing science focusing on organisms and ecosystems.

          No, 0 isn’t absolute zero. But outside of some very specific organisms, very little respiration is going on in cells at zero. This is part of the reason scientists are so interested in planets that have liquid water on them.

          The other thing I think non-systems people don’t appreciate is that there is far too little known about the exact physiology of any specific organism, let alone a whole class of
          organisms. Using 0C as proxy for temperate plants leafing out is beyond reasonable.

          We may not know enough detail about specific plants to address Raghu ‘s statement that there is “no measure by which differences relative to 0C are proportional to one another” exactly, we certainly have enough knowledge about plants in general. As you (Lizzie) say we know there is a not a linear relationship along the whole scale of possible temperatures. And we know that inside some optimum range (which will depend on species) the rate of growth/development is somewhat linear. And then again slows down until some maximum temp at which no additional growth/development occurs. Additionally there are temperature extremes above and below which even plants and animals that are dormant will not survive. Since we don’t know the exact threshold temperatures for the periods of minimal growth and maximal growth for more than a few species of plants and animals, using a log relationship to approximate the curve seems reasonable.

          I was surprised by reading this entry that phenology wasn’t approached in a way similar to insect development (and similarly germination). Which is measuring accumulated degree days (similar to your bucket). This is usually pertinent to economically important taxa, so the exact temperature thresholds for them are often known and development degree days are accumulated above that threshold.

          We know the details for a relatively small subset of taxa (relative to the overwhelmingly large number of taxa) that are of economic importance.

          But one could reliably say the threshold is above 0. It is usually well above 0.

          I can imagine another reasonable way to scale your data would be using degree days above zero (so a day that was 20C would accumulate 20 degree days). If you wanted to do it in warmer climes, perhaps using some mean winter temp in place of zero might make sense. I’m thinking about this only because there is definitely a dormant/chilling period required in plants, even in areas that don’t get below 0…. but maybe soil temperature – air temperature relationship accounts for this. I’m an insect-plant ecologist… but more insect than plant.

          Fascinating story, thanks for the post.

      • “Zero degrees Celsius is biological zero.”

        No, it certainly is not. There’s no such thing as “biological zero,” and no measure by which differences relative to 0C are proportional to one another. 0C is just the freezing point of *pure* water — not even the salty solutions making up cells. Arrhenius rates, for example, are not exponential in degrees C, nor can I think of a single biological / biophysical example for which 0C is a “biological zero” in any meaningful sense.

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        • (Sorry for delayed response) Thanks Raghu, I am equally mystified by Matt’s response – setting centigrade zero at freezing point for pure water does not make it a ‘real zero’ for biology, nor does the observation that some biological process such as plant growth rate tends to slow down as you approach 0C. Are you claiming that some meaningful range of biological processes have been observed to cease completely at exactly 0C? I’m not sure even that would justify using centigrade temperature ratios.

  7. Thanks for sharing! I see this as a great example of how even a bit of theory (your “bucket” model) trumps even the most elaborate statistical tinkering.

    As an interesting aside, models like yours that are based on accumulation to a response threshold are widely used in cognitive psychology to explain distributions of response times. The specific model you coded up reminded me of one proposed by Grice in 1968 (citation below), in which there is a normally distributed initial level (or, equivalently, normally distributed threshold across the population) coupled with a linear ballistic approach to that threshold. Stimuli that are more intense result in a faster approach to threshold. In your model, the normal perturbations are uncorrelated from day to day, so it is not exactly the same. Even so, it is a reasonable analogy to say that leafout is like hitting the brakes in response to a squirrel darting into the road*.

    The details of response time distributions have proven extremely useful for testing theories of this kind in psychology, and I wonder if the same will be true in phenology? In other words, looking at the full distribution of leafout times could teach us a lot about the nature of the stochastic accumulation process leading up to leafout as well as how relevant factors vary from day to day and from plant to plant. For example, in psychology, different classes of serial and parallel model can make identical predictions for mean response times but can be distinguished based on the shapes of the distributions of response times (e.g., the work of James Townsend and colleagues).

    Grice, G. R. (1968). Stimulus intensity and response evocation. Psychological Review, 75(5), 359–373.
    https://doi.org/10.1037/h0026287

    * Unless you are my father who would hit the accelerator instead.

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  8. Dear Lizzie,

    I am an undergraduate at the Department of Life Science, National Taiwan University. I’m quite interested in the effects of climate change on organisms, and I did learn a lot after reading through this nice post. I have a question though: In the simulation R code, there is a line “temp <- delta * (1:100) + rnorm(100, 0, 50)". Is this for generating a sequence of daily temperatures that the plant will experience over the simulation period (here 100 days)? If so, why do these daily temperatures increase over time ("temp" is a vector with increasing values)? Is that because you expect the temperature to increase over time (from early spring to late spring)? Alternatively, can you use "temp <- rep(delta, 100) + rnorm(100, 0, 50)" instead if we assume the mean temperature does not change that much over the simulation period?

    Thanks for answering my questions!

    Reply ↓

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