A macroecological approach to evolutionary rescue and adaptation to climate change

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ECOGRAPHY

Ecography

––––––––––––––––––––––––––––––––––––––––

Subject Editor:

David Nogués-Bravo

Editor-in-Chief: Miguel Araújo Accepted 22 January 2019

42: 1124–1141, 2019

doi: 10.1111/ecog.04264

Despite the widespread use of ecological niche models (ENMs) for predicting the responses of species to climate change, these models do not explicitly incorporate any population-level mechanism. On the other hand, mechanistic models adding population processes (e.g. biotic interactions, dispersal and adaptive potential to abiotic conditions) are much more complex and difficult to parameterize, especially if the goal is to predict range shifts for many species simultaneously. In particular, the adaptive potential (based on genetic adaptations, phenotypic plasticity and behavioral adjustments for physiological responses) of local populations has been a less studied mechanism affecting species’ responses to climatic change so far. Here, we discuss and apply an alternative macroecological framework to evaluate the potential role of evolutionary rescue under climate change based on ENMs. We begin by reviewing eco-evolutionary models that evaluate the maximum sustainable evolutionary rate under a scenario of environmental change, showing how they can be used to understand the impact of temperature change on a Neotropical anuran species, the Schneider’s toad Rhinella dip- tycha. Then we show how to evaluate spatial patterns of species’ geographic range shift using such models, by estimating evolutionary rates at the trailing edge of species distribution estimated by ENMs and by recalculating the relative amount of total range loss under climate change. We show how different models can reduce the expected range loss predicted for the studied species by potential ecophysiological adaptations in some regions of the trailing edge predicted by ENMs. For general applications, we believe that parameters for large numbers of species and populations can be obtained from macroecological generalizations (e.g. allometric equations and ecogeographical

A macroecological approach to evolutionary rescue and adaptation to climate change

José Alexandre F. Diniz-Filho, Kelly S. Souza, Luis M. Bini, Rafael Loyola, Ricardo Dobrovolski,

João Fabricio M. Rodrigues, Matheus de S. Lima-Ribeiro, Levi C. Terribile, Thiago F. Rangel, Igor Bione, Roniel Freitas, Iberê F. Machado, Tainá Rocha, Maria L. Lorini, Mariana M. Vale, Carlos A. Navas, Natan M. Maciel, Fabricio Villalobos, Miguel A. Olalla-Tarraga and Sidney Gouveia

J. A. F. Diniz-Filho (https://orcid.org/0000-0002-0967-9684) ✉ ([email protected]), L. M. Bini, R. Loyola, T. F. Rangel and N. M. Maciel (http://orcid.

org/0000-0001-5654-0645), Depto de Ecologia, ICB, Univ. Federal de Goiás (UFG), Goiânia, GO, Brasil. – K. S. Souza, Graduate Program in Genetics and Molecular Biology, ICB, UFG, Goiânia, GO, Brasil. – R. Dobrovolski, Inst. de Biologia, Univ. Federal da Bahia, Salvador, BA, Brasil. – J. F. M. Rodrigues (http://orcid.org/0000-0002-1914-4093), R. Freitas and T. Rocha, Programa DTI/CNPq, INCT em Ecologia, Evolução e Conservação da Biodiversidade, UFG, Goiânia, GO, Brasil. – M. de S. Lima-Ribeiro and L. C. Terribile, Inst. de Biociências, Regional Jatai, UFG, Jatai, GO, Brasil. – I. Bione, Graduate Program in Ecology and Evolution, ICB, UFG, Goiânia, GO, Brasil. – I. F. Machado, Inst. Biotatá and PDJ/CNPq, Rio de Janeiro, Brasil. – M. L. Lorini, Inst. de Biociências, UNIRIO, Rio de Janeiro, Brasil. – M. M. Vale, Laboratorio Internacional en Cambio Global (LincGlobal), Depto de Ecologia, UFRJ and Rede Brasileira de Pesquisas em Mudanças Climáticas Globais (Rede CLIMA), Ministério de Ciência, Tecnologia, Inovação e Comunicação (MCTIC), Rio de Janeiro, Brasil. – C. A. Navas, Inst. de Biociências, Univ. de São Paulo, São Paulo, Brasil. – F. Villalobos, Red de Biología Evolutiva, Inst. de Ecología, A.C., Xalapa, Veracruz, Mexico. – M. A. Olalla-Tarraga, Biodiversity and Macroecology Lab, Dept of Biology and Geology, Physics and Inorganic Chemistry, Rey Juan Carlos Univ., Madrid, Spain. – S. Gouveia, Depto de Ecologia, CCBS, Univ. Federal de Sergipe, Aracaju, Sergipe, Brasil.

Review and synthesis

16000587, 2019, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ecog.04264 by CAPES, Wiley Online Library on [30/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

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rules), so our framework coupling ENMs with eco-evolutionary models can be applied to achieve a more accurate picture of potential impacts from climate change and other threats to biodiversity.

Keywords: adaptation, anurans, climate change, ecological niche models, eco-evolutionary models, geographical ranges, Grinnelian niche, Rhinella, trailing edges

Introduction

The potential impacts of short-term human-induced climate change on biodiversity have been extensively evaluated (Parmesan and Yohe 2003, Parmesan 2006, Bellard et al.

2012, Garcia et al. 2014, Pecl et al. 2017). This research program found widespread evidence that phenology and demog- raphy of species are correlated with different dimensions of climate, with varying strength across geographical and environmental gradients. Thus, under climate change, projected responses potentially include shifts, contractions and even collapses of species’ geographic ranges, with consequences for emergent broad-scale biogeographic patterns, such as species richness gradients, community turnover and patterns of phylogenetic and functional diversity (Thuiller 2004, Diniz- Filho et al. 2009, Thuiller et al. 2011, Loyola et al. 2014, Sales et al. 2017).

Most predictions of shifts in species’ geographic ranges due to climate changes rely on ecological niche models (ENMs hereafter; Franklin 2009, Peterson et al. 2011, Guisan et al.

2017). Despite the widespread use of ENMs for predicting the responses of species to climate change, some conceptual and practical limitations have been identified (Peterson et al.

2011, Guisan et al. 2017). A major limitation is that ENMs do not explicitly incorporate population-level mechanisms, and their predictive abilities rely on the assumption that all underlying mechanisms are captured by the empirical cor- relations between occurrences and environmental (climatic) factors used as explanatory variables. On the other hand, mechanistic models adding population processes, such as biotic interactions, dispersal and adaptive potential to abiotic conditions (Kearney and Porter 2009), are much more complex and difficult to parameterize, especially if the goal is to predict range shifts for many species simultaneously (Norberg et al. 2012).

So far, the adaptive potential (based on genetic adaptations, phenotypic plasticity and behavioral adjustments for physiological responses) of local populations has been the most neglected mechanism affecting species’ responses to climatic change (Urban et al. 2016). This may be due to the difficulty of estimating genetic components of trait variation and their responses to climate change in a demographic context (Lavergne et al. 2010, Hoffmann and Sgró 2011, Franks and Hoffmann 2012, Diniz-Filho et al. 2013, Thuiller et al.

2013, Urban et al. 2016, Diamond 2018). The importance

of adaptive responses to climate change has been discussed in the context of the so-called evolutionary rescue, i.e. the persistence of populations under rapid environmental changes through fast adaptations (Bell 2017). This process has been widely investigated both theoretically and empiri- cally outside macroecology, mainly under the domain of

‘eco-evolutionary analyses’ (Hendry 2017). Theoretically, in a classic Neo-Darwinian reasoning, evolution should be slow and gradual, so that genetic adaptations are unlikely under rapid changes (Quintero and Wiens 2013 for a macroevolu- tionary approximation). However, novel theoretical models emphasize the plausibility of fast adaptations through genetic changes, genetic assimilation, epigenetic variation and evolution of reaction norms by phenotypic plasticity (Kopp and Matuszewski 2014).

Thuiller et al. (2013) proposed a metapopulation framework to incorporate several processes, including abiotic constraints (as in ENMs), dispersal, biotic interactions and adaptive potential to predict species’ responses to climate change. Following this framework, Cotto et al. (2017) recently developed a spatially-explicit, individual-based model to evaluate the possibility of adaptation to climate change in Alpine plant species. Using known demographic parameters and assuming genetic control of traits that medi- ated their response to climate, they suggested that evolutionary rescue is unlikely, and populations are threatened with extinction by climate change. A similar approach was proposed by Bush et al. (2016, see also Kearney et al. 2009), who developed a mechanistic population model that combined adaptation and dispersal with standard ENMs. These refined individual-based and population models can thus be viewed as part of a ‘bottom–up’ approach, in a methodological and theoretical framework, in which low level of knowledge is used to predict a response to climate change. Despite the conceptual and methodological interest of these eco-evolutionary models models, they are still hardly generalizable given their extensive data requirements on species’ population genetics and demographic parameters (Norberg et al. 2012).

Here, we discuss and apply an alternative macroecological framework to evaluate the potential role of evolutionary rescue in the context of climate change. Our approach is similar (but much simpler) to those recently proposed by Bush et al.

(2016) and Cotto et al. (2017), in the sense of modeling a spatially-explicit response to climate change. We begin by reviewing simple models that evaluate the potential of evolutionary rescue based on maximum sustainable evolutionary rate derived from population genetic models, showing how they can be used to understand the impact of temperature change on an amphibian species. Then, using ENMs, we propose a spatial generalization of these genetic models. This approach allows us to estimate evolutionary rates at the trailing edge of the species distribution, assuming multiple populations therein, and to evaluate the relative amount of range loss under climate change. We illustrated the approach using a widespread Neotropical anuran species, the Schneider’s toad Rhinella diptycha (Anura: Bufonidae) (until recently

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known as Rhinella schneideri; Lavilla and Brusquetti 2018), which is expected to undergo a strong range collapse under standard ENMs.

A brief overview of evolutionary rescue models

Evolutionary rates and adaptation to changing environments

We begin by reviewing some simple models for adaptive response to environmental change. First of all, it is necessary to define the mechanisms by which different phenotypic traits respond to climate and their genetic basis, so one can predict how they could evolve under climate change (Hoffmann and Sgró 2011, Mills et al. 2018). Here, we used a macroecological approach and evaluated changes in mean temperatures within the overall range of R. diptycha as a trait.

This trait is thus a synthetic ecological and physiological rep- resentation of the phenotype, i.e. an important component of species niche that is explained by the combined effect of several underlying traits (Skelly et al. 2007, Angilletta 2009).

We will sequentially discuss the basics of quantitative genetics models for adaptation under changing environments, based on additive genetic effects and incorporating phenotypic plasticity, in univariate and multivariate contexts.

First, we estimated the mean temperature across R. diptycha geographic range (under current and future con- ditions) and assumed that these values express a dimension of the species’ niche, and can be viewed as a ‘target’ response

variable (sensu Skelly 2007, Bush et al. 2016). Based on 159 geographically unique records at a 0.5° spatial resolution and on current data (1950–2000) from the community climate system model (CCSM), we evaluated the statistical distribution of mean annual temperature across the regions occupied by the species (Fig. 1a), which has a mean of 22.7 ± 2.3°C (SD). The distribution of mean annual temperature projected for 2080–2100 under the RCP 8.5 scenario of the CCSM suggests an increase of mean temperature to 27.9°C (± 2.3) within the geographic range of R. diptycha (Fig. 1b).

To estimate the evolutionary change required by the species to maintain its population in the future and to give a biological and evolutionary meaning to the difference in temperature that the species will undergo (i.e. 5.2°C), we can calculate:

H

Y Y g

T

=

0-

s (1)

This quantity H is given in a unit called ‘Haldanes’, named after the British geneticist J. B. S. Haldane (1892–1964) (Gingerich 2001); Y₀ and Y_T are the mean temperatures in the present and in the future, respectively, divided by the SD (σ) of Y (thus assuming a constant variance between generations). These two means are separated by a given number of generations g. Thus, Haldanes express evolutionary change expected for the temperature, in units of standard deviations (SD), per generation (Gingerich 2001, Kopp and Matuszewski 2014). In a certain sense, a high Haldane indicates a distance between future and current climate, and so

Figure 1. Frequency distribution of temperature within the geographic range of Rhinella diptycha. (a) Current; (b) predicted for 2080–2100, based on 159 occurrence records throughout species geographic ranges.

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is correlated with vulnerability to warming climates (assuming that species are currently in equilibrium with climate;

Garcia et al. 2019 for a recent review of indices).

Estimating the phenotypic SD (the parameter σ) is the most challenging part in deriving Haldanes based on macroecological data. Here, we suggest three ways of estimating species’ tolerance, understood as the limits that will allow species to maintain populations (i.e. a positive population growth rate). Note that our goal is to capture population- level limits, which are more restricted than maximum and minimum critical temperature levels that are experimen- tally measured (CTmax and CTmin). First, σ can be estimated using the values of temperature recorded within the species’ geographic distribution (in this case, a SD of 2.3°C). This approach tends to underestimate the fundamental niche (Soberón and Arroyo-Peña 2017). Second, we can estimate σ based on the potential geographic distribution for the species, using ENMs (see next section). Using our data, this resulted in a value of 2.02°C. However, R.

diptycha is a widely distributed species, so that fundamen- tal niches (FN) should not be too underestimated. Third, σ can be obtained by using experimental data, which is ca 2.5°C (see Fig. 5 from Anderson and Andrade 2017; see also Noronha-de-Souza et al. 2015). Thus, we can assume values of SD ranging between 2.0°C and 2.5°C for the species to calculate the Haldanes.

Assuming a generation time of 2–2.5 yr, we can define about 40–50 generations for the period between 2000 and 2090 used in our example. Arantes et al. (2015) observed that females of R. diptycha achieve sexual maturity at about 1.3 yr (435 d), although this does not necessarily indicate that there would be reproductive success at this stage. According to Oliveira et al. (2017), the average generation time for all amphibians and for anurans is 3.0 and 2.5 yr, respectively.

Thus, we believe that allowing g to vary between 40 and 50 is defensible.

By randomly sampling (5000 times) values of SD and generation time (g) from a uniform distribution in the range described above, evolutionary change in temperature is predicted to be equal to 0.051 ± 0.0047 Haldanes.

Therefore, the species will persist only if it evolves at rates equal or larger than that. We note that in this first analysis we are assuming limited dispersal towards regions where the species is already adapted (i.e. within the current species’ tolerance envelope). The question now becomes: how plausible a H = 0.051 is?

A heuristic rule suggests that rates lower than 0.1 are plausible (and even higher values are found in animal and plant population; Pitchers et al. 2014). As such, an evolutionary rate of 0.051 Haldanes within 50 generations for mean temperature is plausible (assuming this is the single adaptive peak of the species), so that R. diptycha could persist in the new climatic conditions. However, this critical value of 0.1 actually depends on a series of genetic and demographic parameters that will vary among populations and species, as discussed below.

Theoretical expectations for evolutionary rates

Quantitative genetic models developed by Lynch and Lande (1993) on adaptation under changing environments have been widely discussed and expanded by several authors (Burger and Lynch 1995, Gomulkiewicz and Holt 1995, Angilletta 2009, Hoffmann and Sgrò 2011; see Kopp and Matuszewski’s 2014 appendix 1 for a full derivation). In these models, the idea is to derive theoretical expectations for ‘critical Haldanes’, or maximum sustainable evolutionary rate (MSER), to which the expected H values (Eq. 1) can be compared. For instance, under a pure ‘genetic’ model of adaptation, referred to hereafter as Lynch–Lande model, this MSER is given by

MSER

ln

= +

æ

èçç ö

ø÷÷

s s +

l w

s

g p s

A S

V V

2

2 2 2

2

/ (2)

where σ²A is the additive genetic variance, λ is the maximum rate of population increase in the adaptive optimum (labeled B in the original notation of Kopp and Matuszewski 2014), V_S is the sum of the length of the adaptive landscape (ω²) and the environmental variance σ²E, which is the extreme limit of adaptation across the entire amphibian clade (below). The additive genetic variance is given by the phenotypic variance times the heritability of the trait (h²), so that overall phenotypic variance (σ²) is then given by σ²A + σ²E. We then take ω² as the amplitude estimated from the minimum and maximum thermal limits of amphibians, around −4 and 42.5°C (Araújo et al. 2013, Bennett et al. 2018), equivalent to a moderate selection intensity when compared with estimated σ²A (Burger and Lynch 1995). This value of ω² generates a function in which there is a reduction in fitness of about 50%

at three SD from the optimum, which is roughly coherent with the thermal curves from Anderson and Andrade (2017).

As we do not have precise estimates of these parameters for R. diptycha, we can use intervals of these parameters to get an approximate distribution of MSER given this uncertainty, to which we can compare expected Haldanes under climate change calculated above. Specifically, we assumed h² values ranging from 0.2 and 0.4 (see the meta-analyses by Diamond 2017 and Cotto et al. 2017, who also assumed a mean h² of 0.3). Growth rates estimated for amphibian species from Animal Matrix Database COMADRE data (i.e. the first eigenvalue of the Leslie matrix) (Salgueiro-Gómez et al.

2016) vary between about 0.8 and 1.4, with a mean of 1.18 (excluding the negative growth rate values). Therefore, we assume here λ ranging from 1.1 to 1.25 as the maximum growth rate, which corresponds to intrinsic growth rates (r) between 8.6% and 22.3% per generation.

The distribution of the MSER under Lynch–Lande model obtained by generating 5000 random combinations of parameters described above has an average of 0.0373 ± 0.0089 (Fig. 2a). For the same combination of

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parameters, the expected Haldanes for temperature would be lower than MSER in 11.2% of the times, which is then the probability of evolutionary rescue given the uncertainty in model parameters. Heritability, growth rate and phenotypic SD all have positive relationships with MSER (and MSER_P below), so rescue becomes more likely. This is expected and indicates that if there is more inherited genetic variance and populations grows faster, there is high adaptive potential and

species will easily overcome climate changes (in the sense that maximum critical rates will be higher). Note that our approach should be viewed as a proof of concept. Thus, it is not aimed to show that adaptations will occur, only if this process is plausible (i.e. there is adaptive potential) in some circumstances and in the sense that rates of environmental changes can be counterbalanced by genetic and demographic processes associated with the traits underlying species Figure 2. Distribution of maximum sustainable evolutionary rate (MSER) (a) and MSER allowing phenotypic plasticity (MSER_P) (b), considering uncertainties in model parameters. The vertical lines indicate the mean expected Haldane based on mean temperature shifts (solid line, Haldane = 0.047) in Rhinella diptycha and its variation due to uncertainty values of SD and generation time (dashed lines). All simulations were performed in R-scripts available in Diniz-Filho et al. (2019)).

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physiological tolerance. As we are using the RCP 8.5 emission scenario, the probability of rescue will be higher under other more optimistic scenarios (as the theoretical expectations are not dependent of empirical data, only on demographic and genetic parameters).

The change in a trait, as a response to global warming, may also be explained by phenotypic plasticity (Urban et al.

2014, Valladares et al. 2014) with a linear reaction norm, in which an optimum phenotype will shift according to the environment. For example, in a model incorporating phenotypic plasticity (Chevin et al. 2010), the MSER is given by

MSER_P=

+ -

2

2 2

log( ) 2 2

l . w s

s T

h

B b (3)

where B is the rate of environmental change, b is a parameter controlling phenotypic plasticity (i.e. how much of the total response is due to plasticity in respect to the overall change) and T is the generation length. We set B = 1 and b is thus the proportion of variance in relation to the expected rate of environmental change of the species (i.e. the variance of tolerance). While these values of b are not high, as demon- strated below, they still yield a very conservative prediction of range loss (i.e. an increase in b would give a much more optimistic scenario in terms of rescue). For instance, Anderson and Andrade (2017) showed that the peak of tolerance changes with precipitation, which we could roughly interpret as reflecting a reaction norm (i.e. the optimum in temperature interacts with other environmental variable). Based on this reasoning, we used b values ranging from 0.1 to 0.15, obtained as the ratio between the variance of the optimum

temperatures based on peak shifts in different levels of hydra- tion (equal to 0.64) and the variances of thermal tolerance for the 80% performance curve, which is similar to the variance of temperature in species’ geographic (from 4 to 6.4).

Using again 5000 random combinations of these ranges of parameters in Eq. 3, the mean MSER_P was 0.051 ± 0.0098, and rescue would potentially occur in about 51% of the simulations (Fig. 2b). Also, as expected, when b tends to 0 (i.e. no phenotypic plasticity), the MSER from the two models tend to converge, whereas by increasing b, the MSER_P also increases rapidly to 1 when b = 1 and all change is due to plasticity (Fig. 3).

Kopp and Matuszewski (2014) also provide multivariate versions of MSER by replacing the SD with the pairwise genetic covariance matrix, G, among the traits (in this case, niche dimensions). An analogous MSER_P can be derived by replacing variances by a covariance matrix. Using these multivariate versions increases the uncertainty because it requires inputting much more parameters, thus such applications should be viewed with caution. However, for illustrative purposes, we analyzed the following variables simultaneously, also derived from CCSM both in current time and assuming the RCP 8.5 scenario for a mean between 2080 and 2100:

mean annual temperature (Bio1); mean diurnal range (Bio2);

isothermality (Bio3) and precipitation in the wettest and driest quarters (Bio16 and Bio17) (see below). We assumed Cheverud’s conjecture (Dochtermann 2011; see also Hansen and Houle 2008, Chevin et al. 2014) and obtained G by multiplying the realized geographic (phenotypic) covariance matrix P by the heritability, which was previously increased by ca 10%, as done in the univariate case. We also generated the multivariate landscape by multiplying P by 50, close to the univariate case. The five variables were standardized

Figure 3. Relationship between the MSER_P and the strength of phenotypic plasticity (parameter b), for the mean shift in temperature of Rhinella diptycha. The horizontal and dashed lines indicate the mean and SD of MSER with the same parameters (but with b = 0).

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across the study areas (Neotropics) and the values of these variables were recorded within the species’ range. We also assumed, in the absence of further information, a linear relationship between P and G and that the pairwise covariance in adaptive landscape was proportional to the difference in the univariate case.

We thus obtained MSER and MSER_P for each trait by taking the covariance structure into account, first for Lynch–

Lande model. Thus, mean Haldane for the multivariate case (0.045) was only slightly smaller than the univariate one (0.051). The same was observed for the frequency in which adaptation to temperature is plausible (ca 11 and 8% in the univariate and multivariate cases, respectively). Thus, if all five variables are considered simultaneously, the frequency of rescue would be similar, as temperature is the most restrictive variable (i.e. when adaptation is plausible for temperature, it is also plausible for other niche dimensions). Precipitation in the driest quarter is the second variable with the lowest rate of evolutionary rescue, with adaptation plausible in 20%

of the simulations. When considering a multivariate version of Chevin et al.’s (2010) model, rescue is plausible in 99%

of the simulations, even with a value for b as low as 0.15.

The convergence between the univariate and multivariate approaches (for temperature) is expected because there was a low structure in G, with the first two eigenvalues explaining 38% and 31% of the overall covariance among the five variables (i.e. these eigenvalues are very similar). However, this should not be always the case.

In this section we used models to evaluate adaptive potential based on temperature patterns across species ranges.

Thus, we assumed a single optimum and uniform responses throughout geographical space. However, it is possible to use the same models to explore adaptive potential in an explicit geographical context, based on data from different ‘populations’ across to the species’ range that could respond more locally to changing environments. Moreover, we can couple the models described above with well-known ENMs, incorporating adaptive potential to avoid strong assumptions on niche conservatism and population equilibrium, and thus make more dynamic predictions of the species’ responses to climate change through time. This will be the focus of the next section.

Geographic patterns of evolutionary rescue

Ecological niche models and species responses to climate change

ENMs have been widely used as phenomenological models that can be easily applied to thousands of species simultaneously, based on the expected effects of different aspects of temperature and precipitation on ecological niche dimensions (Peterson et al. 2011, Guisan et al. 2017, see Shelford 1911 for a pioneering reasoning relating niche and distribution). There are several shortcomings in using ENMs,

including scale issues (mainly related to the grain size more appropriated to capture different environmental effects on population and individual levels), and the selection of environmental variables and of mathematical/statistical functions that should be used to described the bioclimatic envelope (Franklin 2009, Guisan et al. 2017). In addition to these more operational issues, there are also several assumptions underlying the application of ENMs that arise because they do not realistically incorporate every aspect of the biology, ecology and evolutionary history of species. This will be the focus of the framework proposed here.

Considering the geographic range shift of a species predicted by an ENM, the two main processes of extinction and dispersal allow one to define three regions of the species’ geographic range. First, there is a leading edge, a region that will become suitable and occupied assuming unlimited dispersal, without the need to assume adaptation because it falls within the species’ tolerance range. Second, also assuming strong niche conservatism, there is a trailing edge, a region where populations should go extinct because they will not have the environmental limits tolerable by the species in one or multiple niche dimensions (Ackerly 2003; Fig. 4). Finally, there is an intermediate region that is currently occupied by the species and that will remain suitable under climate changes, which could be called ‘stable’ region.

The assumptions of ENMs pointed out above, which are a consequence of the more general equilibrium assumption, have been widely discussed (Varela et al. 2009). First, because climate is always changing in relatively short time-scales and because there may be spatial constraints to past dispersal, species will not be usually in equilibrium with climate (Araújo and Pearson 2005, Soberón 2007). Thus, fundamental niches (FN) will tend to be larger than realized (spatial) niches (RN).

Even under equilibrium, the fundamental niche may not be fully occupied because the (multivariate) conditions simply do not exist in the real world, so it is also necessary to think in existing fundamental niches (EFN) (see nomenclature in Peterson et al. 2011, Soberón and Arroyo-Peña 2017).

However, in many cases, the climatic envelope described as the so-called ‘Grinnelian niche’, may be a useful surrogate of EFN or FN, particularly for widely distributed species (Diamond and Chick 2018).

Still, there must exist an unpredictable downward bias in establishing these Grinnelian niches by environmental conditions from occurrence records (Holt 2003, Soberón and Arroyo-Peña 2017). In any case, interest has increased about the possibility of estimating niches from species’ experimental physiological tolerances and the use such estimate to analyze geographic and evolutionary patterns of species niches with mechanistic models (Araújo et al. 2013, Bennett et al. 2018).

Despite such advances, dealing with these complex mechanistic models for several species is not straightforward so far.

In this regard, the incorporation of demographic processes would be a key improvement to make ENM more reliable in predicting the effect of climate change on species’ leading and trailing edges. This has been done for dispersal process,

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first by assuming a more conservative scenario of complete dispersal limitation while projecting future distributions (Thuiller 2004, Buisson et al. 2010) and more recently by explicitly incorporating dispersal using cellular automata and related approaches (Bocedi et al. 2014). However, much less attention has been paid to the demographic patterns in species trailing edges.

It has usually been assumed that if the species’ current range falls outside the static defined niche, populations inhabiting these regions will go extinct. However, under environmental stress adaptive processes could be triggered and result in a rescue of populations from climate-driven extinction (Visser 2008, Bell and Gonzalez 2009, Bell 2013, 2017, Gonzalez et al. 2013, Lindsey et al. 2013, Carlson et al.

2014). Adaptations could occur in several demographic, physiological, morphological, behavioral and life history traits (e.g. shifting reproductive periods and increasing thermal tolerance). Such adaptive responses represent niche evolution, which challenge the ‘niche conservatism’ assumption (Wiens et al. 2010, Rangel et al. 2018). The FN resulting from this evolutionary rescue would allow species to occupy a larger region in the future, even considering the loss of

the trailing edge (Fig. 4). On the other hand, local adaptive processes may be counteracted by gene flow from neighbor- ing populations, depending on the spatial heterogeneity and scale (i.e. grain size) of the selective agents, thus constraining geographic range expansions (Kirkpatrick and Barton 1997, Holt 2003, Richardson et al. 2014). Note that if dispersal is limited (an assumption of some modelling approaches particularly valid in highly human-modified landscapes), there is no leading edge and the main challenge in predicting species distribution is understanding the adaptive potential of species at their trailing edges. In the framework proposed here the idea is to apply the models for evolutionary rescue described earlier to the species’ trailing edges defined by the ENMs, as discussed below.

Adaptive potential in species’ trailing edges

Continuing with the R. diptycha example discussed before earlier before, we now used occurrence records to fit ENMs based on eight modelling methods (i.e. Bioclim, ENFA, Mahalanobis distances, Euclidean distances, GLM, Maxent, Neural networks and Random Forest), considering five Figure 4. Distribution of a hypothetical species in the environmental space (E-space; with two dimensions representing precipitation (P) and temperature (T)) and in the geographic space (G-space). Under climate change, a poleward range shift is expected (southern, in the figure), creating three regions (A = stable region; B = leading edge; C = trailing edge). This result is consistent with the perspective of a strong niche conservatism and equilibrium with current conditions. But, under evolutionary rescue, an expansion of the geographic distribution is expected because of the niche expansion due to adaptation of some local populations (represented here as small circles) to new climate conditions in the trailing edge.

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bioclimatic variables (mean annual temperature (Bio1);

mean diurnal range (Bio2); isothermality (Bio3) and precipitation in the wettest and driest quarters (Bio16 and Bio17) (Franklin 2009, see Terribile et al. 2012 for a description of the modeling protocol and Lima-Ribeiro et al. 2015 for data sources). We projected these models under RCP 8.5 scenario for the end of the century based on CCSM and used ensemble majority consensus to show the geographic range maps for the present and future. For simplicity and considering the similar results from univariate and multivariate analyses shown in the previous section, we will focus on the potential evolutionary rescue in the mean annual temperature as a target response variable, representing the main niche dimension for adapting to climate changes. The main steps in the framework described below are shown in Fig. 5.

ENMs predicted a substantial range contraction of about 80% for the R. diptycha, creating thus a wide trailing edge.

The leading edge is geographically constrained by the Atlantic coast and is thus minimum for the species (Fig. 6). In the framework proposed here, ENMs are used as a ‘baseline geographical structure’, so in the stable region and in the leading

edge the persistence of local populations will not depend on new adaptations, for these two regions encompass the current species’ FN. So, for practical purpose, evolutionary rescue is not worth considering in these regions, although continuous adaptations to any environment changes may occur anywhere in the range. Also, expansion of populations to the leading edge may trigger adaptations to more efficient dispersal or related to other non-climate selective factors, such as those due to new biotic interactions (and if these adaptations fail, leading edge will be overestimated by ENM). These processes are, however, beyond the scope of the approach proposed here to couple ENMs with eco-evolutionary models. The following are our main questions: are there populations in the trailing edge that could adapt to future conditions? If so, are ENMs being too conservative by assuming equilibrium and ignoring adaptive potential? How can we use the two MSER models discussed in the previous section to evaluate the plausibility of adaptation in different parts of the trailing edge and reduce it?

Following Cotto et al. (2017), we assumed that different

‘local populations’ (i.e. cells in our map derived from ENMs)

Figure 5. A schematic view of the steps proposed here to evaluate adaptive potential in the trailing edge of a species under climate change.

In short, we started by fitting ENMs and defining the species’ trailing edge. We select a target response variable (usually temperature; but see text for potential of using multivariate analyses) and for different ‘populations’ in the trailing edge (grid cells) we calculate the Haldanes (H) as the standardize (by variability and time) shift in the response variable. We then compared this H with theoretical expectations from maximum sustainable evolutionary rates (MSER and MSER_P), but due to uncertainty in parameter values, this was performed by randomly selecting parameters from pre-defined ranges 5000 times. Also, parameters can be spatially structured, so it is necessary to define which spatial autocorrelation model underlies this variation. Finally, the procedure is repeated for each cell or population in the trailing edge, allowing mapping the rescue probability across the trailing edge and calculating, at a given threshold, the proportion of the trailing edge that could be rescued.

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in the species trailing edge are locally adapted to their environmental conditions, and will track local environmental changes independently (or under a metapopulation model;

Fitzpatrick and Keller 2015, and below). Thus, rather than assuming average adaptive peaks across the species range in current and future climates (as in the previous section), we will assume that each population will need to adapt to local shifts in environmental conditions. However, downscaling this approach raises some new issues. First, we needed to define the denominator of the Haldane (i.e. the SD) for each

‘local population’. On the one hand, SD based on the realized niche may be underestimated relative to the fundamental niche, as previously pointed out. On the other hand, it is unrealistic to assume that the niche breadth of local populations will match the niche breadth for the entire species, especially for a widespread species like R. diptycha (Gotelli and Stanton‐Geddes 2015, Marcer et al. 2016, Ikeda et al.

2017). If some phylogeographical or broad-scale population genetics analysis is available, one can calculate the SD within groups of populations or lineages and use them to calculate H for populations within each group. A simpler solution would be to assume a relative amount of genetic variation within and among populations, as given by Wright’s F_ST, and use 1 − FST to ‘correct’ the SD. There is no broad-scale study on the population genetics for R. diptycha, but a study found

F_ST values around 5% in a small region in São Paulo State (Arruda et al. 2011). Although F_ST is not linearly correlated with distance (Epperson 2003), we conservatively assume that large F_ST values (ca 0.25) could be found for geographically separated populations. Indeed, much higher values were found for another species of the genus Rhinella (up to 0.7; Gallardo et al. 2011). In our simulations, we randomly generated F_ST values ranging from 0.1 to 0.25 to reduce the overall SD of the species. Although local adaptations would reduce the variance in a trait responding to climate change (as in Cotto et al. 2017), there is a simultaneous downward bias in the variance tolerance due to the difference between realized, existing and fundamental niches. Therefore, our local estimates would not be widely reduced by population structure (in the sense that 1 − FST will be equal to 0.75 at maximum) although it is difficult to balance upward and downward biases due to these opposite issues (see below).

After setting the model parameters as in previous simulations, we calculated the values of H, MSER and MSER_P for each cell in the trailing edge. We used a simultaneous autoregressive model to create a structure among parameter values in each simulation (with an autocorrelation coefficient of 0.9 and a neighbor distance of about 500 km). This procedure mimics short distance dispersal that causes neighbor populations to resemble each other (Richarson et al. 2014).

Figure 6. Potential geographic range of Rhinella diptycha as predicted by ensemble forecasting of 8 ENMs based on 5 environmental variables and projected into RCP 8.5 CCSM scenario (see text for details). The current and the future geographic ranges predicted by ENMs are shown in light and dark grays, respectively.

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For population growth λ, the spatial pattern was obtained directly from the suitability of ENMs, assuming that maximum λ = 1.25 coincide with regions of maximum suitability (and decreasing linearly to 1.1 in the range limits defined by the ENMs). Then, for each of the 5000 simulations, we evaluated the frequency of simulations in which each cell in the trailing edge could be potentially rescued (i.e. H < MSER or H < MSERP). We also counted, for each simulation, the proportion of cells in the trailing edge that could be evolu- tionarily rescued.

From the Lynch–Lande model, in 60% of the simulations, no cell in the trailing edge would be rescued, with only 6%

of the simulations resulting in more than 5% of the trailing edge with potential adaptation (Fig. 7a). Only the eastern border of the trailing edge, close to the geographic range predicted for 2090, would be populations rescued more frequently (Fig. 7b). However, when phenotypic plasticity is allowed (Chevin et al. 2010), the distribution is much wider, yet right-skewed, with a median of 27% of the trailing edge being rescued across simulations. In 86% of the simulations R. diptycha could maintain more than 5% of its trailing edge (Fig. 8a). Because this frequency is obtained for each cell in the grid, almost the entire trailing edge could be rescued under this model. The higher frequency of rescue in the eastern border of the trailing edge close to the persistence region is also apparent (Fig. 8b).

In summary, the probability of evolutionary rescue based for R. diptycha, based on a genetic model, is low and thus range shift predicted by ENMs would be not too conservatism by ignoring adaptive potential. However, some previous studies suggest that predictions from eco-evolutionary models tends to actually be more pessimistic than those from ENMs, in terms of population persistence under global warming (Sinervo et al. 2010, Alexander 2013, Bourne et al.

2014, Valladares et al. 2014, Dobrowski and Parks 2016, Cotto et al. 2017). Indeed, when we consider here a single adaptive peak of mean temperature for the entire species, the chance of persistence is only about 11% under purely genetic models for MSER (so results for ENM that predict a relatively wide stable may be too optimistic). In the spatial generalization, there is also a low chance of adaptation in the trailing edge (less than 5%, representing a rare combination of parameters). Predictions from MSER for the entire species’ range (i.e. combining current and future ENMs) is also low. In fact, part of the future geographic range predicted by ENMs is outside the possibility of adaptation if only MSER is considered. Temperature shifts will be larger than could be supported, thus ENMs makes more liberal predictions than MSER if the entire species range is considered (but, if only trailing edges are considered, then the opposite is of course true by definition; Bush et al. 2016).

Finally, our analyses show that even relatively low levels of phenotypic plasticity will increase the potential of evolutionary rescue. Indeed, probability of rescue in terms of optimum can increase up to 99%, so that nearly 80% of the trailing edge could be rescued in many simulations. The levels of plasticity

in temperature tolerances assumed here may be too low and not realistic (Urban et al. 2014), so our results based on MSER_P would be viewed as too pessimistic. Tolerance curves are in general fitted in such a way that there is an optimum for a proxy of fitness (i.e. some performance measure) and, by definition, populations would be driven by this optimum (Angilletta 2009). Of course, different metrics would provide different optima, but we assumed here that the variance of plasticity is given by the peak shifts in optimum under different humidity levels in the study by Anderson and Andrade (2017). Even so, it is hard to see whether these experimental levels are realistic in nature and whether more complex factors related to larval development, or other behavioral and ecological factors, would buffer these effects.

Challenges and perspectives for further macroecological generalizations

Generalizing the models for multiple species

Here we showed how models of evolutionary rescue can be used to understand the effects of climate change on species’

ranges, using mean temperature as a biological/evolutionary trait of the species. First, we showed how species’ mean temperature across the geographic range, viewed as the species’

optimum, could shift with climate changes under a pure genetic model of adaptation and when incorporating phenotypic plasticity. For R. diptycha, a widespread Neotropical species, the possibility of overall adaptation and rescue was estimated to be around 11%. Accordingly, assuming the ENMs are able to correctly estimate regions of persistence of the species, the adaptive potential in trailing edge is very low. We also showed that this likelihood would increase considerably, even if low levels of phenotypic plasticity are allowed for.

Applying the same approach to several species across wider regions (e.g. the globe) would be, in principle, straightforward, but some important issues must be considered first.

The most important one refers to estimating the SD of niche variation. From a theoretical perspective, there is a downward bias when FN is estimated from species geographic ranges (Colwell and Rangel 2009, Soberón and Nakamura 2009, Gouveia et al. 2014). In addition to the bias itself, if factors creating the bias are random across taxa, a lack of correla- tion between geographic ranges and physiological tolerances (as found by Soberón and Arroyo-Peña 2017) is expected.

Moreover, it is important to consider that physiological data are usually expressed in terms of maximum and minimum critical values (CTmax and CTmin), which represent temperatures at which coordinated movements are compro- mised. We know little about the extent to which such physiological limits relate to demographic parameters. However, before temperature reaches such extreme levels, fitness drops sharply according to the common left-skewed shape of thermal performance curves, thus likely driving populations to

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Proportion of trailing edge rescued

Number of simulations

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0 1000 2000 3000

(b) (a)

Figure 7. Frequency distributions of the proportion of cells potentially rescued in the trailing edge region of R. diptycha according to the Lynch–Lande’s (a) and the geographic distribution of the frequency of potential rescue (i.e. when, H < MSER or H < MSERP; across 5000 simulation) for this same model (b).

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(b) (a)

Proportion of trailing edge rescued

Number of simulations

0.0 0.2 0.4 0.6 0.8

0 50 100 150

Figure 8. Frequency distributions of the proportion of cells potentially rescued in the trailing edge region of R. diptycha according to Chevin et al.’s (2010) model (a) and the geographic distribution of the frequency of potential rescue (i.e. when H < MSER or H < MSERP; across 5000 simulation) for this same model (b).

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extinction. For instance, for R. diptycha, the limits of 80%

of performance in the experiments represents about 17% of the variance between CTmax and CTmin (Fig. 4 in Anderson and Andrade 2017).

Another issue is that even for a wide-ranged species, it is more likely that local populations respond differently to climate change and are adapted to local conditions (Fitzpatrick and Keller 2015). More importantly, these widespread species have reduced local genetic variance along niche dimensions because of past adaptations creating population structure (Cotto et al. 2017, below). Here, we used Wright’s overall F_ST statistics to account for this effect, so that the proportion of variance within-population will reduce the overall (specific) variation to account for this population structure in adaptive responses lower levels of genetic variation related to temperature tolerance. Gotelli and Stanton-Geddes (2015, see also Marcer et al. 2016, Ikeda et al. 2017) explicitly proposed that ENMs should consider population structure, as a better approach to predict responses to climate change. Thus, when it is possible to geographically split the species into several groups of populations, one could apply the framework proposed here for each of them, combining a posteriori the geographical patterns in evolutionary rescue (and in this case reducing the F_ST wouldn’t be necessary, because population structure had already been taken into account). Also, the estimated parameter for niche variance would make better sense as the pool of conditions allowing an individual to behave as ecological processes leading to reproduction. Therefore, any analysis based on the absolute tolerances of individuals must severely overestimate niche, and so population-level tolerances must be much narrower.

Thus, in one hand, the fundamental niche from occurrence records may be underestimated in our framework, and this would be more serious for small-ranged species. On the other hand, population structure can also strongly reduce local genetic variance for wide-ranged species, and conse- quently their ability to cope with climate change (and one could deal with this by reducing genetic variance using the overall F_ST or by applying ENMs to groups of populations).

It is critical to balance these two opposing effects for generalization purposes. Using a broader range of parameters than we did here may not be helpful because uncertainties will scale up. For instance, we used a SD of 2.5 in the adaptive peaks of R. diptycha, slightly increasing the observed ones, matching the 80% performance curve by Anderson and Andrade (2017). If we increased this value to 6, for example, as expected from CTmax and CTmin limits, the probability of rescue would increase from 16% to 90%. If we combined this higher SD with a FST around 0.7 (Gallardo et al. 2011), it would reduce from 90% to about 70%. Therefore, further data and analyses are necessary to more accurately define this parameter balance balance between parameters.

Another important parameter that may vary among species is the width of the adaptive landscape (ω²), assumed here as the variance of the range of thermal tolerance among amphibians (which turns to be a moderate stabilizing

selection, about 20 times the additive genetic variance; Burger and Lynch 1995). This parameter defines the relative fitness of individuals a given distance apart from the optimum. This value produces a function that is coherent with the thermal curves from Anderson and Andrade (2017), with a reduction of fitness around 50% with a shift of three SD from the optimum. However, further studies are necessary to better evaluate this parameter in natural populations and whether this value should be constant across species with distinct evolutionary histories and physiological requirements.

Finally, in addition to the problems with MSER parameters pointed out above, one should consider more basic problems of ENMs when dealing with several species at the same time. For instance, in amphibians there are many species with restricted geographic ranges, which can create difficulties not only for estimating SD of tolerance, but even to apply ENMs to define leading and trailing edges. Thus, it is important to highlight that although the applications shown here is based on ENM (i.e. to define trailing edge), this is only a geographical baseline. The key and important idea presented here is to apply the MSER to cells in the geographic range, akin to local populations, so if somehow the current range can be expanded and projected into the future (i.e. based on maximum dispersal distance, for example) it may be possible to simply skip the use of ENMs and to directly estimate adaptive potential and evolutionary rescue across future projected species range.

Top–down and bottom–up approaches to evolutionary rescue

Our approach based on ENMs can be viewed as a macroecological expansion (or approximation) of models such as those of Bush et al. (2016) AdaptR and Cotto et al.’s (2017) Dynamic eco-evolutionary models (DEEMs). However, there are important differences between our approach and these two others. Bush et al.’s (2016) AdaptR couples ENMs (analogous to BIOCLIM or more complex models) with adaptive models based on the breeders’ equation for a target trait (i.e. as temperature used here) that evolves in populations linked by dispersal at a generation basis given by

R ih= ^{2 2}sG

where R is the response to selection, i is the intensity of selection and h² and σ²G are the heritability and phenotypic variance, respectively, as defined above. Given i, a response is added to the trait from the previous generation. Hence, the Haldanes used in our framework are a rearrangement (and a generalization) of this classic breeder’s equation (Kopp and Matuszewski 2014). Thus, our approach is similar to AdaptR in the use of ENMs to define suitability and geographic ranges and a target variable. However, AdaptR is a more mechanistic model similar to DEEMs, requiring environmental shifts in multiple time-steps and spatially-explicit dispersal towards suitable areas rather than a macroecological

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approach. AdaptR requires several quantitative genetic parameters of limits to adaptation and demographic stochas- ticity. In contrast, our framework assumes dispersal as limited or unlimited, as in any ENM, although it can be coupled with available models that explicitly incorporate dispersal (Bocedi et al. 2014), and the adaptive focus is given on the trailing edge. Because we are addressing potential future evolutionary rates between two time steps (current and future), the number of parameters in our approach is much smaller than those required by Bush et al. (2016), making a macroecological generalization much easier.

Similarly, Cotto et al.’s (2017) DEEMs is a more complex spatially-explicit, individual-based model (i.e. IBM) that simulates demographic processes involving adaptation to a shifting environment (Thuiller et al. 2013). Similar to our approach, each local population is assumed to be locally adapted to the environmental conditions (i.e. in the initial conditions, adaptive peak will match the environmental conditions, assuming homogeneous environment at a coarse grain size). In DEEMs, the genetic variance is also determined by the additive genetic variance of the simulated poly- genetic traits associated with each niche dimension obtained from genotypes of the individuals in each population. Thus, depending on population structure, this local variance will be much lower than the overall variance of the species. Climate shifts will determine the amount of selective pressure in each population, promoting gradual changes in demographic parameters affecting mean fitness. Because this is an IBM, it is possible to track changes across generations and incorporate explicit spatial dynamics of alleles that can lead to failures in local adaptations (under little spatially autocorrelated environments).

In the macroecological expansion proposed here, we used a similar reasoning to that of DEEMs, in which each cell of the grid can be viewed as a local population with a local adaptive peak, but rather than simulating a polygenic trait underlying each niche dimension (i.e. temperature in our case), we used the niche directly as a trait that will track the changing climate (Skelly et al. 2007, Angilletta 2009, Bush et al. 2016;

see also Rangel et al. 2018 for a recent simulation study).

We thus determined the phenotypic variance to calculate the Haldanes directly from the species’ niche, as pioneered by Skelly et al. (2007). As we are comparing rates, we are thus implicitly assuming linear responses of the genetic variation associated with temperature responses, and it is important to highlight that this will work only for short time scales, as non-linear responses may create more complex ways by which species’ respond to climate changes (i.e. if there is an adaptive threshold, extinctions rates would actually be underestimated) (Fitzpatrick and Keller 2015).

Finally, we also lack detailed information on how within- population adaptive genetic variance is linked to niche dimensions, thus we assumed relatively low heritability values (i.e. h²< 0.4) and a given Wright’s FST statistic to reduce local variance from a species-level SD. Even so, at macroecological and biogeographical scales, climatic variables are strongly

autocorrelated, thus having similar adaptive peaks and under- going similar selective pressures. Thus, we are assuming that mal-adaptations due to gene flow counteracting local adaptations will be negligible, which may not be true for local populations structured within small geographic ranges ( Richardson et al. 2014).

Concluding remarks

In conclusion, the eco-evolutionary approach combines different research methods (experiments and computer simulations based on theoretical population genetics and demographic models) to evaluate species adaptation potential, which improve our understanding of how climate change will affect biodiversity. Conclusions about species adaptive potential vary and, in general, studies seem to rein- force the view that current rates of human-driven climate change are probably too fast for species to adapt. Probability of rescue is, in general, low. Yet, it may be too soon to be conclusive on this, given the difficulties in using evolutionary models and data in a predictive (and not retrospective) way. However, some researchers have already highlighted that project anthropogenic changes are not actually much higher than climate change rates during the Pleistocene (Hof et al. 2011). Although there may be obvious biases even in the more recent fossil record creating difficulties to correctly assess extinction rates, many species from the Pleistocene are still living, so it is possible that many species persisted to local and global faster climate changes though adaptation.

We believe it is fundamental to acknowledge the limitations of currently available macroecological approaches (i.e.

ENMs) to predict the impact of climate changes on biodiversity. Although the relative simplicity of macroecological models allows application to large datasets (i.e. multiple species across multiple scales), improving such models by coupling them with population-level processes, particularly dispersal and evolutionary adaptation, is critical to improve our understanding of the potential impacts of climate change on species’ geographic ranges. We propose here a relatively simple approach to improve ENMs by adding eco-evolutionary analyses of rescue in the trailing edge. But there may be still many challenges before its widespread use, because estimating both H and MSER requires many parameters that, unfortunately, are not available for many species.

Therefore, it is important to make these caveats explicit and then develop a research program to overcome them in the near future. For instance, many parameters for large numbers of species and populations can be obtained from macroecological generalizations (e.g. allometric equations and ecogeographical rules). So, we believe that our framework could be applied to achieve a better compromise between complexity and applicability, providing a more accurate picture of potential impacts from climate changes and other threats to biodiversity.

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Data deposition

Data available from the Dryad Digital Repository: < http://

dx.doi.org/10.5061/dryad.11d0f29 > (Diniz-Filho et al.

2019).

Acknowledgements – We thank to Ana Carnaval, Rob Colwell, David Nogués, Joaquin Hortal, Jorge Soberon, Dan Rosauer, David Ackerly, Wilfried Thuiller, Francois Guillaume and Monique Simon for suggestions and discussion that helped us improving the framework presented here, especially during talks at the XXXII Brazilian Zoology Meeting, Foz do Iguaçu, Brasil and at the International Biogeography Society meeting on ‘Climate Change Biogeography’, in Evora, Portugal, early 2018. We thank two anonymous reviewers for comments and suggestions that improved previous version of the manuscript.

Funding – This manuscript results from a working group on

‘Evolutionary Rescue’ promoted by our National Institutes for Science and Technology (INCT) in Ecology, Evolution and Biodiversity Conservation, supported by MCTIC/CNPq (proc.

465610/2014-5) and FAPEG (proc. 201810267000023). Work by J. A. F. D.-F., L. M. B., R. L., S. G., C. N., N. M. M., L. C.

T. is supported by CNPq productivity fellowships. R. L.’s research is funded by CNPq (grant 308532/2014-7), O Boticário Group Foundation for Nature Protection (grant PROG_0008_2013).

Work by S. G., C. N., M. A. O. T. and J. A. F. D.-F. on ecophysiology has been supported by Serrapilheira Inst. (proc G-1709-18372).

The work of M. M. V., R. L., J. A. F. D.-F. and M. L. L. is supported by the Brazilian Research Network on Climate Change (CNPq No.

550022/2014 and FINEP No. 01.13.0353.00).

Author contributions – J. A. F. Diniz-Filho and S. G. designed the overall framework and proposed the study, S. G., C. N., F. V. and M. A. O.-T. contributed to ecophysiological discussions, M. S.

L. R., M. V., R. D., L. L., T. R. and L. C. T. worked on ENMs issues, T. F. R., K. S. S., F. R. and I. B. helped coding and ran the ecoevolutionary models, N. N. M. and I. F. M. provided all data on anurans. All authors significantly contributed to the final version of the manuscript.

Conflicts of interest – All authors agreed on both the submission and full content of any article carrying their name and declare no conflict of interests.

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