# Predicting adaptation and evolution of plasticity from temporal environmental change

Cristóbal Gallegos, Luis-Miguel Chevin, Kathryn Hodgins, Keyne Monro

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Cristóbal Gallegos, Luis-Miguel Chevin, Kathryn Hodgins, Keyne Monro. Predicting adaptation and evolution of plasticity from temporal environmental change. Methods in Ecology and Evolution, 2024, 16 (1), pp.84-96. 10.1111/2041-210x.14462. hal-04993961

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# Predicting adaptation and evolution of plasticity from temporal environmental change

Cristóbal Gallegos<fnref n="1" /> ID | Luis-Miguel Chevin<fnref n="2" /> ID | Kathryn A. Hodgins<fnref n="1" /> ID | Keyne Monro<fnref n="1" /> ID

**Correspondence**

Cristóbal Gallegos

Email: cfgallegos@live.com

Keyne Monro

Email: keyne.monro@monash.edu

**Funding information**

Holsworth Wildlife Research Endowment;
Australian Research Council

Handling Editor: Pablo Duchen

## Abstract

1. Environmental change can drive evolutionary adaptation and determine geographic patterns of biodiversity. Yet at a time of rapid environmental change, our ability to predict its evolutionary impacts is incomplete. Temporal environmental change, in particular, involves a combination of major components such as abrupt shift, trend, cyclic change, and noise. Theoretical predictions exist for adaptation to isolated components, but knowledge gaps remain regarding their joint impacts.

2. We extend classic evolutionary theory to develop a model for the evolution of environmental tolerance by the evolution of an underlying developmentally plastic trait, in response to major components of temporal change. We retrieve and synthesise earlier predictions of responses to isolated components, and generate new predictions for components changing simultaneously. Notably, we show how different forms of environmental predictability emerging from the interplay of cyclic change, stochastic change (noise) and lag between development and selection shape predictions.

3. We then illustrate the utility of our model for generating testable predictions for the evolution of adaptation and plasticity when parameterised with real time series data. Specifically, we parameterise our model with daily time series of sea-surface temperature from a global marine hotspot in southern Australia, and use model simulations to predict the evolution of thermal tolerance, and geographic differences in tolerance, in this region.

4. By synthesising theory on evolutionary adaptation to temporal environmental change, and providing new insights into the joint effects of its different components, our framework, embedded in a Shiny app, offer a path to better predictions of biological responses to climate change.

## KEYWORDS

climate change, environmental change components, evolutionary adaptation, evolutionary prediction, evolutionary theory, phenotypic plasticity, temporal change, tolerance curve

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<footnote n="1">¹School of Biological Sciences, Monash University, Melbourne, Victoria, Australia</footnote>

<footnote n="2">²CEFE-CNRS, UMR 5175,1919 route de Mende 34293, Montpellier Cedex 05, France</footnote>
# 1 | INTRODUCTION

Environmental change is ubiquitous and can shape diversity at different levels of biological organisation. Changes in environmental temperature, for example, affect biochemical reactions within cells, whole-organism physiology and fitness, and species' geographic distributions from local to global scales (Clarke, 2017; Pecl et al., 2017; Peters et al., 2016). Environmental change can also shape evolutionary processes—including selection, adaptation, speciation, and extinction (e.g. Bell & Gonzalez, 2009; Hoekstra et al., 2001; Hoffmann & Sgrò, 2011; Schluter, 2001)—that underpin biodiversity and its geographic distribution (Connallon & Sgrò, 2018; Polechová & Barton, 2015). Yet, at a time of rapid and increasing climate change, our ability to predict its evolutionary impacts on biodiversity is far from complete (Catullo et al., 2019).

In parallel with accelerated climate change, interest in understanding and modelling geographic patterns in biodiversity has grown rapidly in recent decades, with two approaches typically used. First, niche models predict species' distributions based on correlations between occurrence and climatic conditions (Elith & Leathwick, 2009; Fleishman et al., 2001), but are criticised for ignoring biological processes that dictate occurrence (Davis et al., 1998; Dormann et al., 2012). Mechanistic niche models address such criticism to a large extent (Kearney & Porter, 2009), but remain out of reach except for well-studied species (Dormann et al., 2012; Evans et al., 2015), and efforts to incorporate adaptation (e.g. Bush et al., 2016) are hampered by limited understanding of how it varies in response to climate (Catullo et al., 2019; Diamond, 2018). Second, mechanistic population models combine evolutionary genetics and demography to predict how adaptive changes in key traits that affect population growth aid persistence in the face of environmental change (Bürger & Lynch, 1995; Lande & Shannon, 1996; Lynch & Lande, 1993). However, such models cannot accurately predict adaptation without including environmental variables and, importantly, their effects on trait expression and selection at different temporal or spatial scales—information that is challenging and costly to gain empirically (Chevin et al., 2010). There is thus a need to better predict how adaptation varies in time and space, and link predictions to relevant patterns of environmental change in ways that apply broadly across species.

Environmental tolerance curves, relating fitness to environmental variables either directly or mediated by underlying traits (Figure 1), are powerful tools for linking evolutionary outcomes to environmental change (Lynch & Gabriel, 1987; Sexton et al., 2017). Combining them with climate data, for example, predicts global shifts in geographic distributions, population growth rates, and extinction risks of ectotherms in response to projected changes in temperature (Deutsch et al., 2008; Pinsky et al., 2019; Vasseur et al., 2014; Woods et al., 2018). Such insights, however, often assume that environmental tolerance is static in time and space, when it may instead evolve over time as populations adapt to environmental change, and vary geographically with different forms and magnitudes of change (Gabriel & Lynch, 1992; Sheth

& Angert, 2014; Wieczynski et al., 2018). Progress on this front requires a better understanding of, and ability to predict, how complex, real-world patterns of environmental change shape environmental tolerance. Given the daunting task of managing this empirically, a unified theoretical framework for predicting the evolution of tolerance under real-world change, and the implications for geographic patterns in biodiversity, is therefore a pressing endeavour for evolutionary biology with clear relevance for conservation and management.

Temporal change in any environmental variable can be decomposed into different components—namely, abrupt change in the mean, constant directional change (trend) in the mean, cyclic change around the mean and stochastic change (noise) unexplained by other components (Figure 2; Dillon et al., 2016; Ruokolainen et al., 2009; Vasseur & Yodzis, 2004). These components should have different impacts on the evolution of environmental tolerance. To the extent that an environmental variable affects fitness, for example, its trend imposes directional selection on a population through sustained, directional movement in the optimum phenotype. In the absence of constraints (e.g. lack of suitable genetic variation), the population's mean phenotype should evolve to adaptively track the moving optimum (Lande & Shannon, 1996), shifting the peak of the environmental tolerance curve ($ε_{opt}$ in Figure 1) towards lower or higher environmental values (left or right in Figure 1). While trend remains by far the best-studied component of environmental change due to the pivotal role of directional selection in evolutionary responses to climate change (Hoffmann & Sgrò, 2011), and adaptation

<figure><img src="image_3.png" /></figure>

**FIGURE 1** Environmental tolerance curves relating fitness (W) to an environmental variable ($ε$). Each curve is described by a few key terms: $ε_{opt}$ is the environmental optimum at which fitness is maximised ($W_{max}$) and $ε_{min}$ and $ε_{max}$ are the lower and upper environmental limits at which fitness is minimised (at 0 or an arbitrary lower threshold). Tolerance breadth is then the range of environmental values in between, akin to the fundamental niche. Breadth depends on phenotypic plasticity in an underlying trait, described by the slope of the linear reaction norm relating trait expression to the environment (inset). The red curve is broader than the blue curve due to greater plasticity in the trait, but also has a lower peak due to costs of plasticity (weaker costs reduce the trade-off between breadth and peak; Lande, 2014).
uncorrelated white noise when $\rho = 0$ to positively correlated reddened noise when $\rho > 0$, without changing its variance (see Figure 2).

## 2.1.2 | Modelling evolution of adaptation and plasticity

We applied simulated time series above to a quantitative genetic model for the evolution of environmental tolerance, via adaptive changes in a plastic trait (linear reaction norm) that determines fitness. We modelled an individual's expression of the quantitative trait (z) as the sum of genetics, phenotypic plasticity, and random residual variation as

$$z = x + b\epsilon_t + y, \quad (3)$$

where x is the additive genetic breeding value for the trait (the intercept of the linear reaction norm relating it to $\epsilon_t$, the environmental variable in Equation 1), b is plasticity in the trait (the slope of the reaction norm), and y is residual variation. Terms x, b, and y are independent and normally distributed random variables, $x \sim N(\bar{x}, \sigma_x^2)$, $b \sim N(\bar{b}, \sigma_b^2)$, $y \sim N(\bar{y} = 0, \sigma_y^2 = 0.1)$, where overbars denote means and $\sigma^2$ denote variances.

The trait shows developmental plasticity, so that its expression is determined by environmental cues early in life and remains fixed thereafter (Nettle & Bateson, 2015). For simplicity, and to explore the effect of a lag between the environments of development and selection on the trait, we modelled selection operating at the end of life via fertility, as in semelparous organisms (e.g. Young & Augspurger, 1991). Selection could alternatively be modelled operating throughout the life-cycle (as in Cotto & Chevin, 2020), which could be explored in future work. We assumed that generations are discrete and non-overlapping, and expressed generation time (T) in arbitrary time-steps so that populations experience multiple environmental states (modelled by Equation 1) if $T > 1$. Therefore, in each generation G, trait expression is determined by the environment of developing individuals a fraction of a generation (or developmental lag, $\tau$) before selection ($\epsilon_{GT-\tau}$, where $\tau < T$), and selection is determined by the environment at the end of life ($\epsilon_{GT}$). Hence, if $T = 1$ (no environmental change within generations), or if $\tau = 0$ (no developmental lag), the environments of development and selection are the same ($\epsilon_{GT-\tau} = \epsilon_{GT}$). We further assumed that all individuals in the population experience the same environment, that population size is infinite and constant (no drift), and that selection is both frequency and density independent.

We allowed evolution by natural selection to change the trait's mean breeding value ($\bar{x}$) and mean plasticity ($\bar{b}$) in the population. The variances for x and b ($\sigma_x^2$ and $\sigma_b^2$), as well as for the residual effects (y), were assumed to be constant. Given the states of $\bar{x}$, $\bar{b}$ and $\epsilon_{GT-\tau}$ in each generation, the trait is normally distributed with mean and variance of

$$\bar{z} = \bar{x} + \bar{b}\epsilon_{GT-\tau}, \quad (4a)$$

$$\sigma_z^2 = \sigma_x^2 + \epsilon_{GT-\tau}^2 \sigma_b^2 + \sigma_y^2, \quad (4b)$$

Fitness in each generation is then a Gaussian function of trait expression as follows

$$W(z) = W_{\max} \exp\left(-\frac{(\theta - z)^2}{2\omega_z^2} - \frac{b^2}{2\omega_b^2}\right), \quad (5)$$

where $\theta$ is the trait optimum, $W_{\max}$ is the maximum individual fitness, $1/\omega_z^2$ is the strength of stabilising selection on the trait, and $1/\omega_b^2$ is the cost of plasticity in the trait (modelled as the strength of stabilising selection on the reaction norm slope; Chevin et al., 2010; Lande, 2014). The trait optimum is a linear function of the environment at the time of selection, $\theta = A + B\epsilon_{GT}$, where A is the optimum at $\epsilon_0 = 0$ (the initial or reference environment) and B is linear change in the optimum with environmental change (known as the environmental sensitivity of selection; Chevin et al., 2010). Selection then occurs at each generation following Chevin and Lande (2010) and evolved mean breeding value and mean plasticity at the end of the simulation were used to obtain the evolved environmental tolerance curve (see details in Supporting Information A in Data S1).

We validated the model by replicating scenarios in earlier studies and ensuring it retrieved similar predictions (Supporting Information B in Data S1). We then used this model to assess the evolution of environmental tolerance (Section 2.2), plasticity under different forms of environmental predictability (Section 2.3), and outcomes predicted by parameterisation with real environmental time series (Section 2.4).

Data processing and modelling was done in R v4.0.5 (R Core Team, 2021), with code (including Shiny app for implementation) provided on GitHub (https://github.com/CristobalGS/Adaptation-to-TemporalChange).

## 2.2 | Evolution of environmental tolerance

We simulated evolution under different forms of temporal change using new time series with components manipulated relative to a baseline, other parameters held constant, and evolutionary equilibrium determined, as in Supporting Information C and D in Data S1. The baseline had an initial mean environment ($\epsilon_0$) of 5, no trend ($\eta_{trend} = 0$), equal amounts (or contributions to environmental variance) of cyclic change and noise ($\eta_{cycle} = \sqrt{2}$, $\eta_{noise} = 1$, noting that $\sigma^2 = \eta_{noise}^2 + \eta_{cycle}^2/2$), and noise that was uncorrelated or white ($\rho = 0$). To assess the isolated effects of different components on evolved tolerance, we simulated an abrupt shift (two-fold increase) in the initial mean environment ($\epsilon_0 = 10$), a positive trend ($\eta_{trend} = 0.0001$), a two-fold increase in the amplitude of cyclic change ($\eta_{cycle} = 2\sqrt{2}$), a two-fold increase in noise ($\eta_{noise} = 2$, maintaining the same variance as the increase in cyclic change), and noise that was positively correlated or reddened in colour ($\rho = 0.65$). For brevity, we did not simulate more extreme events, but new time series (e.g. with extreme noise) could easily be generated to do so. To assess the combined effects of different components
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on evolved tolerance, we simulated pairwise combinations of the
changes above and a scenario with all changes combined (three-
and four-way combinations were also omitted for brevity, but re-
main avenues for future work).

## 2.3 | Evolution of plasticity under different forms of environmental predictability

To assess evolved plasticity under different forms and magnitudes of environmental predictability, we simulated environments with the same mean and variance, but comprising cyclic change only ($\eta_{cycle} = 2\sqrt{2}; \eta_{noise} = 0$), noise only ($\eta_{cycle} = 0; \eta_{noise} = 2$), or equal amounts of cyclic change and noise ($\eta_{cycle} = 2; \eta_{noise} = \sqrt{2}$). Values were chosen to maintain constant environmental variance across scenarios and divide it equally between components in the last one (given $\sigma_e^2 = \eta_{noise}^2 + \eta_{cycle}^2 / 2$). We further manipulated predictability in terms of noise colour ($\rho = 0, \rho = 0.5$ and $\rho = 0.9$) and developmental lag ($\tau$) relative to the baseline cycle period ($p=10$), which determines the correlation between environments of development and selection (Lande, 2009). In each case, we assessed equilibrium plasticity, and variation around equilibrium values, as in Supporting Information D in Data S1.

To validate simulations and assess their generality, we derived an equation for expected plasticity at equilibrium from our model (Supporting Information E in Data S1), and compared our simulation results to theoretical predictions for equivalent parameter values. To unify different forms of predictability, moreover, we derived an equation for the autocorrelation of the entire environmental time series (Equation 1), and compared it to the equation for plasticity (Supporting Information E in Data S1).

## 2.4 | Case study: Predicting thermal adaptation and plasticity in a global marine hotspot

To predict thermal adaptation and plasticity across the southern Australian hotspot, we parameterised our model with daily time series of sea surface temperature for three locations differing in mean, cyclic change, and noise colour (Box 1). Note that we depart from the usual practice of de-trending time series to analyse noise in the absence of deterministic components (e.g. cycling), given our interest in responses to temporal change in its entirety, and its importance for adaptation and evolution of plasticity.

In an attempt to parameterise our model with empirical estimates of biological variables, we set generation time (T) to 30 days

<figure><img src="image_6.png" /><figcaption>BOX 1 Temporal change in temperature across the southern Australian marine hotspot</figcaption></figure>

Southern Australia is a global hotspot of marine biodiversity and warming faster than the global average rate (Costello et al., 2022; Hobday & Pecl, 2014). Seasonal currents flowing south from the tropics and east from the Indian Ocean meet subantarctic water in Bass Strait, causing sea-surface temperature to vary temporally, geographically, and with localised features like bays and upwellings (Wijffels et al., 2018). To illustrate this variation, we estimated the mean, range (approximating seasonal cycling), and noise colour of temperature in 1×1 km grid cells observed daily from 2011 to 2018 (www.ghrsst.org), then mapped components (panels a-c). Mean and cyclic change were estimated as averages of the WorldClim variables BIO1 (annual mean temperature) and BIO7 (temperature annual range), after Fick and Hijmans (2017). Noise colour was estimated as $\beta$ (see Figure 2) for ease of calculation, and is used here purely for illustration without feeding into the model. Other components varied little across the hotspot so are omitted for brevity. Based on maps, we extracted raw time series for each of three locations (labelled points in panels a-c): southwestern Tasmania (TAS), Port Phillip Bay in Victoria (VIC), and southern New South Wales (NSW). We then parameterised our model with these time series (see Section 2).
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to simulate a common scenario in marine invertebrates (Levin & Bridges, 1995), and developmental lag (τ) to 29 to simulate plasticity in early development. We reanalysed data on early viability at 16.5–24°C for a marine tubeworm from the middle location (Chirgwin et al., 2021) to estimate additive genetic variation for the trait at the mean temperature ($σ_x^2 = 0.0839$), additive genetic variation for plasticity across temperatures ($σ_b^2 = 0.0002$), and heritability of plasticity across temperatures ($h_b^2 = 0.4451$). Since early viability may incur stabilising selection via trade-offs with other fitness traits, we consider these adequate approximations to trait values. We set the strength of stabilising selection ($1/ω_z^2$) to $|0.10|$, the median estimate from Kingsolver et al. (2001) and held other parameters (including costs of plasticity and environmental sensitivity of selection) at baseline values in the absence of suitable estimates. We assumed all parameters were uniform across locations for the same reason.

Since outcomes did not reach equilibrium during the time series, and trend was near-zero at each location, we ran longer simulations (concatenating the series 3000 times) to ensure that simulations reached equilibrium before predicting tolerance curves from outcomes (see details and caveats in Supporting Information D in Data S1).

# 3 | RESULTS

## 3.1 | Evolution of environmental tolerance

We briefly synthesise the isolated effects of environmental components changing relative to the baseline (diagonals in Figure 3), then assess their combined effects (off-diagonals in Figure 3). Although we focus on evolved tolerance curves with fitness against the

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**FIGURE 3** Predicted evolution of environmental tolerance under (a) an abrupt change in the mean environment, (b) a constant rate of change in the mean environment (trend), (c) an increase in the amplitude of cyclic change in the environment, (d) an increase in the amount of stochastic change (noise) in the environment, and (e) an increase in the autocorrelation of stochastic change (noise colour). The evolved tolerance curve for the baseline scenario (Supporting Information C in Data S1) is in black and curves for alternative scenarios differing in components of environmental change (see main text) are in red. Diagonal plots (a–e) show the effects of components changing in isolation, off-diagonal plots (f–o) show the effects of combined changes, and the top-right plot (p) shows all components changing simultaneously. Insets show excerpts of the environmental time series for which evolution was simulated, with the baseline in black and alternative scenarios in red (axes are omitted for clarity but match Figure 2). Curves were predicted using mean breeding values and plasticities at dynamic equilibrium as described in Supporting Information A in Data S1. Shaded areas show variation in tolerance breadths due to variation in plasticities around equilibrium values.
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environment, reaction norm intercepts (breeding values in mean environment) and plasticities underlying them (Figure 1) are presented in Table S1. Note that results are primarily illustrative and depend on parameter values chosen for scenarios.

### 3.1.1 | Effect of abrupt environmental change

The abrupt increase in mean environment produced an abrupt increase in environmental optimum, shifting the peak of the evolved tolerance curve to match the new mean without eventually affecting tolerance breadth (Figure 3a), although transient increases in plasticity and tolerance breadth may still occur (Chevin & Lande, 2010; Lande, 2009).

### 3.1.2 | Effect of trend

The isolated trend produced a gradual increase in environmental optimum, again shifting the peak of the evolved tolerance curve to track the moving optimum. This was now accompanied by an increase in tolerance breadth due to higher plasticity at equilibrium (Figure 3b).

### 3.1.3 | Effect of cyclic change

The isolated increase in cycle amplitude saw higher plasticity evolve (analysed further in relation to developmental lag and cycle period in Section 3.2), increasing both tolerance breadth and variability in breadth (Figure 3c). This produced little decrease in maximum fitness (curve height), given the weak cost of plasticity assumed here.

### 3.1.4 | Effect of noise

The isolated increase in noise decreased plasticity and tolerance breadth (Figure 3d) whereas the isolated increase in noise colour (autocorrelation of noise) had little effect (Figure 3e).

### 3.1.5 | Combined effects of different components

Notably, the joint increase in mean and trend (Figure 3f) not only produced a higher environmental optimum than increasing each component alone, but also greater tolerance breadth (via a 10% increase in plasticity; Table S1) than the increase in trend alone. Jointly increasing trend and cycle amplitude (Figure 3j) also produced greater tolerance breadth (via a 12%–25% increase in plasticity; Table S1) than increasing each component alone. However, jointly increasing noise and non-noise components (Figure 3h,k,m) produced narrower tolerance breadth than increasing non-noise components alone. In particular, jointly increasing cycle amplitude and noise (Figure 3m)

reduced tolerance breadth (via a 51% decline in plasticity) relative to the increase in amplitude alone, emphasising how stochastic change counters the effect of cyclic change on plasticity. Further, changing all components simultaneously (Figure 3p) produced a similar tolerance curve to the effect of trend in isolation, suggesting that trend dominates curve evolution when cyclic change and noise counter each other's effects (as in Figure 3m). Other combined changes had similar effects to components changing in isolation.

## 3.2 | Evolution of plasticity under different forms of environmental predictability

Expected plasticity at evolutionary equilibrium (Figure 4) proved to be as follows:

$$E(\bar{b}/B) = \frac{2\eta_{\text{noise}}^2 \rho + \eta_{\text{cycle}}^2 \cos\left(\frac{2\pi\tau}{P}\right)}{2R_{\text{cost}} + \eta_{\text{cycle}}^2 + 2\eta_{\text{noise}}^2}, \quad (6)$$

where $R_{cost} = v_b / v_z$ is the relative strength of the cost of plasticity, scaled to the strength of stabilising selection on the trait (Supporting Information E in Data S1). Equation (6) shows that with no cost of plasticity ($R_{cost} = 0$), mean plasticity $\bar{b}$ at equilibrium (scaled to the slope of the optimum $B$) is simply a weighted average of (i) the predictability of environmental noise (measured by its autocorrelation $\rho$), and (ii) similarity in the cyclic component of the environment over the fraction $\tau / P$ of a period, weighted by their relative contributions to the total environmental variance (measured by $\eta$ parameters). Importantly, the autocorrelation of the entire environmental time series, not separating cycle from noise (Equation 6 and Supporting Information E in Data S1), is

$$\frac{\text{Cov}(\varepsilon_t, \varepsilon_{t-\tau})}{\sigma_{\varepsilon}^2} = \frac{2\eta_{\text{noise}}^2 \rho + \eta_{\text{cycle}}^2 \cos\left(\frac{2\pi\tau}{P}\right)}{\eta_{\text{cycle}}^2 + 2\eta_{\text{noise}}^2} = \lim_{R_{\text{cost}} \to 0} \left(E\left(\bar{b}/B\right)\right). \quad (7)$$

In other words, when costs of plasticity approach zero, equilibrium plasticity evolves towards the overall autocorrelation of the environment over the developmental lag, accounting for both stochastic and deterministic (cycling) components. With costs of plasticity, Equation (6) shows that the magnitude of plasticity will be all the more reduced as $R_{cost}$ becomes large relative to the total environmental variance ($\eta_{cycle}^2 + 2\eta_{noise}^2$); conversely, a given cost of plasticity may be overcome by larger environmental fluctuations selecting more strongly for plasticity.

These predictions were confirmed in our simulations. When cyclic change dominated, equilibrium plasticity depended purely on the ratio of developmental lag ($\tau$) to cycle period ($P$), following the predicted cosine function (Figure 4a). In particular, $\bar{b}/B$ was negative (plasticity opposed changes in optimum) when lag was between $1/4$ and $3/4$ of a period (being lowest at half a period), and highest when lag was zero or equal to one period (where minimum and maximum $\bar{b}/B = \pm \frac{\eta_{cycle}^2}{2R_{cost} + \eta_{cycle}^2} = \pm 0.794$), which both produce identical environments of development and selection. The same pattern repeated for
<figure><img src="image_11.png" /><figcaption>FIGURE 4 Evolution of plasticity under different forms of predictability in environments with (a) cyclic change only ($\eta_{cycle} = 2\sqrt{2}$; $\eta_{noise} = 0$), (b) noise only ($\eta_{cycle} = 0$; $\eta_{noise} = 2$), and (c) equal amounts of cyclic change and noise ($\eta_{cycle} = 2$; $\eta_{noise} = \sqrt{2}$). Lines are theoretical predictions of mean plasticity at equilibrium, with developmental lag ($\tau$) ranging from none to equalling the cycle period ($P = 10$), and noise colour ranging from white or uncorrelated ($\rho = 0$, depicted by an unbroken line) to reddened or positively correlated ($\rho = 0.5$ and $\rho = 0.9$, depicted by dashed and dotted lines respectively). Points are results of equivalent simulations, coloured by the correlation between environments of development and selection (or black for simulation means). Note that values of cyclic change and noise maintain constant environmental variance across scenarios while dividing it equally between components in (c), and (b) still shows developmental lag relative to cycle period, even though $\eta_{cycle} = 0$. Other environmental parameters: $P = 10$, $\epsilon_0 = 5$; $\eta_{trend} = 0$. Evolutionary parameters: $\sigma_x^2 = 0.5$; $\sigma_b^2 = 0.05$; $\omega_b^2 = 50$; $\omega_z^2 = 50$; $y = 0$; $\sigma_y^2 = 0.1$; $W_{max} = 1$; $h_b^2 = 0.5$; $\bar{x}_0 = 0$; $\bar{b}_0 = 0$; $A = 0$; $B = 1$.</figcaption></figure>

lags longer than a period, and held regardless of generation time $T$, provided $T$ exceeds lag (not shown).

When noise dominated (Figure 4b), plasticity decreased as longer lags decreased the correlation between development and selection. As predicted for a first-order autoregressive process (simulated here), plasticity declined geometrically as lags increased, and more gradually as noise became more autocorrelated (redder; compare dashed vs dotted lines, and light-red vs red points, in Figure 4b). Conversely, at the limit of completely-unpredictable white noise ($\rho = 0$), plasticity declined abruptly from one to zero for any non-zero lag (grey points and continuous lines in Figure 4b). Note that unlike the cycling environment, plasticity never became strongly negative when noise was positively autocorrelated, as assumed here (and consistent with most natural observations).

Equal magnitudes of cyclic change and noise (Figure 4c) produced a blend of the dynamics above. For example, equilibrium plasticity cycled as developmental lag increased (as in Figure 4a), but was moderated by noise colour pushing plasticity upwards or downwards (as in Figure 4b). Likewise, cyclic change moderated the effect of noise colour on plasticity, diminishing differences in equilibrium

values under white noise ($\rho = 0$) versus moderately reddened noise ($\rho = 0.5$), especially, as cyclic change increased from Figure 4b to Figure 4c. These results were well predicted on average by the theoretical prediction in Equation (6), with additional noise in simulations owing to stochasticity.

## 3.3 | Case study: Predicting thermal adaptation and plasticity in a global marine hotspot

Temperature time series for selected locations (Figure 5a) translated to predictions of geographic variation in thermal adaptation at evolutionary equilibrium for our hypothetical marine invertebrate with a 30-day generation time (Figure 5b). Tolerance curves differed in the positions of optima (vertical lines), predicting higher thermal tolerance through evolution of higher mean breeding values in locations (like New South Wales) with higher mean temperatures (Table S2). Evolved plasticities and thermal breadths also varied geographically, being highest in locations (like Victoria) with the greatest thermal range (Figure 5b; Table S2). That thermal breadths exceeded expectations based on known empirical
<figure><img src="image_12.png" /></figure>

FIGURE 5 Predicted thermal adaptation and plasticity in the southern Australian hotspot for a hypothetical marine invertebrate with a 30-day generation time. (a) Temperature time series used to simulate evolution at selected locations, with dashed horizontal lines showing trends in means. (b) Evolved tolerance curves at equilibrium for each location, with dashed vertical lines showing thermal optima. Shading around curves (showing variation in breadth, per Figure 3) is unnoticeable due to low variation in plasticity at equilibrium.

estimates (e.g. Chung & Schulte, 2020; Rebolledo et al., 2020) and thermal ranges (Figure 5a) could reflect an overly weak strength of stabilising selection ($1/\omega_z^2 = 0.10$), which influences tolerance breadth in our model. Alternatively, it could reflect unrealistic estimates of other evolutionary parameters, especially at more extreme temperatures.

4 | DISCUSSION

Environmental change is a key driver of evolutionary adaptation and diversification, yet our ability to predict biological responses to it is far from complete. To address this gap, we extended classic quantitative genetic theory to develop a model for the evolution of environmental tolerance (combining adaptation and developmental plasticity) in response to major components of temporal environmental change. First, we used the model to synthesise predicted responses to components changing in isolation, then generated new insights into their combined effects. Second, we analysed the evolution of plasticity—which underpins tolerance breadth in the model—in relation to different forms of environmental predictability. Specifically, we show that predictability (a) emerges from the interplay of cyclic change, stochastic change (noise), and lag between development and selection; and (b) is ultimately a function of the autocorrelation of temporal environmental change (with all components combined) and costs of plasticity. Third, we parameterise the model with real temperature time series to predict geographic patterns of thermal adaptation and plasticity in a priority region for conservation where biodiversity may be particularly sensitive to climate change. Together, our findings highlight the need to fully integrate temporal environmental change into predictions of adaptation, and plasticity in the context of climate change.

Our predictions of environmental tolerance in response to isolated components of temporal change synthesise earlier results. For example, an abrupt increase in mean environment increased the mean phenotype as in Gomulkiewicz and Holt (1995), shifting

the optimum environment for the tolerance curve, and an increase in environmental trend saw adaptive tracking of the optimum phenotype with a constant lag, as in Lande and Shannon (1996) and population responses to directional selection in nature (Hoekstra et al., 2001; Kingsolver & Diamond, 2011). Likewise, an increase in cycle amplitude led to greater plasticity and tolerance breadth, as in previous theoretical (e.g. Ezard et al., 2014) and empirical studies (Ketola et al., 2013), in addition to greater variation in plasticity. By comparison, greater noise reduced plasticity and tolerance breadth, in line with its tendency to reduce environmental predictability (Reed et al., 2010; Tufto, 2015), but the negligible effects of noise colour were in contrast to previous studies (Lande, 2009; Leung et al., 2020; Tufto, 2015). Those studies, however, assessed noise colour in purely stochastic environments, whereas our results flag the need to assess it in combination with cyclic change (as will often be the case in nature). Analysing the joint effects of these components revealed, moreover, the opposing effects of cycle amplitude and noise on plasticity, emphasising that their relative contributions to environmental variability may shape environmental tolerance more than currently appreciated.

Since organisms need reliable cues to respond to, environmental predictability is vital for adaptive plasticity to evolve (Reed et al., 2010). Less recognised, however, is that different components of temporal change can generate different forms of predictability, with potentially different outcomes (Botero et al., 2015; Ezard et al., 2014; Marshall & Burgess, 2015). Unifying different forms here highlights the correlation between environments of development and selection as an integrated measure that best explains the evolution of plasticity (see also Bitter et al., 2021; Gavrillets & Scheiner, 1993; Lande, 2009). When costs of plasticity are weak, moreover, we show that its evolution is equal to the autocorrelation of temporal environmental change in its entirety, independent of biological variables other than developmental lag relative to cycle period. Since lag relative to cycle period will be tied to generation time, this emphasises that life history may critically shape how plasticity responds to different components of
temporal change. For example, we might expect plasticity evolution to respond more to noise colour in short-lived microbes that do not experience environmental cycles (e.g. Leung et al., 2020), or seasonality relative to developmental lag in longer-lived species that do (Williams et al., 2017). Our results also predict circumstances (e.g. species with generation times one- to three-quarters the cycle period) where negative plasticity may evolve (see also King & Hadfield, 2019; van Dooren, 2001). Interestingly, few models have explored how labile traits (approximated by little or no lag) respond to predictability (Lande, 2014; Rescan et al., 2022), flagging a need to better understand the evolution of plasticity in these cases.

Temperature will almost certainly drive adaptation, given its pervasive biological effects (Clarke, 2017). Predicting thermal adaptation in nature is therefore crucial in predicting species' responses to ongoing climate change (Hoffmann & Sgrò, 2011). We illustrate the utility of our model in this regard by applying it to a case study of a global marine hotspot in southern Australia (Costello et al., 2022; Hobday & Pecl, 2014). Marine hotspots like this not only harbour exceptional biodiversity, but have warmed more and faster than terrestrial hotspots (Costello et al., 2022), and biodiversity in them is especially prone to redistribution, given that marine species track climate velocities more closely than terrestrial species (Lenoir et al., 2020; Sunday et al., 2015). Our simulations predict local thermal adaptation across this region, with populations differing in both the positions and breadths of their thermal tolerance curves. These predictions could be validated empirically, for example, by targeted estimates of local adaptation and plasticity (Blanquart et al., 2013), selection and heritability (Shaw & Etterson, 2012), and genomic tools like environment-allele associations and expression analyses (Mallard et al., 2020; Rellstab et al., 2015), for species with known generation and developmental times. Given that predicted thermal breadths were wider than realistically expected based on known thermal limits (e.g. Chung & Schulte, 2020; Rebolledo et al., 2020), such validations are a priority at temperatures where physiological and biophysical constraints are reached.

We aimed to make our model general and, at a minimum, adaptable to any system with temporal data available. For example, it could be used with climatic variables scaled to different temporal resolutions to match relevant scales of climate change, or with climate projections to predict adaptation in future climates, or to extend current insights into plastic responses to climate extremes (Chevin & Hoffmann, 2017). Nevertheless, all models are compromises of generality, precision, and realism (Levins, 1966), and ours is no exception. Evolution may of course depend on other factors that were not explored here. For example, local adaptation might not evolve if gene flow among populations is high (Hadfield, 2016), if populations lack genetic variation for adaptation (Hoffmann & Sgrò, 2011; Lande & Shannon, 1996), or if genetic correlations inhibit adaptation (Lande, 1979). Information about these factors, especially near physiological or biophysical limits, would all improve model predictions and their geographic contexts. Much of this information, if available,

could already be imputed in our model or incorporated by slight modifications. Future research could also explore how relaxing the shapes of tolerance curves or reaction norms affects predictions, or how different parameter values affect evolutionary rates, rather than outcomes (our focus here).

There is growing recognition of the need to better integrate real-world patterns of temporal environmental change into biological predictions (Bates et al., 2018; Dillon et al., 2016; Helmuth et al., 2014; Vinton et al., 2022). Translating theory from paper to environmental conditions in nature is an important next step in testing and validating predictions, with the potential to improve our understanding of biological responses to climate change. Overall, by expanding and re-analysing a classic evolutionary model, our study offers new insights into the evolution of adaptation and plasticity in response to temporal environmental change. Moreover, we have illustrated how this model—with its acknowledged limitations—might be used to generate testable predictions of adaptation and plasticity in natural environments facing accelerated climate change, and provide supporting materials (including Shiny app) to facilitate this. Our approach offers a well-established, broadly-applicable, and pragmatic framework for understanding adaptation to complex, real-world environments, with scope to enhance the management and conservation of biological systems.

## AUTHOR CONTRIBUTIONS

Cristóbal Gallegos and Keyne Monro conceived and designed the study, and led writing with input from Kathryn A. Hodgins and Luis-Miguel Chevin. Cristóbal Gallegos performed simulations and data analyses, and Luis-Miguel Chevin developed analytical results. All authors contributed critically to drafts and gave final approval for publication.

## ACKNOWLEDGEMENTS

We specially thank Tim Connallon for help developing the model and previous manuscript versions. This research was supported by funding awarded to GC by the Holsworth Wildlife Research Endowment and Ecological Society of Australia, and to KM and KH by the Australian Research Council's Discovery Scheme.

## CONFLICT OF INTEREST STATEMENT

We have no conflicts of interest to declare.

## PEER REVIEW

The peer review history for this article is available at https://www.webofscience.com/api/gateway/wos/peer-review/10.1111/2041-210X.14462.

## DATA AVAILABILITY STATEMENT

Data, R scripts and Shiny app to reproduce the results are available via GitHub https://github.com/CristobalGS/Adaptation-to-TemporalChange and Zenodo https://zenodo.org/records/14029488 (Gallegos et al., 2024).
ORCID

Cristóbal Gallegos https://orcid.org/0000-0002-0454-0552

Luis-Miguel Chevin https://orcid.org/0000-0003-4188-4618

Kathryn A. Hodgins https://orcid.org/0000-0003-2795-5213

Keyne Monro https://orcid.org/0000-0002-0956-3032

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## SUPPORTING INFORMATION

Additional supporting information can be found online in the Supporting Information section at the end of this article.

**Data S1:** Mathematical model for adaptation and evolution of plasticity under different forms of temporal environmental change.

**How to cite this article:** Gallegos, C., Chevin, L.-M., Hodgins, K. A., & Monro, K. (2025). Predicting adaptation and evolution of plasticity from temporal environmental change. *Methods in Ecology and Evolution*, 16, 84–96. https://doi.org/10.1111/2041-210X.14462
# Supporting Information

## Mathematical model for adaptation and evolution of plasticity under different forms of temporal environmental change

A) Model details. Following Chevin & Lande (2010), we assumed that selection in each generation acts first on the trait's plasticity and then on its mean. After selection on plasticity, the distribution of b is normal with mean and variance of

$$ \bar{b}^* = \frac{\bar{b}\omega_b^2}{\omega_b^2 + \sigma_b^2} \quad (\text{eq. 6a}) $$

$$ \sigma_b^{2*} = \frac{\sigma_b^2 \omega_b^2}{\omega_b^2 + \sigma_b^2} \quad (\text{eq. 6b}) $$

(e.g., Lande, 1976; Svensson & Connallon, 2019), so that the trait distribution is normal with mean and variance of

$$ \bar{z}^* = \bar{x} + \bar{b}^* \varepsilon_{GT-\tau} \quad (\text{eq. 7a}) $$

$$ \sigma_z^{2*} = \sigma_x^2 + \varepsilon_{GT-\tau} \sigma_b^{2*} + \sigma_y^2 \quad (\text{eq. 7b}). $$

Mean lifetime fitness of the population then becomes

$$ \bar{W} = W_{\max} \sqrt{\frac{\omega_b^2 \omega_z^2}{(\omega_b^2 + \sigma_b^2)(\omega_z^2 + \sigma_z^2)}} \exp \left( - \frac{\bar{b}^2}{2\omega_b^2 + 2\sigma_b^2} - \frac{(\theta - \bar{z}^*)^2}{2\omega_z^2 + 2\sigma_z^2} \right) \quad (\text{eq. 8}), $$

and the evolution of the mean breeding value and mean plasticity per generation is given by

$$ \Delta \bar{x} = \sigma_x^2 \frac{\partial \ln(\bar{W})}{\partial \bar{x}} \quad (\text{eq. 9a}) $$

and

$$ \Delta \bar{b} = \sigma_b^2 h_b^2 \frac{\partial \ln(\bar{W})}{\partial \bar{b}} \quad (\text{eq. 9b}), $$

where $h_b^2$ is the heritability of plasticity (Lande, 1976).

Finally, substituting $\theta = A + B\varepsilon_{GT}$ and eq. 4a into eq. 8 gives fitness as a function of $\bar{x}$, $\bar{b}$, and $\varepsilon_t$ as follows

$$ \bar{W}(\bar{x}, \bar{b}, \varepsilon_t) = W_{\max} \sqrt{\frac{\omega_b^2 \omega_z^2}{(\omega_b^2 + \sigma_b^2)(\omega_z^2 + \sigma_z^2)}} \exp \left( - \frac{\bar{b}^2}{2\omega_b^2 + 2\sigma_b^2} - \frac{(A + B\varepsilon_{GT} - \bar{x} - \bar{b}\varepsilon_{GT-\tau})^2}{2\omega_z^2 + 2\sigma_z^2} \right) \quad (\text{eq. 10}). $$

We then predicted the evolved environmental tolerance curve (per Figure 1) by using the evolved breeding value ($\bar{x}$), and plasticity ($\bar{b}$) to estimate fitness across an arbitrary environmental range ($\varepsilon$). Breeding value determined curve position along the range (equivalent to $\varepsilon_{opt}$ in Figure 1), plasticity determined curve breadth (with higher plasticity leading to higher breadth, per eq. 10 and Figure 1), and a broader curve entailed a lower peak (maximum fitness) depending on the cost of plasticity (Figure 1).
**B) Model validation.** To validate our model, we simulated scenarios from earlier studies and compared our outcomes against those previous predictions. As per Lande & Shannon (1996), when setting plasticity to zero and not allowing it to evolve ($\bar{b} = 0, \sigma_b^2 = 0$), the mean phenotype evolved rapidly towards a new fixed optimum, or tracked an optimum moving at a constant rate with a constant lag at equilibrium. In the latter case, the observed lag (difference between optimum and trait value) closely matched the expected lag ($\eta_t \omega_z^2 / \sigma_x^2$). When setting initial plasticity to zero but allowing it to evolve ($\bar{b} = 0, \sigma_b^2 = 0.045$), our model retrieved a similar evolutionary dynamic to Lande (2009), in which adaptation to an abrupt, extreme change in environment first occurs by a rapid transient increase in plasticity, which slowly declines to a final equilibrium value (> 0) as the breeding value slowly approaches the new optimum by genetic assimilation. For further details of validation, see accompanying R scripts on GitHub (https://github.com/CristobalGS/Adaptation-to-TemporalChange/blob/main/Model%20validations.R).

**C) Baseline scenario.** As a baseline for comparison, we simulated 200,000 time-steps (e.g., hours, days, or months) of evolution for a population that was optimally adapted to its environment initially. Initial mean breeding value was $\bar{x}_0 = 0$, and initial mean plasticity was $\bar{b}_0 = 0$. To simplify the evolutionary analysis, and following Lande (2014), we assumed that the breeding value of the optimum phenotype in the reference environment was $A = 0$ and its optimum plasticity was $B = 1$, so that mean plasticity relative to its optimum equals mean plasticity ($\bar{b}/B = \bar{b}$; as in Ashander et al., 2016). As visualised in Figure S1A, the initial mean environment ($\varepsilon_0 = 5$) had no trend ($\eta_{trend} = 0$), equal amounts (or contributions to environmental variance) of cyclic change and noise ($\eta_{cycle} = \sqrt{2}, \eta_{noise} = 1$), a cycle period of $P = 10$ (10 time-steps per cycle), and noise that was white (no autocorrelation, $\rho = 0$). Generation time was $T = 11$ and developmental lag was $\tau = 10$. Thus, given the cycle period, each generation experienced a complete cycle of environmental change before selection (as in Lande, 2019), following the environmental determination of trait expression early in life. Other parameters had values of $\sigma_x^2 = 0.5, \sigma_b^2 = 0.05, \omega_b^2 = 50, \omega_z^2 = 50, y = 0, \sigma_y^2 = 0.1, W_{max} = 1, h_b^2 = 0.5$ (higher and lower costs of plasticity, $1/\omega_b^2$, were explored, but led to lower or higher evolved plasticity without qualitatively changing results).

We then tracked the evolution of the mean intercept ($\bar{x}$) and mean plasticity ($\bar{b}$) across generations under this baseline environmental scenario, and predicted the mean tolerance curve (along with its range as a measure of variability) using equilibrium values from generation 10,000 onwards (see below for determination of equilibrium). At this point, the mean breeding value (Figure S1B) and mean plasticity (Figure S1C) reached dynamic equilibrium (as in Chevin & Lande, 2015), fluctuating stably in ways that made the evolved reaction norm vary in slope (Figure S1D, shaded area), and the evolved tolerance curve vary in both breadth (Figure E, shaded area) and position (shown together in Figure S2). For simplicity, and given variation in curve position did not qualitatively change our results, we focus on variation in breadth only here.

**D) Determination of equilibrium.** To determine equilibrium, we fitted a standard (Michaelis–Menten) saturation curve to the evolution of the mean breeding value, then found the number of generations when the
derivative of that curve approached zero (10⁻⁴). After testing this method in different simulations, we chose the value above (10,000 generations) for consistency across simulations. Given the simulated time steps and generation time above, this value ensured all simulations (bar the case study; see below) were at equilibrium for at least a few thousand generations before predicting tolerance curves from outcomes (see Figure S1).

For the case study, simulations did not reach equilibrium during the real time series (daily observations of temperature at selected locations from 2011 to 2018) and remained biased by initial conditions. Therefore, since trend was near-zero at each location, we concatenated the series 3000 times to extend simulations long enough to meet the requirement for equilibrium above. This approach allowed us to parameterise our model with real time series of limited length, but has two caveats: (1) environments separated by the length of the original time series will be perfectly autocorrelated, and (2) generations before vs after each point of concatenation will be completely uncorrelated, even when environmental autocorrelation is high. These artefacts should have little effect on equilibrium outcomes if the total time series is long enough, but will affect outcomes otherwise. An alternative approach could be to infer the parameters of an actual time series of interest, then re-simulate a new time series of desired length from them.

**E) Theoretical prediction of expected plasticity at equilibrium.** Assuming the long-run average of the expected intercept (x̄) equals A, deriving equations from our model above (see details in attached Mathematica notebook) results in

$$E\left(\frac{\bar{b}}{B}\right) = \frac{2\eta_{noise}^2\rho + \eta_{cycle}^2 \cos\left(\frac{2\pi}{P}\right)}{2R_{cost} + \eta_{cycle}^2 + 2\eta_{noise}^2} \quad (\text{eq. 11}),$$

where Rcost = γb/γz is the relative cost of plasticity scaled to the strength of stabilizing selection on the trait, such that γb = ωb²/σb² and γz = ωz²/σz². Note that this approach neglects the role of the cost of plasticity in reducing the additive genetic variance for plasticity and for the trait, which is most appropriate in the case of weak selection for the cost of plasticity.

Therefore, when costs of plasticity are very small (γb ≈ 0), equilibrium plasticity can be approximated by

$$E\left(\frac{\bar{b}}{B}\right) \approx \frac{2\eta_{noise}^2\rho + \eta_{cycle}^2 \cos\left(\frac{2\pi}{P}\right)}{\eta_{cycle}^2 + 2\eta_{noise}^2} \quad (\text{eq. 12}),$$

and becomes completely dependent on the environment along with developmental lag relative to cycle period (τ/P). Importantly, deriving the autocorrelation of the entire environmental time series (i.e., dividing its autocovariance by its variance; see details in attached Mathematica notebook) produces the same equation:

$$\frac{\text{cov}(\varepsilon_t, \varepsilon_{t-\tau})}{\sigma_e^2} = \frac{2\eta_{noise}^2\rho + \eta_{cycle}^2 \cos\left(\frac{2\pi\tau}{P}\right)}{\eta_{cycle}^2 + 2\eta_{noise}^2} = \lim_{R_{cost} \to 0} \left(E\left(\frac{\bar{b}}{B}\right)\right) \quad (\text{eq. 13}).$$
F) References

Ashander, J., Chevin, L.-M., & Baskett, M. L. (2016). Predicting evolutionary rescue via evolving plasticity in stochastic environments. Proceedings of the Royal Society B: Biological Sciences, 283(1839), 20161690.
https://doi.org/10.1098/rspb.2016.1690

Chevin, L. M., Lande, R., & Mace, G. M. (2010). Adaptation, plasticity, and extinction in a changing environment: towards a predictive theory. PLoS Biology, 8(4). https://doi.org/10.1371/journal.pbio.1000357

Chevin, L.-M., & Lande, R. (2010). When do adaptive plasticity and genetic evolution prevent extinction of a density-regulated population? Evolution, 64(4), 1143–1150. https://doi.org/10.1111/j.1558-5646.2009.00875.x

Chevin, L.-M., & Lande, R. (2015). Evolution of environmental cues for phenotypic plasticity. Evolution, 69(10), 2767–2775. https://doi.org/10.1111/evo.12755

Chevin, L.-M., Lande, R., & Mace, G. M. (2010). Adaptation, plasticity, and extinction in a changing environment: Towards a predictive theory. PLoS Biology, 8(4). https://doi.org/10.1371/journal.pbio.1000357

Lande, R. (1976). Natural selection and random genetic drift in phenotypic evolution. Evolution, 30(2), 314–334.
https://doi.org/10.2307/2407703

Lande, R. (2009). Adaptation to an extraordinary environment by evolution of phenotypic plasticity and genetic assimilation. 22, 1435–1446. https://doi.org/10.1111/j.1420-9101.2009.01754.x

Lande, R. (2014). Evolution of phenotypic plasticity and environmental tolerance of a labile quantitative character in a fluctuating environment. Journal of Evolutionary Biology, 27(5), 866–875. https://doi.org/10.1111/jeb.12360

Lande, R. (2019). Developmental integration and evolution of labile plasticity in a complex quantitative character in a multiperiodic environment. Proceedings of the National Academy of Sciences, 116(23), 11361–11369.
https://doi.org/10.1073/pnas.1900528116

Lande, R., & Shannon, S. (1996). The role of genetic variation in adaptation and population persistence in a changing environment. Evolution, 50(1), 434–437. https://doi.org/10.1080/15555270601041821

Svensson, E. I., & Connallon, T. (2019). How frequency-dependent selection affects population fitness, maladaptation and evolutionary rescue. Evolutionary Applications, 12(7), 1243–1258. https://doi.org/10.1111/eva.12714
<figure><img src="image_13.png" /><figcaption>**Figure S1.** Evolution under the baseline environmental scenario (see above). (A) Excerpt of the environmental time series for which evolution was simulated. (B) Evolution of mean breeding value. (C) Evolution of mean plasticity. (D) Evolved trait reaction norm at equilibrium, with shaded area showing variation in mean plasticity around the equilibrium value. (E) Evolved tolerance curve at equilibrium, with shaded area showing variation in tolerance breadth around the equilibrium value. The dotted line is equivalent to $\varepsilon_{opt}$ in Figure 1.</figcaption></figure>
<figure><img src="image_14.png" /></figure>

**Figure S2.** Variation in tolerance curve position (determined by the mean breeding value) and breadth (determined by mean plasticity) for the baseline environmental scenario. The black curve is the mean tolerance curve at dynamic equilibrium (generation 10,000 onwards), with shaded area showing variation in tolerance breadth predicted from maximum and minimum plasticities at equilibrium. The dotted line is equivalent to ε<sub>opt</sub> in Figure 1. Dashed red and blue curves are predicted from maximum and minimum mean breeding values at equilibrium, respectively.
<table><caption>**Table S1.** Mean breeding values ($\bar{x}_{eq}$) and plasticities ($\bar{b}_{eq}$), with minima and maxima beneath, under changes in environmental mean, trend, cyclic change, noise, and noise colour (autocorrelation of noise). Diagonal elements are values after environmental components changed in isolation and off-diagonal elements are values after combined changes. Values were calculated at dynamic equilibrium (generation 10,000 onwards) and used to predict tolerance curves in Figure 3.</caption><thead><tr><th></th><th>Change in mean</th><th>Trend</th><th>Cyclic change</th><th>Noise</th><th>Noise colour</th></tr></thead><tbody><tr><td>Change in mean</td><td>$\bar{x}_{eq} = 6.552$<br>$[6.251, 6.834]$<br>$\bar{b}_{eq} = 0.344$<br>$[0.269, 0.404]$</td><td></td><td></td><td></td><td></td></tr><tr><td>Trend</td><td>$\bar{x}_{eq} = 10.289$<br>$[7.761, 10.453]$<br>$\bar{b}_{eq} = 0.650$<br>$[0.578, 0.694]$</td><td>$\bar{x}_{eq} = 9.957$<br>$[7.356, 10.138]$<br>$\bar{b}_{eq} = 0.592$<br>$[0.494, 0.637]$</td><td></td><td></td><td></td></tr><tr><td>Cyclic change</td><td>$\bar{x}_{eq} = 3.415$<br>$[3.258, 3.606]$<br>$\bar{b}_{eq} = 0.657$<br>$[0.584, 0.711]$</td><td>$\bar{x}_{eq} = 6.298$<br>$[4.325, 6.461]$<br>$\bar{b}_{eq} = 0.741$<br>$[0.665, 0.796]$</td><td>$\bar{x}_{eq} = 1.678$<br>$[1.464, 1.892]$<br>$\bar{b}_{eq} = 0.662$<br>$[0.603, 0.717]$</td><td></td><td></td></tr><tr><td>Noise</td><td>$\bar{x}_{eq} = 8.419$<br>$[8.120, 8.698]$<br>$\bar{b}_{eq} = 0.158$<br>$[0.044, 0.260]$</td><td>$\bar{x}_{eq} = 14.512$<br>$[10.639, 14.800]$<br>$\bar{b}_{eq} = 0.405$<br>$[0.246, 0.488]$</td><td>$\bar{x}_{eq} = 2.795$<br>$[2.323, 3.155]$<br>$\bar{b}_{eq} = 0.439$<br>$[0.328, 0.564]$</td><td>$\bar{x}_{eq} = 4.215$<br>$[3.791, 4.537]$<br>$\bar{b}_{eq} = 0.157$<br>$[0.061, 0.268]$</td><td></td></tr><tr><td>Noise colour</td><td>$\bar{x}_{eq} = 6.592$<br>$[6.281, 6.89]$<br>$\bar{b}_{eq} = 0.340$<br>$[0.276, 0.395]$</td><td>$\bar{x}_{eq} = 10.166$<br>$[7.436, 10.341]$<br>$\bar{b}_{eq} = 0.583$<br>$[0.498, 0.618]$</td><td>$\bar{x}_{eq} = 1.673$<br>$[1.516, 1.833]$<br>$\bar{b}_{eq} = 0.663$<br>$[0.629, 0.698]$</td><td>$\bar{x}_{eq} = 4.195$<br>$[3.753, 4.548]$<br>$\bar{b}_{eq} = 0.160$<br>$[0.081, 0.260]$</td><td>$\bar{x}_{eq} = 3.358$<br>$[3.165, 3.517]$<br>$\bar{b}_{eq} = 0.327$<br>$[0.290, 0.369]$</td></tr></tbody></table>

Baseline values for comparison: $\bar{x}_{eq} = 3.368$ [3.179, 3.521], $\bar{b}_{eq} = 0.325$ [0.277, 0.375].

All changes together: $\bar{x}_{eq} = 11.432$ [9.665, 13.217], $\bar{b}_{eq} = 0.549$ [0.445, 0.633].
<table><caption>**Table S2.** Mean breeding values ($\bar{x}_{eq}$) and plasticities ($\bar{b}_{eq}$), with minima and maxima beneath, for locations in the case study. Values were calculated at dynamic equilibrium (generation 150,000 onwards) and used to predict tolerance curves in Figure 5.</caption><thead><tr><th>Location</th><th>Mean breeding value (x̄)</th><th>Mean plasticity (b̄)</th></tr></thead><tbody><tr><td>Southern New South Wales</td><td>x̄<sub>eq</sub> = 6.162<br>[6.035, 6.280]</td><td>b̄<sub>eq</sub> = 0.699<br>[0.697, 0.702]</td></tr><tr><td>Port Phillip Bay in Victoria</td><td>x̄<sub>eq</sub> = 2.947<br>[2.834, 3.072]</td><td>b̄<sub>eq</sub> = 0.819<br>[0.817, 0.822]</td></tr><tr><td>Southwestern Tasmania</td><td>x̄<sub>eq</sub> = 4.515<br>[4.420, 4.603]</td><td>b̄<sub>eq</sub> = 0.684<br>[0.682, 0.686]</td></tr></tbody></table>