The push and pull between theory and data in understanding the dynamics of invasion
Shifts from pulled to pushed range expansions caused by reduction of landscape connectivity
Abstract
Recommendation: posted 16 December 2020, validated 16 December 2020
Phillips, B. (2020) The push and pull between theory and data in understanding the dynamics of invasion. Peer Community in Evolutionary Biology, 100118. 10.24072/pci.evolbiol.100118
Recommendation
Exciting times are afoot for those of us interested in the ecology and evolution of invasive populations. Recent years have seen evolutionary process woven firmly into our understanding of invasions (Miller et al. 2020). This integration has inspired a welter of empirical and theoretical work. We have moved from field observations and verbal models to replicate experiments and sophisticated mathematical models. Progress has been rapid, and we have seen science at its best; an intimate discussion between theory and data.
An area currently under very active development is our understanding of pushed invasions. Here a population spreads through space driven, not by dispersal and growth originating at the leading tip of the invasion, but by dispersal and growth originating deeper in the bulk of the population. These pushed invasions may be quite common – they result when per capita growth and dispersal rates are higher in the bulk of the wave than at the leading tip. They result from a range of well-known phenomena, including Allee effects and density-dependent dispersal (Gandhi et al. 2016; Bîrzu et al. 2019). Pushed invasions travel faster than we would expect given growth and dispersal rates on the leading tip, and they lose genetic diversity more slowly than classical pulled invasions (Roques et al. 2012; Haond et al. 2018; Bîrzu et al. 2019).
Well… in theory, anyway. The theory on pushed waves has momentarily streaked ahead of the empirical work, because empirical systems for studying pushed invasions are rare (though see Gandhi et al. 2016; Gandhi, Korolev, and Gore 2019). In this paper, Dahirel and colleagues (2020) make the argument that we may be able to generate pushed invasions in laboratory systems simply by reducing the connectedness of our experimental landscapes. If true, we might have a simple tool for turning many of our established experimental systems into systems for studying pushed dynamics.
It’s a nice idea, and the paper goes to careful lengths to explore the possibility in their lab system (a parasitoid wasp, Trichogramma). They run experiments on replicate wasp populations comparing strongly- v poorly-connected arrays, and estimate the resulting invasion speeds and rate of diversity loss. They also build a simulation model of the system, allowing them to explore in-silico a range of possible processes underlying their results.
As well as developing these parallel systems, Dahirel and colleagues (2020) go to careful lengths to develop statistical analyses that allow inference on key parameters, and they apply these analyses to both the experimental and simulation data. They have been motivated to apply methods that might be used in both laboratory and field settings to help classify invasions.
Ultimately, they found reasonable evidence that their poorly-connected habitat did induce a pushed dynamic. Their poorly connected invasions travelled faster than they should have if they were pulled, they lost diversity more slowly than the highly connected habitat, and replicates with a higher carrying capacity tended to have higher invasion speeds. All in line with expectations of a pushed dynamic. Interestingly, however, their simulation results suggest that they probably got this perfect result for unexpected reasons. The strong hint is that their poorly-connected habitat induced density dependent dispersal in the wasps. Without this effect, their simulations suggest they should have seen diversity decreasing much more rapidly than it did.
There is a nuanced, thoughtful, and carefully argued discussion about all this in the paper, and it is worth reading. There is much of value in this paper. Theirs is not a perfect empirical system in which all the model assumptions are met and in which huge population sizes make stochastic effects negligible. Here is a system one step closer to the messy reality of biology. The struggle to align this system with new theory has been worth the effort. Not only does it give us hope that we might usefully be able to discriminate between classes of invasions using real-world data, but it hints at a rule that Tolstoy might have expressed this way: all pulled invasions are alike, each pushed invasion is pushed in its own way.
References
Bîrzu, G., Matin, S., Hallatschek, O., and Korolev, K. S. (2019). Genetic drift in range expansions is very sensitive to density dependence in dispersal and growth. Ecology Letters, 22(11), 1817-1827. doi: https://doi.org/10.1111/ele.13364
Dahirel, M., Bertin, A., Haond, M., Blin, A., Lombaert, E., Calcagno, V., Fellous, S., Mailleret, L., Malausa, T., and Vercken, E. (2020). Shifts from pulled to pushed range expansions caused by reduction of landscape connectivity. bioRxiv, 2020.05.13.092775, ver. 4 peer-reviewed and recommended by PCI Evolutionary Biology. https://doi.org/10.1101/2020.05.13.092775
Gandhi, S. R., Korolev, K. S., and Gore, J. (2019). Cooperation mitigates diversity loss in a spatially expanding microbial population. Proceedings of the National Academy of Sciences, 116(47), 23582-23587. doi: https://doi.org/10.1073/pnas.1910075116
Gandhi, S. R., Yurtsev, E. A., Korolev, K. S., and Gore, J. (2016). Range expansions transition from pulled to pushed waves as growth becomes more cooperative in an experimental microbial population. Proceedings of the National Academy of Sciences, 113(25), 6922-6927. doi: https://doi.org/10.1073/pnas.1521056113
Haond, M., Morel-Journel, T., Lombaert, E., Vercken, E., Mailleret, L. and Roques, L. (2018). When higher carrying capacities lead to faster propagation (2018), bioRxiv, 307322, ver. 4 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/307322
Miller et al. (2020). Eco‐evolutionary dynamics of range expansion. Ecology, 101(10), e03139. doi: https://doi.org/10.1002/ecy.3139
Roques, L., Garnier, J., Hamel, F., and Klein, E. K. (2012). Allee effect promotes diversity in traveling waves of colonization. Proceedings of the National Academy of Sciences, 109(23), 8828-8833. doi: https://doi.org/10.1073/pnas.1201695109
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article. The authors declared that they comply with the PCI rule of having no financial conflicts of interest in relation to the content of the article.
Evaluation round #2
DOI or URL of the preprint: https://doi.org/10.1101/2020.05.13.092775
Version of the preprint: version 3
Author's Reply, 15 Dec 2020
Dear Dr Phillips,
We thank you for your swift decision on our manuscript, and are happy to see it soon recommended by PCI!
The new version is now online on bioRxiv; all final changes have been done according to the revision notice. Just to detail the couple changes that may need to be detailed:
1- (former) line 328: we replaced by vF < vF[continuous] to be clearer 2- all requirements were already fulfilled but one. We added a two-sentence short “Ethical note” paragraph to the Methods, after the description of the experiment.
We also corrected a few typos we noted during final typesetting.
All the best,
Maxime Dahirel, on behalf of all authors
Decision by Ben Phillips, posted 15 Dec 2020
Dear Author,
Congratulations! Your preprint submitted to PCI Evol Biol has been accepted and is about to be recommended.
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L28: suggest, "where invasion speed conforms to pushed expectations, but the decline in genetic diversity does not."
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L328: should this be vF[true] < vF[discrete] ?
L332 "between pulled and [fully] pushed expansions"
L522: Suggest, "In our simulations, these pushed expansions..."
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Evaluation round #1
DOI or URL of the preprint: https://doi.org/10.1101/2020.05.13.092775
Author's Reply, 12 Dec 2020
Decision by Ben Phillips, posted 27 Sep 2020
I apologise for the slight delay in providing a decision. I received two very high quality reviews within 30 days, but (as requested by the author) waited to take into account a third review from an open peer review exercise. This also was an excellent review and I have included it as part of the formal review process here.
This is a thought-provoking manuscript, and represent a lot of careful thinking, experiment, and analysis. I congratulate the authors on the work. I found the conceptual broadening of what might constitute a pushed wave to be interesting, and certainly a worthy topic for exploration.
Both of the reviewers I commissioned, however, had substantial concerns, so I cannot recommend the manuscript at this time. I would instead suggest a major revision with option to resubmit.
These reviewers' primary concerns lay with the modelling. Both reviewers 2 and 3 raise serious concerns around calculation of vF. Given the fundamental importance of vF to the argument of the manuscript, these are concerns that need to be seriously considered. On one hand we have a concern that the model is not appropriate for the continuum description, giving a biased vF; and on the other we have a concern that the stochastic component of the model will also generate a bias in vF. These concerns need to be addressed before the manuscript can be recommended.
The reviewers also both had concerns about the interpretation of the experimental data. The big surprise here is that the invasion speed appears unaffected by connectedness, and the authors argue that v_F must be lower. Both had concerns about the arguments for this, and R3 had the additional useful suggestion that the ceteris paribus assumptions could/should be checked.
R2 and R3 also express concern about the exponential approach to v. Given the long-term approach to v over time in stochastic invasions, I see why you have taken this approach (and thought it a good idea), but R3 points out that a power law might be the more appropriate scaling.
Both reviewers clearly felt that the work could benefit from greater attention to the work of Gandhi et al, Birzu et al, and Hallatschek and Korolev. I thought this was good advice. For my part, I would also suggest that the experimental work of Williams et al 2016 (Science 353:482), and the theoretical work of Peischl et al 2015 (Am Nat 185:E81) might also be relevant (for different reasons).
I hope these reviews have been helpful. If the issues around calculation of v_f can be resolved, and a more thorough case made for the interpretation of the experimental results, the manuscript could be recommended.
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Reviewed by anonymous reviewer 1, 11 Sep 2020
Pulled and pushed behavior of population waves, the parameters controlling this behavior, transitions between both types of population waves, and the evolutionary consequences have garnered quite some interest in recent years. Dahirel and coauthors contribute to this work by asking how changing migration between patches / metapopulations affects the classification of the population wave and the genetic consequences. I find their study thought provoking and would like to thank the authors for providing me with the opportunity to dive deeper into the topic than I would have otherwise done. I would also like to applaud the authors for sharing the source code and many details of the analysis openly.
While I enjoyed reading the manuscript, I found it hard to properly convince myself, within the time available, of some of the key arguments. In the following, I will first outline my main questions and concerns, inevitably biased by my own research focus (range expansions, continuum limit, not working on pushed/pulled transitions).
1) The authors investigate range expansions occurring within a set of patches or metapopulations. ‘Connectedness’ thereby refers to migration rate between patches (or structure facilitating migration in case of experiments). My main concern is that the parameter regime / setup the authors use is not suitable for a continuum description, around which key arguments are or at least might be based. Specifically, I think this is a concern for computing vf (around line 264 in the manuscript). Were r0 or D0 slightly higher, vF would reach the maximum possible value of 1. I think there are two possibilities: Either I am wrong, in which case slight modification of the manuscript could prevent other readers from making the same erroneous conclusion. Or I am at least partially right, in which case a thorough discussion of connected metapopulations vs. continuum limit and discussion of applicability of results by Gandhi et al. and Birzu et al. to this study would be needed. 2) I struggle following the paragraphs in which different treatments are compared in simulations because sometimes both v and v_F change. Why did the authors not choose to keep one constant (compare to Gandhi et al., 2019)? 3) Given the high stochasticity in the system and the authors’ aim to make inference from limited information (as is the case out in the field), the use of Bayesian inference appears reasonable. However, I am afraid that this approach makes the paper less accessible and ‘less sticky’, at least to readers like me, who understand the concept of Bayesian analysis but are not be able to scrutinize the details. This approach might also make the findings more vulnerable to misinterpretation than necessary. One example is the exponential approach to v. Is this assumption supported by the data? Is this assumption actually necessary to extract v? I suggest the authors include more of the raw data (front profile, speed as function of time) in the manuscript without sacrificing any of their Bayesian inference. Fig. 3 is a good example of how statistical rigor (to the extent I can judge) and intuition can be combined. 4) Heterozygosity – experiments: I’d appreciate a quick introduction on what is measured and the consequences of wasp mating. Could the authors also share their interpretation of Table S4.2? 5) Heterozygosity – simulations: Why did the authors choose to use only two alleles? 6) Is non-neutral evolution of the wasp population a concern that can be ruled out?
A number of minor comments:
• Line 82: Is the statement that disaccharides lead to an Allee effect correct in this generality?
• Line 146: Visualise the function?
• Line 154: Is there a prefactor N missing?
• Line 189: I would have enjoyed a picture of the setup. For the general reader, this might be the first paper with this experimental setup they come across. Similarly, a flow diagram of the experiment might help visualize the experiment.
• Line 197: What does “16:8 L:D” mean?
• Line 199: Is there a concern of infecting the same egg twice?
• Line 208: ‘until emergence of first adults’. Why not wait for all adults?
• Lines 248: With this definition of vt, approaching v might take a long time. Why not define a moving average of the local speed which would allow one to disregard the initial phase of approaching v?
• Line 270: How much does vF change when changing from r0 to r1 and r2 and D0 to D1 and D2? (See also next point.)
• Line 315: As the reference scenario’s speed is very close to vF, the dependence on K is a bit surprising. A brief comment might be helpful. Relatedly, what do the authors attribute the fact to that v
