The coevolution of lifespan and reversible plasticity

Reversible phenotypic plasticity, the ability to change one’s phenotype repeatedly throughout life, can be selected for in environments that do not stay constant throughout an individual’s lifetime. It might also mitigate senescence, as the mismatch between the environment and a non-plastic individual’s traits is likely to increase as time passes. To understand why reversible plasticity may covary with lifespan, studies tend to assume unidirectional causality: plasticity evolves under suitable rates of environmental variation with respect to life history. Here we show that if lifespan also evolves in response to plasticity, then long life is not merely a context that sets the stage for lifelong plasticity. Instead, the causality is bidirectional because plasticity itself can select for longevity. Highly autocorrelated environmental fluctuations predict low investment in reversible plasticity and a phenotype that is poorly matched to the environment at older ages. Such environments select for high reproductive effort and short lifespans.

conclusions are to be found here. It is possible that with a significant rewrite the message here can be made sufficiently clear but I am not sure that this is the case. Here are my criticisms.
1. Given that the paper is singularly devoid of any mathematics, it Is not clear to me what assumptions matter to the model. At the simplest level, I could argue that the parameter s that is identified here as plasticity (and is actually some kind of sampling) determines the mismatch, and the paper assumes that mortality increases with mismatch. My conclusion is that increasing s will decrease mismatch and so mortality and so lengthen life.
What the paper actually does is to make assumptions about (a) The environment and its autocorrelation --it is not clear to me that the authors allow for the fact that changing autocorrelation automatically changes the long term environmental variance. It is also not clear to me what drives the relationship between autocorrelation and lifespan. (b) There are in fact no genes here: everything is phenotypic, so the sudden appearance of genes in the specification of the model is, at the least, not useful. (c) What does finite population size is have to do with the results? Would you not get exactly the same thing with a population that is growing in size? (d) I know that it is popular to describe fitness as a property of individuals, but here it is a property of the phenotypic characteristics.
2. The model is actually simple and your discussion would make a great deal more sense if you presented the model first. In my opinion an appendix Is useful only when it contains developments that can be effectively summarized in the main text. That is not the case here. Without some explicit development of the quantitative underpinnngs, I found the discussion extremely confusing.

Response to reviewers
Reviewer #1 (Remarks to the Author): In this manuscript, Ratikainen an Kokko develop a model to explore the co-evolution of phenotypic plasticity (sampling), and reproductive investment (with an implicit trade-off between current and future reproduction). They show that fluctuating environments (with low autocorrelation) select for higher sampling (i.e., phenotypic plasticity), which in turn favours low investment in current reproduction, resulting in increased survival. Hence, selection for higher plasticity results in longer lifespans. This is a novel result, and is contra to the common assumption that long lifespans are required first in order for selection to favour higher levels of plasticity. I think this model provides an important contribution that will be of broad interest, including to researchers interested in the lifehistory evolution, sampling behaviour, and phenotypic plasticity. I have a few general comments that I hope could be useful in strengthening this contribution.

Thank you!
First, in the introduction, age-dependent plasticity, age-dependent expectation of phenotypic mismatch, and senescence are all referenced in developing the rationale for this study. These are all within-individual processes, yet all the results (including in the appendix) are presented as population means. Providing figures that illustrate the within-individual processes would be a meaningful addition, and would create greater coherence between the introduction and results.

This is a good suggestion. We have combined it with a need to explain the model assumptions more clearly (reviewer #2). Our new figure 1 shows all the main individual level trade-offs from the model, while the other figures show population-level means for a reason: many of our predictions are of an interspecific nature, such as "how does the evolution of plasticity impact lifespan"?
Second, I think it would be nice to know whether some of the model assumptions affect the outcomes. Specifically, how robust are the results to variation in the cost of sampling (cs)? Also, the model assumes that phenotypic mismatch confers both a survival and reproduction cost. Do the results change if the cost is on one or the other?

We have now run various modified versions of the model to answer these questions, finding that the results are generally very robust to these assumptions. These additional results are now described in the new section "Model robustness" and in the new ESM.
Finally, in the discussion, you write that the lack of empirical tests might be due to the difficulty in placing species along a unidimensional axis of plasticity, but that such quantifications would be an interesting avenue for future research (lines 130-133). Please give concrete suggestions here. What type of systems, what type of traits, would you recommend for future empirical work? What are the key assumptions of your model that such systems should fulfill? If this model doesn't lend well to empirical tests, and is meant to serve as an untestable proof of concept, that's also fine in my opinion, as it's still illuminating as a model. But this should be made explicit to avoid future empirical tests being purported to test this model when in fact they don't (e.g., because they violate critical assumptions).

We agree: it is more helpful to provide concrete suggestions than mere hand-waving. Although we are constrained by the need to keep our text concise, we now write (lines 290-294, in trackchanges version of ms):
"A possible way forward could be to investigate a single very important trait that varies in the degree of plasticity across populations or species. Alternatively, experimental evolution approaches could investigate the coevolutionary patterns of lifespan and plasticity when environments vary in their autocorrelation structure; this approach could be made more powerful by posing lifespan limitations on some lines but not others." Minor comments: Line 15: "reversible phenotypic plasticity… is expected to evolve if environments vary relatively predictably within…..". Please rephrase to make clear that what is predicatable is that there is variance in the environmental conditions, but that the specific state of the environment is not predictable (and hence requires sampling).
We have rephrased the sentence to clarify; also we now refrain from making an "will always evolve" type prediction, as we merely mean that these are the conditions when one can expect there to be selection for plasticity (lines 19-20): "Reversible phenotypic plasticity, the ability to change ones phenotype repeatedly throughout life, can be selected for in environments that do not stay constant throughout an individual's lifetime." Line 40: how do you combine insights from age-dependent plasticity? You do not model agedependent effects.

We have rephrased -'complement' is a better word to describe what we do than 'combine', as we indeed do not model sampling effort as a function of age. In other words, we view our model as complementary to others' efforts, who have different research foci.
Line 117: use of "merely" and "simply" in same sentence is redundant. Delete one.

Thank you, we have deleted "simply".
Lines 224-225: "the maximum potential fitness is equal for all environments, and there are therefore no "good" or "bad" environments". If the probability of achieving maximum fitness differs, then I would consider that there are "good" and "bad" environments. Please rephrase.
We agree, and believe this sentence offered potential to lead to misunderstandings more than it helped to understand that is going on. We have simply deleted the sentence.

Thank you! We have now split this into two separate figures as suggested, and this should also clarify any confusing legends.
Reviewer #2 (Remarks to the Author): I started reading this paper with the sense that I would learn things that were really interesting and novel. Unfortunately I found the paper confusing so it is not clear to me that any such insights or conclusions are to be found here. It is possible that with a significant rewrite the message here can be made sufficiently clear but I am not sure that this is the case. Here are my criticisms.
1. Given that the paper is singularly devoid of any mathematics, it Is not clear to me what assumptions matter to the model. At the simplest level, I could argue that the parameter s that is identified here as plasticity (and is actually some kind of sampling) determines the mismatch, and the paper assumes that mortality increases with mismatch. My conclusion is that increasing s will decrease mismatch and so mortality and so lengthen life.

This is correct. That said, we are not entirely sure how to interpret the reviewer's tone when commenting on the relationship between plasticity and sampling ('actually some kind of sampling'). Plasticity cannot occur without sampling the environment -except if one wishes to use it as an umbrella term that also includes phenotype switching (which can occur and be selected for without the organism measuring the state of the environment in any way, e.g. Beaumont et al. 2009 Nature). Our aim is to consider the more usual case of plasticity which necessitates that the organism measures the state of the environment. We now clarify this:
"Phenotypic plasticity is defined as the ability of one genotype to produce more than one phenotype depending on some environmental variable 1 (in this view, which we follow here, plastic traits necessarily involve sampling the environmental state at least once, and our work does not consider the alternative of phenotypic switching 2 that can occur without any sampling effort by the organism)."

We have also moved the model description into the "results" section after advice from the editor, and all the equations are now easily available.
What the paper actually does is to make assumptions about (a) The environment and its autocorrelation --it is not clear to me that the authors allow for the fact that changing autocorrelation automatically changes the long term environmental variance. It is also not clear to me what drives the relationship between autocorrelation and lifespan.
The reviewer identifies a real concern here. Changing the environmental parameter p (Figure 1

The relationship between autocorrelation and lifespan can be explained as follows. A lowautocorrelation environment presents survival challenges that are fundamentally more difficult to deal with than high-autocorrelation environments: the same phenotype that did well in year 1 will not do well in year 2 if the environment is now dramatically different. Plasticity (via sampling the new environmental state) can in principle mitigate this effect, but plasticity has its own costs (we assume a cost on fecundity) and the environmental state is unlikely to be measured perfectly. Contrast this with a perfectly autocorrelated, i.e. constant, environment, where the mismatch can between the phenotype and the environment is expected to disappear over evolutionary time, without the need to employ plasticity at all.
(b) There are in fact no genes here: everything is phenotypic, so the sudden appearance of genes in the specification of the model is, at the least, not useful. We have rewritten parts of the model description to make our approach clearer.

We are dealing with a situation where we address a phenomenon in the absence of knowledge of any specific genetic architecture. This means that it is difficult to win an argument over the best level of detail in the genotype-phenotype map. However, we politely disagree that talking about genes / genotypes is not useful. The goal is to see which phenotypes evolve, in the sense of making predictions about observable life-history traits such as lifespan or reproductive effort. But we also need to make a distinction between what can be observed directly and what is assumed to be inherited from parent to offspring. It would clearly be nonsensical (one could use the word Lamarckian) to assume that all components of the phenotype (e.g. the axis labels of the various figures presented) are inherited directly. Instead, clarity is maximized when we use genotypes (previously 'genes') to refer to those aspects that are passed on to offspring. Note that our
(c) What does finite population size is have to do with the results? Would you not get exactly the same thing with a population that is growing in size?

Lion, S. 2018. Theoretical approaches in evolutionary ecology: environmental feedback as a unifying perspective. Am. Nat. 191:21-44.
(d) I know that it is popular to describe fitness as a property of individuals, but here it is a property of the phenotypic characteristics.

We use the word 'fitness' in contexts where it gives intuitive insight into the reasons why certain traits spread in the population (long life and good reproductive success both make an individual more fit). The modelling work itself does not use the concept: we are not assigning fitness values to individuals to then decide on the parents of the next generation. It is true that we are following a popular route here, but we do not really see a reason to avoid doing so, as it helps heuristically to see what is going on.
2. The model is actually simple and your discussion would make a great deal more sense if you presented the model first. In my opinion an appendix is useful only when it contains developments that can be effectively summarized in the main text. That is not the case here. Without some explicit development of the quantitative underpinnngs, I found the discussion extremely confusing.