* The value of the mutation rate was picked according to results of a
simulation model on the evolution of the mutation rate after 300
generations of a population experiencing stochastic environmental
conditions (no climate change, and no plasticity, Romero-Mujalli et al.
2019a). In addition this value is within the range of mutation rates
used in other simulation models (reviewed in Romero-Mujalli et al.
2019b).
3. Results
3.1 Implications of assuming limits and flexible development for the
modeling of phenotypic plasticity
Considering the degree of adaptation under directional deterministic
environmental change (no stochastic noise, typical of laboratory
experiments), any form of adaptive phenotypic plasticity was of
advantage over non-adaptive plasticity and absence of plasticity (i.e.,
genetic determinism) (Fig. 5A). When the slope equals one, linear
reaction norms yield perfect plasticity, while the “perfect match” of
the phenotype with the environmental optimum depends on whether the
limits are exceeded or not for those forms of plasticity that account
for limits (Fig. 5A).
Fig. 5 (A) Mean degree of adaptation (fitness proxy) in
populations with and without adaptive phenotypic plasticity experiencing
directional deterministic environmental change (rate of change η =
0.03 , density dependence effect ψ = 1.0 , mutation rate µ =
0.001 ). A scenario of no adaptation (µ = 0 ) was also simulated,
for comparison. The simulation was run for 100 generations. (B) Genetic
variance (average ± standard error from 100 replicates) present in a
population experiencing constant environmental conditions (no climate
change, no stochasticity; for example, laboratory conditions) per
scenario of phenotypic plasticity. (C) Time series of the genotypic and
phenotypic variances present in a population experiencing deterministic
directional environmental change (no stochasticity), under the scenarios
of adaptive sinusoidal and logistic phenotypic plasticity (upper panel).
When the population is locally adapted (initial part), there is less
phenotypic than genetic variation (developmental canalization , at
the population level, Posadas and Carthew 2014). Under the assumption of
adaptive sinusoidal plasticity, as the environment changes and the
population is pushed towards its limits of plasticity, cryptic
phenotypic variation arises, and the mean fitness (here, degree of
adaptation) of the population reduces (lower panel). In linear reaction
norms, the genotypic and phenotypic variances are directly proportional.
Interestingly, adaptive sinusoidal and logistic plasticity led to stable
functioning phenotypes (close to the optimum) despite of variation at
the genetic level (developmental canalization at the population
level, Posadas and Carthew 2014) (Figure 5B, C). A consequence of this
property is that they maintained higher genetic variance than the
alternative methods even when the population was exposed to a constant
environment (e.g., laboratory conditions) for several generations (Fig.
5B). Additionally, in the model assuming a sinusoidal reaction norm,
cryptic variation appeared in the population when it was pushed towards
the limits (Fig. 5C). Cryptic variation refers to genetic variation that
normally has little or no effect on phenotypic variation but that under
atypical conditions generates phenotypic variation (Paaby and Rockman
2014).
3.2 Phenotypic plasticity: life histories under environmental change
Under scenarios of weak density dependence effect (ψ = 0.5 ), in
which breeding females in the population could produce relatively few
offspring, adaptive phenotypic plasticity played a major role promoting
persistence as compared to organisms with higher ψ (Fig. 6, 7).
Particularly for this life history strategy under slow climate change,
adaptive phenotypic plasticity became of high importance promoting
adaptation under positively autocorrelated environmental stochasticity
(red noise). When the rate of change η was too rapid, adaptive
phenotypic plasticity (particularly, linear reaction norm and logistic
plasticity) became of advantage for all simulated environmental
conditions of noise color (Fig. 6).
Fig. 6 The effect of non-adaptive (random) and adaptive
(linear, sinusoidal, and logistic) phenotypic plasticity on probability
of persistence (100 replicates, 250 generations each) of a population in
which breeding females are limited to produce relatively few offspring
(ψ = 0.5 , weak density dependence effect). The linear reaction
norm had a slope b = 0.5 . A scenario of genetic determinism
(narrow sense heritability h2 = 1 ) was also
simulated, for comparison. The color bar illustrates the color of the
stochastic noise.
Fig. 7 Effect of non-adaptive (random) and adaptive
(sinusoidal, logistic, and linear) phenotypic plasticity on the
probability of persistence (100 replicates, 250 generations each) of a
population of intermediate and strong density dependence effect (ψ
= 1.8 and 2.5 , respectively). The linear reaction norm had a slopeb = 0.5 . A scenario of genetic determinism (narrow sense
heritability h2 = 1 ) was also simulated. The
color bar illustrates the color of the stochastic noise. Scenarios ofη < 0.03 were not shown, because all treatments led to
maximum probability of persistence.
In contrast, results of strong and very strong density compensation
(ψ = 1.8 and 2.5 , respectively) always persisted under conditions
of only environmental stochasticity (no directional climate change) and
relatively slow to medium rate of environmental change (η = 0,
0.01, 0.02 ), regardless of the type of environmental stochasticity
(noise color). For these life history strategies, genetic determinism
and all forms of plasticity performed equally well (Fig. 7).
Under scenarios of relatively rapid directional climate change, adaptive
linear and logistic phenotypic plasticity performed the best for
organisms of intermediate and high density dependence effects (ψ =
1.8 and ψ = 2.5 ) (Fig. 8, η = 0.04 ). The life history
strategy with weak density compensation was not included in this
analysis, since its populations always went extinct, except for the
scenarios of linear and logistic plasticity. On the other hand, adaptive
sinusoidal, non-adaptive random phenotypic plasticity, and genetic
determinism showed similar performance across all scenarios of rapid
rate of directional climate change (Fig. 7).
The performance of random plasticity was notably prominent for organisms
of intermediate and high density dependence effects under scenarios of
lower mutation rates (μ = 10-4, Fig. 8).
Similar results were observed when considering μ =
10-3 and mutational effects according to the model of
slightly deleterious mutations (Ohta 1973; Eyre-Walker et al. 2002), as
in Romero-Mujalli et al. (2019b) (Fig. S2, Appendix B: Supplementary
material). When genetic mechanisms producing novel variation are somehow
constrained, these organisms can cope with changing environmental
conditions relaying on non-adaptive phenotypic plasticity only (Fig. 8).
This ability was not observed for organisms of weak density
compensation, typical of large mammals and some bird species. However,
populations of organisms with strong density compensation (ψ =
2.5 ) were considerably more vulnerable to extinction due to stochastic
fluctuations in the carrying capacity (Fig. 9).
Fig. 8 Relative
importance of forms of non-adaptive (random) and adaptive (sinusoidal,
logistic and linear) phenotypic plasticity affecting persistence of
populations differing in levels of density compensation (ψ ) and
experiencing moderate rate of directional stochastic environmental
change (η = 0.01 , ψ = 0.5 ; η = 0.025 , ψ =
1.8 and ψ = 2.5; 100 replicates, 250 generations each) under
scenarios of low mutation rate (μ = 10-4). A
higher η , results for ψ = 0.5 were not shown, because
scenarios of random and sinusoidal plasticity, and genetic determinism
(narrow sense heritability h2 = 1 ) went usually
extinct. The color bar illustrates the color of the stochastic noise.
Fig. 9 Probability of persistence (100 replicates, 250
generations each) per life history strategy (levels of ψ ) under
stochastic fluctuations in both, the carrying capacity (sd = 10and 20% of K ) and the phenotypic optimum (white noise, no
directional climate change).
When the plastic response precedes the environmental change (i.e.,
change after a sensitive period of plastic trait development), the
dynamic can considerably change for those life history strategies of
weak density compensation (ψ = 0.5 ) under blue stochastic noise
(Fig. S3, Appendix B: Supplementary material). Whether plastic responses
precede or follow the environmental change seems to have little impact
under life history strategies with stronger density compensation (Fig.
S3, Appendix B: Supplementary material).
4. Discussion
The objectives of this study were: (i ) to evaluate the effect of
assuming plasticity as a developmentally flexible phenotypic response
with limits, and (ii ) to assess the relative importance of
adaptive and non-adaptive plasticity for populations of sexual species
with different life history strategy experiencing scenarios of
directional climate change and environmental stochasticity (noise
color). The simulated environmental conditions, though simplified as in
every model, mimic realistic expected scenarios of environmental climate
change (Björklund et al. 2009; Kopp and Matuszewski 2014; Vincenzi
2014). Our results show that the relative importance of phenotypic
plasticity varies among life history strategies. Furthermore, they show
that the advantage of non-adaptive and adaptive forms of phenotypic
plasticity on population persistence depends on the type of
environmental stochasticity (noise color) and the rate of directional
climate change. In addition, the advantage of adaptive and non-adaptive
forms of plasticity depends on whether plasticity precedes or follows
the environmental change. Finally, assuming limits to plasticity lead to
genetic accommodation (in the absence of costs to plasticity) and to the
appearance of cryptic genetic variation when limits are exceeded.
Moreover, assuming plasticity as the result of genotypes responding
flexibly to feedback from their environment leads to developmental
canalization at the population level (Posadas and Carthew 2014),
many-to-one genotype-phenotype map (Wagner 2008; Aguilar-Rodríguez et
al. 2018) promoting the coexistence of polymorphism, and higher
maintained genetic variation, potentially increasing evolvability, as
compared to traditional approaches (e.g., linear reaction norms).
4.1 On the limits and the model implementations of adaptive phenotypic
plasticity
Our work explicitly accounts for limits to plasticity. Though a thorough
analysis of limits to plasticity was beyond the scope of this study,
there are some aspects worth consideration. Linear reaction norms have
no limits and their evolution can theoretically result in organisms
displaying perfectly adapted phenotypes under all environmental
contexts, if no cost is imposed, which is unrealistic. Plastic responses
certainly have energetic demands (i.e., costs), but also limits to
plasticity – in the absence of costs – can result from the properties
and characteristics of the underlying machinery producing the phenotypic
response. Therefore, linear adaptive phenotypic plasticity can
overestimate the probability of persistence. In our simulations this was
prevented by having a slope of 0.5 instead of 1. Even so, linear
adaptive phenotypic plasticity had the best performance (in terms of
increasing population persistence) in comparison to the other methods of
adaptive plasticity. In the model, it took approximately 80, 60 and 40
generations or years to cross the limits of plasticity for a rate of
directional change of 0.02, 0.03 and 0.04, respectively. Thus, for the
population to persist the 250 generations under such scenarios of
environmental change, genetic changes need to necessarily follow to
enable survival beyond plasticity limits. Only linear adaptive
phenotypic plasticity, as simulated in the model, could – for some life
history strategies, ψ = 1.8 and 2.5 – lead to persistence
of the population with minimal, if any, genetic changes. Thus, the
existence of limits to plasticity (without the consideration of costs;
i.e., when costs are negligible, see Murren et al. 2015) can lead to a
transition from an “environmentally induced” to a “genetically
encoded” state of a trait (genetic accommodation, Sommer 2020). The
process of genetic accommodation occurs when phenotypic variants that
are environmentally induced, become genetically determined by natural
selection (West-Eberhard 2003; Schlichting and Wund 2014), and has been
observed in nature (Schlichting and Wund 2014; Kulkarni et al. 2017).
Moreover, our model shows that when the environmental change pushes
towards the limits of plasticity, cryptic phenotypic variation may
arise. This means higher phenotypic than genotypic variance, a ratio
that could be measured in nature. This feature comes along with a
reduction in mean fitness of the population (in the model, degree of
adaptation) and could potentially be used as an early warning signal for
the inability of a population to sustain environmental change (Boettiger
et al. 2013).
In our model, forms of phenotypic plasticity with limits are assumed to
enable diverse functional responses through flexible interactions of the
genotype with the environment (Laland et al. 2015; van Gestel and
Weissing 2016). This assumption leads to, first, stable functioning of
the phenotype (close to the optimum) despite the variation at the
genetic level (developmental canalization at the population
level, Posadas and Carthew 2014). Second, multiple genotypes can have
the same phenotype (many-to-one genotype-phenotype map, Ahnert 2017;
Aguilar-Rodríguez et al. 2018), which does not occur under linear
reaction-norms, thus enabling coexistence of polymorphism when different
genotypes have the same fitness. Third, genotypes with the same
phenotype are mutationally interconnected, such that small mutations can
transform these genotypes into one another without altering the
phenotype (robustness), or lead to new phenotypes (evolvability), at the
same time (Wagner 2008; Ahnert 2017; Aguilar-Rodríguez et al. 2018;
Payne and Wagner 2019). Moreover, it can act as a mechanism that
maintains genetic variation, potentially increasing evolvability (van
Gestel and Weissing 2016). In our implementation of adaptive plasticity
this is evidenced by the sinusoidal and logistic plasticity scenarios
resulting in the highest maintained genetic variation – higher than
linear reaction norms and genetic determinism – even when the
population is exposed to a constant environment (e.g., laboratory
conditions) for several generations. This agrees with observations on
the maintenance of adaptive capacity in populations (often clonal
populations) kept in enclosed environments (e.g., chemostats) for
several generations (Maharjan et al. 2006; Fussmann et al. 2007).
Modelling approaches have been limited by the tendency of the trait
variance to unrealistically decline to zero over time (Merico et al.
2014; Romero-Mujalli et al. 2019b). Our study shows that a simulation of
trait dynamics more in line with developmental systems responding
flexibly to internal (genotype) and external inputs (environment)
enabling highly diverse functional responses, as done for logistic and
sinusoidal plasticity, could help to overcome this limitation. So far,
our implementation offers a phenomenological alternative only. Future
theoretical work should focus on unraveling the mechanisms that make the
above-discussed phenotypic response (trait dynamics) possible.
Furthermore, and in contrast to other forms of plasticity, flexible
development of the phenotype can provide an adaptive response in a novel
environment that need not to have been pre-screened by earlier
selection, which is particularly true for learning (Laland et al. 2015;
Watson and Szathmáry 2016; Romero-Mujalli et al. 2017).
4.2 The relative importance of adaptive and non-adaptive phenotypic
plasticity differs between life history strategies
According to our model, any form of adaptive phenotypic plasticity is of
advantage over non-adaptive plasticity under controlled systematic
changes of environmental conditions, as it is the case of laboratory
experiments. However, under stochastic environmental fluctuations
typical of natural habitats, adaptive phenotypic plasticity is
particularly of advantage when facing positively autocorrelated
environmental fluctuations (i.e., red noise) and slow directional
environmental change; and for a broader spectrum of climatic
fluctuations when there is a faster trend in the mean environmental
optimum. Particularly, all forms of adaptive phenotypic plasticity were
superior to lack of plasticity for life history strategies with
relatively slow growth rate (weak density compensation). This life
history strategy resembles characteristics of many vertebrate species
(e.g., birds and mammals). In contrast, for life history strategies with
strong density dependence effects and therefore, fast growth rate,
genetic determinism and all forms of plasticity performed equally well.
For these life history strategies, only under relatively high rates of
directional climate change, some forms of adaptive phenotypic plasticity
(i.e., linear and logistic phenotypic plasticity) and, interestingly,
random non-adaptive plasticity, were of advantage. The difference in the
relative importance of adaptive and non-adaptive plasticity among life
history strategies was even more evident under scenarios of genetic
constraints (in our model, scenarios of relatively low mutation rate,
and of slightly deleterious mutations fitness effects). Under such
scenarios, life history strategies with strong density compensation
could cope with the changing environmental conditions relying on random
non-adaptive plasticity only. This was not the case for life history
strategies with weak density compensation, which strongly depended on
adaptive plasticity for their adaptation to the local environment.
Therefore, if organisms with different life history strategies, as
simulated in this model, would experience equivalent environmental
fluctuations and rates of directional climate change, those where
breeding females are limited to few offspring are expected to experience
stronger selection for the development of mechanisms of adaptive
phenotypic plasticity, and stronger selection to expand the limits of
their plasticity mechanisms. Populations of organisms with faster growth
rate can rely on non-adaptive plasticity (translating into bet-hedging,
Donaldson-Matasci et al. 2013) for a broader range of environmental
fluctuations. As linear and logistic phenotypic plasticity does not
generally outperform non-adaptive plasticity, these adaptive plastic
responses are not expected to evolve for life history strategies
producing relatively large numbers of offspring, unless they experience
relatively rapid rates of directional environmental change. A further
life history parameter promoting the evolution of adaptive phenotypic
plasticity is longevity/generation time, leading to a limited genetic
response (Forsman 2014, not tested in our study).
The importance of adaptive phenotypic plasticity for organisms
experiencing directional change of the mean environmental optimum, as
inferred in our simulations, may equally apply to dispersing and sessile
organisms. Dispersing organisms may experience gradual changes in the
mean environmental optimum and will benefit from developing adaptive
forms of phenotypic plasticity as they expand their range, especially if
density dependence is weak, as it occurs in mammal and bird species.
Similarly, sessile organisms exposed to seasonal changes in the mean
environmental optimum will also benefit from adaptive forms of
phenotypic plasticity, particularly if their longevity is high (Borges
2008). Examples are plant species inhabiting temperate regions
(Chmielewski and Rötzer 2001), as well as plants experiencing regular
yearly cycles of rain, drought and fire at the equator (Fajardo et al.
2005).
Despite of their good performance across scenarios of directional
stochastic environmental change (as tested in this study), populations
with strong density dependence are susceptible to extinction under
stochastic fluctuations in environmental quality (i.e., stochastic
carrying capacity). Fluctuations in the carrying capacity can result
from fire, resource contamination, or human land use, among other
factors (Anderson et al. 2015). In contrast, populations with weak
density compensation are less impacted by fluctuations in the carrying
capacity of their environment. This would, for example, suggest that
insect populations are more impacted by fluctuations in habitat quality
(e.g., because of land use) than mammals. It remains however to be
investigated, in how far this observation depends on the specific model
implementation.
4.3 Phenotypic plasticity and environmental noise: when adaptive
plasticity hinders evolution
To date, most studies of phenotypic plasticity (and its evolution) under
stochastic environmental fluctuations have been focused on the level of
correlation among the environmental optimum and the environmental cues
sensed by organisms (Reed et al. 2010; Ashander et al. 2016; Ergon and
Ergon 2016). They show that adaptive phenotypic plasticity can only
evolve under positive correlation of cues with the environmental optimum
(environmental predictability). It is important to note that this type
of predictability is not the same as the predictable (red noise)
year-to-year pattern of our simulations. Specifically, this study adds
that adaptive forms of phenotypic plasticity can decrease extinction
risk under positively autocorrelated environmental stochasticity (red
noise), while extinction risk is expected to be high in the absence of
plasticity (Mustin et al. 2013). However, if the environment changes
after the sensitive period when the trait is susceptible to be modified
by plasticity, those traits initially developed by adaptive plasticity
can lead to a disadvantage under negatively autocorrelated environmental
stochasticity (blue noise), which agrees with results from evolution
experiments (Hallsson and Björklund 2012). This applies for constant
characters, i.e., phenotypic traits plastic early in ontogeny, resulting
in mature phenotypes which cannot be further modified by the environment
(Lande 2014; Romero-Mujalli et al. 2019b). In our model, such
disadvantage of adaptive plasticity under blue noise occurred only for
life history strategies with weak density compensation. Whether the
plastic response precedes or follows the environmental change seems to
have little impact under life history strategies with stronger density
compensation. Thus, for life history strategies with weak density
compensation under blue noise, adaptive phenotypic plasticity amplifies
phenotype-environment mismatches due to the negative autocorrelation in
the environmental stochasticity and, therefore, hinders evolution in the
long run, whilst non-adaptive phenotypic plasticity and genetic
determinism increase population persistence under such scenarios.
Therefore, life history strategies with weak density compensation
relying on any form of adaptive phenotypic plasticity under blue
stochastic environmental conditions are expected to be more vulnerable
– than those with stronger density compensation – unless they are able
to adjust their plasticity strategy. However, adaptive plasticity
(particularly, linear and logistic phenotypic plasticity) becomes of
advantage for all conditions of stochastic noise – even when the
environmental change occurs after the sensitive period – when the rate
of environmental change is relatively rapid. In our model, rapid rates
of directional change of 0.03 and 0.04 change the environment beyond the
range captured by the stochasticity (considering a two-sigma-effect,
95%) of the original reference environment after 100 and 75 generations
(or years), respectively. A “fast” rate of environmental change is not
necessarily an absolute measurement. It should be related to
characteristics – life history strategy – of the population, as shown
in this study, and to the strength of selection (Burger and Lynch 1995).
5 Conclusions
Adaptive phenotypic plasticity promotes population persistence under
positively autocorrelated (red noise) environmental stochasticity and
slow climate change, and for a broader range of fluctuations when the
rate of directional change is faster. This form of plasticity is
particularly important for life history strategies in which breeding
females have a limited number of offspring (low fecundity, and hence
slow population growth rate, typical of many vertebrate species: birds
and mammals). Organisms producing more offspring per female may cope
with environmental fluctuations relying only on genetic changes or
random plasticity, unless the rate of environmental change is relatively
high. Whenever plasticity precedes the environmental change, typical of
constant characters, those life history strategies with weak density
compensation will experience high risk of extinction in bluish habitats,
unless they can adjust their plasticity into a bet-hedging strategy.
Models employing linear reaction norms may overestimate persistence, if
they do not consider limits of plasticity. Furthermore, limits to
plasticity lead to genetic accommodation when costs are negligible and
to the exposure of cryptic genetic variation when the plastic response
is pushed towards the limits of plasticity. In addition, the modelling
of plasticity as developmental systems relying on genotypes interacting
flexibly with their environment enables coexistence of polymorphisms and
highly diverse functional responses, leading to high maintained genetic
variation, many-to-one genotype-phenotype map, and to developmental
canalization at the population level.
In this work, the mechanisms that shape the limits of adaptive
plasticity were not explicitly modeled. Empirical work is needed to
unravel molecular mechanisms that may dictate the limits of plastic
responses.
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