Author response:
Reviewer #1 (Public review):
Summary:
The authors aim to understand, in the context of leaf shape, how the constraints imposed by development inform evolution. Leaf shape is a good place to study the influence of development on evolution because it is a trait that exhibits a lot of diversity, and the developmental mechanisms that give rise to leaf shapes are apparently rather conserved across angiosperms.
As part of the motivation for their work, the authors cite a previous study (Geeta et al), which found that in angiosperm phylogenies, transitions from complex to simple leaf shapes occur through evolution more often than transitions in the opposite direction. Is this due to developmental constraints or adaptation?
The authors undertake two parallel lines of work:
(1) Extending the study of Geeta et al with more data, consisting of both phylogenies and a shape classification dataset. The conclusion from this line of inquiry is that transitions from lobed to unlobed leaves are more common than transitions away from unlobed leaves.
(2) The authors conduct evolution simulations in a computational model of leaf development. Here, they look at {\it neutral} mutations and whether simply neutral evolution is sufficient to drive the observed trend.
The conclusion of the second part of the work is that the driver of the evolution toward simple leaf shape is entropy: there are more ways to make unlobed leaves than to make lobed leaves (at least in terms of gene regulation parameters that will produce the two leaf types). The argument is that random gene regulatory networks are more likely to produce unlobed leaves than lobed leaves; therefore, neutral evolution drives this trend.
Data Analysis
Roughly $9000$ images of leaves were classified into 4 categories: unlobed, lobed, dissected, and compound. These labels were applied to the tips of 5 phylogenetic trees of angiosperms (3 resolved at the genus level and 2 at the species level). By fitting a continuous-time Markov chain to the labelled trees, the authors claim that there is a significantly higher rate of transition to the unlobed leaf shape compared to transitions to more complex shapes.
Simulation
First, the authors validate a computational model (Runions et al) for leaf growth on an experimental dataset. By changing parameters in the model, they can recapitulate the morphological changes in the shapes of Arabidopsis leaves engendered by expression of two particular genes.
Then the authors run an evolutionary model (without selection, just random mutations) on top of the computational leaf development model. As the random walk in parameter space reaches a stationary distribution, they look at both the proportions of the leaf categories in the steady state as well as the transition rates between different categories. The result is that transitions to unlobed leaves are more common than from unlobed leaves.
We thank the reviewer for the helpful and clear summary of our work.
General Comments
The authors use angiosperm phylogenies from other works as the basis for the data analysis part of their work. Given the centrality of these phylogenies for their conclusions, more information is needed about how these phylogenies were constructed and what they mean. What is the timescale that they span? What method is used to infer them? What regions of DNA were sequenced in order to build the phylogenies? Also, maybe some more discussion of angiosperm evolution (e.g., when was the most recent common ancestor of all angiosperms?) would help put the study in context.
We also need a more in-depth discussion of the computational model. What are all the $>100$ parameters doing, and what informs the seemingly strange mutational model that changes parameters by 3 orders of magnitude?
I am confused about how the rates of transitions were inferred from the phylogeny. Here, one has a phylogeny inferred by some method (which needs to be described in more detail), and just the leaves are labelled. It is stated in the methods that BayesTraits was used to infer the transition rates. I realize this method is probably documented elsewhere, but a bit of a summary of how it works and how to interpret its results would (1) make the paper more selfcontained and (2) if the algorithm is credible, make the results firmer.
We thank the referee for the suggestion to make the paper more accessible. The tool we use to infer transition rates from the phylogenies, BayesTraits, is standard in the field. However, the referee is right that for an interdisciplinary journal, it may be helpful to more fully flesh out how these methods work. To that end, we have added an additional section "Phylogenetic rate inference" in the supplementary information that includes a longer description of how BayesTraits works, and how we used it to infer transition rates from phylogenies.
All trees are shown in the supplementary information section "Phylogenetic trees" with scale-bars showing the amount of time or genetic change that the trees span. For a broader discussion of angiosperm evolution, there is supplementary information section "The adaptive significance of leaf shape review".
Regarding the more in-depth discussion of the computational model, we have added supplementary information section S1 "Leaf model details" to give a more detailed description of the leaf model.
I am a bit skeptical of the authors' interpretation of the biological trend (of complex to simple leaf shapes) as being driven by neutral evolution. Why does one expect that the mutations generated by the random walk models described in the work are in fact neutral mutations?
A random walk is a well-established way of modelling the dynamics of neutral evolution in the monomorphic regime, where the population has a narrow diversity of different genotypes. In the higher mutation rate polymorphic regime, where the diversity of genotypes in the population is larger, we also expect that a random walk should still recapitulate the correct average transition rates. The purpose of the simulations is not to model every aspect of population genetics, but to ask whether developmental bias alone is sufficient to generate the observed directional asymmetry. By assigning equal fitness to all viable leaves, we isolate the contribution of development from that of selection. The agreement with the phylogenetic transition rates therefore demonstrates sufficiency rather than exclusivity: selection may also contribute, but it is not required to explain the observed bias We discuss the evidence for the role adaptation in leaf shape further in supplementary information section "The adaptive significance of leaf shape review".
If the entropy of simple leaf shapes is higher than that of complex leaf shapes, why did we have complex leaves at all? I suspect the authors might argue that this is due to selection. In that case, what allows these complex shapes to become simpler? Wouldn't they be losing the selective advantage that drove them to be more complex in the first place? Or maybe the idea is that the rates are inferred assuming some steady state that generates the phylogeny? I did not understand this point.
The entropy language is a useful framing. Within that framework, one can view our study as showing that the entropy (defined here as the logarithm of the volume of parameter space mapping to a phenotype) of simple leaf shapes is higher than that of complex leaf shapes. If this entropy were to be ignored, then all states would be equally likely in our simulations, where we do not take fitness differences into account. What we show is that the differences in entropy -- related to differences in volumes of the parameter space that map to different phenotypes -- also affects the rates. The inferred transition rates for both simulation and phylogeny from unlobed to more complex shapes are lower than vice versa but not zero. Therefore, complex leaf shapes arise stochastically through mutation and in this model would eventually reach a steady state proportion, even in the absence of selection.
Are the rates of transitions between leaf types inferred for the phylogeny assuming that the phylogeny is generated by the steady state of some Markov process? (I think the answer is no: in that case, how does one explain the initial condition?)
The tool we use to infer transition rates from phylogenies—BayesTraits—allows the initial state at the root of the tree to vary during the numerical optimisation (Pagel, 1994). Therefore, it is not assumed that the initial state is generated by the steady state of the Markov process.
If I take the mutation model (random walk) seriously, then shouldn't I expect that this steady state obeys detailed balance? In that case I should have $p_i r_{i\to j} = p_j r_{j\to i}$ for each of the occupancies $\{ p_i\}$ and transition rates $r_{i\to j}$ for the shape categories. How close are the rates inferred from the phylogenies to obeying detailed balance? Presumably, the Markov chain fitted to the simulation data obeys detailed balance because the mutation model itself does?
BayesTraits allows off-diagonal transition rates of the rate matrix to vary freely during numerical optimisation (Pagel, 1994). Therefore, there is no requirement for the detailed balance to hold for the inferred rate matrix. For our simulations, the mutations are symmetric at the parameter level, therefore at this level, the process would be expected to obey the detailed balance.
I find it hard to take the discussion of development seriously without some consideration of mechanics. Presumably, the mechanics are hidden in the computational leaf development model, but this model is not discussed in enough detail for the reader to know. It seems to me that the interesting question is: what are the {\it mechanical} constraints on development that drive the apparent trend in evolution towards simpler leaf shapes? Maybe it is something about the type of differential growth needed to make complex leaf shapes less robust to mutation. But in this case, I would assume that selection plays a role in the complexity of shape. In any case, a better understanding (or explanation) of the computational model is needed to make this interpretation.
We thank the referee for the suggestion to make the paper more accessible. We have added a more detailed and pedagogical description of the model from (Runions, Tsiantis and Prusinkiewicz, 2017) in the supplementary information section S1 "Leaf model details". We also note that Fig. 5 in the methods that gives an overview of how the model works, including some mechanical aspects of development and growth.
More generally, mechanics is one component of the developmental map that determines which parameter combinations produce viable leaf morphologies. Our analysis concerns the geometry of this complete developmental map, irrespective of whether its constraints arise from gene regulation, tissue mechanics, or their interaction.
On the interesting question of what is causal, perhaps the example in figure 2 is helpful. We focus on two parameters, a morphogen repression strength, and a duration of growth. A key physical process here is called webbing, where cellular growth fills in the gaps between branching veins. This process flattens the leaf structure and creates a continuous, solid leaf blade (lamina). Strong webbing, characterized by a significant resistance to stretching and bending, results in a smoother margin (Runions, Tsiantis and Prusinkiewicz, 2017). The morphogen repression strength affects the physical parameters that determine how strong the webbing is. The duration of growth determines how long the leaf has to grow. Varying these two parameters varies the physical processes that determine leaf shape. The mechanics of growth operate downstream of these parameters that we vary in our evolutionary simulations according to the details of the leaf developmental model.
Some discussion of timescales is needed, especially when invoking neutral evolutionary arguments. If a neutral mutation occurs, its time to fix in a population of size $N$ is $\sim N$ generations. What are the relevant angiosperm population sizes and the number of mutations that separate branches on the tree? Are timescales remotely consistent with e.g., the age of angiosperms on Earth?
Neutral processes have a well-established role in key aspects of angiosperm evolution, for example genome complexity (Lynch and Conery, 2003). This would suggest that the relevant time scales and generation times are not completely prohibitive of neutral processes also playing a role in the evolution of angiosperm leaf shape. Effective population sizes in plants are highly variable but estimates span 10^3-10^6. Assuming diploidy (and therefore average fixation time of 4Ne) and generation times of 1-10 years, this gives fixation timescales of 10^3-10^7 years. This is within the timescales of the trees we analyse, which span >150 million years.
Reviewer #2 (Public review):
Strengths:
The paper's underlying question is interesting, extending the authors' prior work on RNA along similar conceptual lines. The paper combines both image analysis of leaves and a computational analysis of a simple model of leaf development.
Weaknesses:
The entire paper is based on the Runion model. More intuition about the Runion model would be useful for a broader readership that cares about the evolutionary aspect of this, but may not know the developmental model in question. Obviously, this is prior well-established work, but 2 - 3 sentences highlighting the key structural aspects of such a model would be great. Currently, that intuition is found implicitly in a sentence on page 2 ("complex leaf shapes need more specificity in their GRNs than their simpler unlobed leaf shape"), but the reader is left wondering - is the Runion model a detailed mechanistic one with multiple interacting genes/proteins? If so, how many? Or is it just 2 - 3 genes but with complexity entirely in how long they are each expressed/when they are turned off, etc.
We thank the referee for the suggestion to make the paper more useful for a broader readership. To that end, we have added a more detailed description of the (Runions, Tsiantis and Prusinkiewicz, 2017) model in supplementary information section S1 "Leaf model details".
The Runions model has nearly 100 free parameters. Random walks in 100dimensional spaces have generic properties like a tendency to move toward regions of larger volume that have nothing to do with leaf biology. How do you disentangle the geometry of high-dimensional random walks from genuinely biological developmental bias? Would a toy model with 100 parameters and arbitrary phenotype categories also show "bias toward simplicity" if "simple" phenotypes occupy more volume?
Our argument is largely independent of the number of parameters. While it is true that most of the volume is near the surface in a high-dimensional space, our argument is about the relative volumes of the sets of parameters that map to each of the four phenotypes, an entropic argument if you wish. The basic intuition is that a simple phenotype needs fewer parameters to be fine-tuned, and so a larger volume of parameter space will map to a simpler phenotype.
The question about a toy-model with arbitrary phenotypes is helpful, because it allows us to clarify that what we are illustrating here with the biologically realistic example of leaf shapes is a much more generic principle. We can say with confidence that if the toy-model generates a many to one set of outputs (phenotypes) through an algorithmic process whose description length does not grow faster than logarithmically with the size of the genotype space, then it should produce a bias towards simplicity regardless of the number of dimensions, see for example Johnston et al. (2022) and Dingle, Camargo and Louis (2018) for a longer discussion of this more general point which is based on arguments from algorithmic information theory (AIT). We don’t use that framing in the current paper because the basic intuition for GRNs that more complex phenotypes need more parameters fine-tuned, and so have relatively smaller volumes, is more straightforward to understand that the more abstract AIT arguments. Our general prediction that this principle should hold more widely for GRNs can be made both by the more formal AIT route, or via the more heuristic fine-tuned parameter route.
The discussion of Figure 4 (PCA of parameter space) uses "area" loosely when what's actually being measured is bin count in a 2D projection of a highdimensional space. I would think that, in general, PCA projections can be misleading about volume in the full parameter space, but I can't tell if that's an issue in this case. Some comments/thoughts here would be useful.
The quantitative estimate of phenotype frequencies is computed directly in the full parameter space and does not depend on PCA. Ie. We estimate that the total volume of viable leaves maps to simple unlobed leaves about 80% of the time. However, the volume is extremely high-dimensional, and so hard to visualise. PCA is used solely to provide an interpretable visualization of this otherwise high-dimensional structure. The PCA plots in Fig 4 and Fig S16 are there to be illustrative, not quantitative. Because the volume differences are large, we do not think that the projections of the main PCA components would be misleading on at least the ordering of the sizes of the parameter space components that map to each leaf shape. We provided a similar analysis for other projections -- PC1-PC6 (supplementary information section "PCA occupancy for higher dimensions"), finding the same trend. To make this point clearer, we have now changed the sentence in the Fig. 4 caption slightly “This (reveals that --> illustrates how) unlobed leaves occupy a larger region of model parameter space than more complex shapes and that this larger space also contains the majority of more complex leaves.”
The classifier validation section is in the Methods section, but it seems critical to the whole story. The < 80% agreement with manual classification could propagate to the rest of the estimates in the paper. Again, some comments/thoughts here would be useful.
We have repeated the analysis of the agreement between by-eye and automatic morphometric classification. Generating a confusion matrix for the two classification methods shows that the agreement is high for unlobed, dissected and compound, with the main source of disagreement being leaves that were classified as lobed by-eye being classified as either unlobed or dissected by the automatic-morphometric method. The proportion of by-eye lobed leaves classified by the automatic morphometric method as either unlobed (27%) or dissected (23%) is relatively balanced, which we think will help cancel out some error as well. Moreover, we find that the agreement between the automatic-morphometric method and by-eye classification increases to 90.0% when using the categories unlobed and all other categories grouped into one. This is the most important classification for our finding that development and phylogeny are both biased towards unlobed.
The authors should explain Mut2 and Mut5 in the main paper with a sentence or two, at least schematically, because how you mutate is obviously very relevant to interpreting a paper about biases in variation.
In the results section we have added a sentence for more detail on the random walk.
"[We mutated the initial sample using a random walk algorithm with two different mutational schemes, MUT2 (alg. 1) and MUT5 (alg. S2).] These algorithms work by iterating through model parameters one by one and perturbing the value by a small amount. We then [automatically classified the resulting shapes...]"
Moreover, in methods section C there is already a more detailed description of both algorithms.
“MUT2 (alg. 1) iterates through the parameters in a random order, and attempts to change the parameter by a value selected at random from an array of numbers randomly generated at 3 different orders of magnitude. MUT5 (alg. S2) is the same as MUT2 except the value each parameter is multiplied by 10% of the range of that parameter within the initial leaves (fig. S1). The aim here was to provide some way of accounting for the biologically relevant sampling range. "
Moreover, the MUT2 algorithm is described in pseudocode in Algorithm 1 in the main text, and the pseudocode for MUT5 is in supplementary information section S1 C, as algorithm S2.
The two mutational schemes use additive perturbations to individual parameters. Real mutations presumably affect regulatory networks in more structured ways (e.g., changing binding affinities that affect multiple parameters simultaneously). How sensitive are the results to the assumption of independent single-parameter mutations?
The referee raises an interesting and well-known issue concerning this widely studied class of GRN models. Without a detailed understanding of how individual genetic mutations map onto model parameters, it is difficult to determine with confidence whether a mutation would produce correlated changes in certain sets of parameters. Our main argument, however, is that the primary source of the observed bias is geometric: the volume of parameter space (or equivalently, the entropy) corresponding to simple leaf morphologies is substantially larger than that corresponding to complex morphologies. As long as mutations explore parameter space approximately symmetrically, even if they involve correlated changes in multiple parameters, larger phenotype regions will tend to be encountered more frequently and retained for longer than smaller regions. We therefore expect the observed bias to be robust to many alternative mutation models, although quantifying this robustness is an interesting direction for future work.
The connectedness argument is made using a 2D PCA projection. Is there a way to check this statement in the full parameter space or perhaps in higher dimensional projections to test the robustness of this result? Connected components can merge/split under different projections.
Constructing the nearest neighbour graph for the full dimensional data results in the following no. connected components: unlobed-146, lobed-274, dissected-255, compound-315. This follows the same pattern identified for the PC1-PC2 projection, that unlobed splits into fewer connected components than other leaf shape categories.
References:
Dingle, K., Camargo, C.Q. and Louis, A.A. (2018) ‘Input–output maps are strongly biased towards simple outputs’, Nature Communications, 9(1), p. 761. Available at: https://doi.org/10.1038/s41467-018-03101-6.
Johnston, I.G. et al. (2022) ‘Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution’, Proceedings of the National Academy of Sciences, 119(11), p. e2113883119. Available at: https://doi.org/10.1073/pnas.2113883119.
Lynch, M. and Conery, J.S. (2003) ‘The Origins of Genome Complexity’, Science, 302(5649), pp. 1401–1404. Available at: https://doi.org/10.1126/science.1089370.
Pagel, M. (1994) ‘Detecting correlated evolution on phylogenies: a general method for the comparative analysis of discrete characters’, Proceedings of the Royal Society of London. Series B: Biological Sciences, 255(1342), pp. 37–45. Available at: https://doi.org/10.1098/rspb.1994.0006.
Runions, A., Tsiantis, M. and Prusinkiewicz, P. (2017) ‘A common developmental program can produce diverse leaf shapes’, New Phytologist, 216(2), pp. 401–418. Available at: https://doi.org/10.1111/nph.14449.
