As a result, the curves from the previous figure emerge. The three distinct phases are just a consequence of picking the sparsest solution to the problem (see the image). This (Occam’s razor) combined with the constraints on the reaction norm—the mechanistic insight—got close to the truth!

Well, they don’t estimate the curves directly. They just observe insect emergence in a variable thermal environment, and iteratively tweak curve parameters in search of the best explanatory model, under some constrains (the main one being how the shape of the curve can vary, see figure).

Rewind to 1997. Three researchers publish a paper on the same topic, with the figure below (doi.org/10.2307/2404...). Very reminiscent of our results. However, this paper has remained in relative obscurity, only racking up 15 citations to date, despite being on a quite popular topic. Why?

Quick background: we did a pretty laborious experiment to empirically determine thermal reaction norms for diapause termination in a butterfly. The result was the two curves below. Also, we found some signs of a third reaction norm for diapause induction that might look something like the red line.

Phew, that’s a long thread! Big thanks to the coauthors, Philipp Lehmanns lab group, and especially Philip Süess (picture) who did a lot of the heavy lifting co-leading this paper with me. Without him none of this would have been possible.

However, diapause #initiation is another story. We find it is plausible that initiation has its own, third, thermal reaction norm (as proposed by Johnsen et al. 1997, see Fig). We standardized initiation conditions, and more studies (e.g., doi.org/10.1016/j.cr...) are needed.

Of course, Košťál (and others) were well aware of this, referring to quiescence as an “exogenously” controlled state (I’m still impressed with how clairvoyant his 2006 paper is). Our only addition is that #development de facto #resumes immediately after termination (c.f. figure).

Revisiting Košťál’s classic figure, we see that in our system, and potentially many others, diapause #quiescence is not a distinct #developmental state. I.e., correlated responses (e.g. #cold-tolerance) can be high while developmental supression is null.

This could potentially act to #synchronize spring #emergence across spatially heterogeneous environments, since cold #microclimates will have rapid termination and slow post-diapause development, and vice-versa in warm microclimates.

Additionally, we could show that post-diapause development follows a typical TPC, and what’s more, that this development follows immediately after diapause has terminated. In other words, individuals jump from one (cold, right-skewed) TPC, to another (normal) in an instant.

We found that diapause termination rates seem to follow this weird, #right-skewed, TPC shape. But does this TPC quantified under #constant conditions translate to novel #fluctuating environments (like our previous work on development rate TPC’s shows)? Yes! (At least in the lab.)

Via some #Bayesian hierarchical #nonlinear modelling, we can force the parameters of these cumulative probability functions (i.e., geometric mean rate, and its relative variance) to be dictated by an underlying TPC, which provides an extremely good fit to the data.

However, this problem can be circumvented by studying diapause termination rates at the level of statistical populations. By consecutively moving pupae from different cold temperatures to warmth, underlying rates can be inferred through cumulative log-normal probability functions

Before our work, nobody had estimated a thermal reaction norm for diapause termination. This is likely because termination is generally a #cryptic state transition that can’t be measured directly (for instance, in our butterflies diapausing and developing pupae look identical).

Quantifying temperature’s effect on #diapause #termination requires fitting #TPCs to binary biological data. In our new paper, out now in #PNAS, we show how to do this, revealing the sequential nature of diapause termination and post-diapause development.

doi.org/10.1073/pnas...

It's always nice with empirical support of expected patterns - and here, the conclusion are quite clear. Check it out now in Ecosphere!

Although perhaps not very surprising (see for instance the work of Bradshaw & Holzapfel), I like our study because we showed this by estimating both TPCs and photoperiodic reaction norms for each population, which all have the same number of yearly generations (but different temps/photoperiods)!

Figured I can use my first post here to plug my (yet to be cited 🥲) short paper in @methodsinecoevol.bsky.social, showing how a decades-old interpolation technique can be used to almost magically interpolate temperature regimes (and other stuff that fluctuates)!

doi.org/10.1111/2041...