**5. Demographic and genetic consequences of CIEC**

Environmental factors and their changes are to a large extent mirrored in the genetic composition of affected populations, which in turn impact the potential for adaptation to future selective forces such as CIEC. Even small alterations of environmental conditions can affect the genetic composition of populations, both via demographic and selective responses (Lande & Shannon, 1996; Björklund et al., 2009). Adaptation is one of the core principles in evolutionary biology and natural selection is universally regarded as the primary cause of evolutionary changes (Vermeij, 1996). The effects of rapid environmental changes, such as global warming, can cause problems particularly for small, isolated populations. Small

individual's characteristics as well as variable and conditional interactions (Travis et al., 2009). Likewise the geospatial implementations of IBM can account for specific spatial effects. This approach can be especially relevant for heterogeneous populations of higher animals in spatiotemporally heterogeneous environments with behaviour depending on its own state, the state of conspecifics, or the specific states of the environment (Bach et al., 2006; Bach et al. 2007). In other words the individual in an IBM does not perceive and interact with 'the average individual' of an abstract averaged population according to an average encounter rate and it does not experience the average environment. However, as entities, interactions and environment can be freely defined it follows that the extreme flexibility can become a challenge when designing simulations to address simple questions. In terms of genetics, another advantage of IBM is the straightforward implementation of genotypes, representing either neutral or selected genes where the latter permit the agents to adapt to changing environments. Such models are often referred to as complex adaptive systems (CAS) (DeAngelis & Mooij, 2005). Also the fact that events in IBM simulations are inherently stochastic may prove an advantage when the goal is to obtain probabilities. Much

depends on the specific question and available data.

al., 2011).

**interactions with other biotic and abiotic factors** 

**5. Demographic and genetic consequences of CIEC** 

**4. Developments in geographical ecology for understanding the consequences of climate-induced environmental changes and its** 

Given that human impacts in terms of both anthropogenic climate warming, habitat loss and fragmentation, are likely to increase over the 21st century (Smith et al., 2009), the consideration of geographical ecology research is an important new avenue of research. Therefore, the inclusion of new developments in geographical ecology towards much improved quantification of the determinants of species distributions and diversity patterns will be interesting (Guisan & Zimmermann, 2000). Notably the role of geographic variation in environmental factors such as climate creates an important basis for predicting responses to future climate change (e.g. Thomas et al., 2004). Furthermore, climatically-driven global geographical variation in metabolic rates may both be of fundamental importance to biodiversity and ecosystems and a determining factor in organism sensitivity to stressors (Dillon et al., 2010). Another motivation to look towards geographical ecology is the question of ascertaining effects of habitat destruction and fragmentation on species distribution changes from the separate effects of stressors, as well as their interactions (as fragmentation may affect exposure and susceptibility to environmental stressors (Gandhi et

Environmental factors and their changes are to a large extent mirrored in the genetic composition of affected populations, which in turn impact the potential for adaptation to future selective forces such as CIEC. Even small alterations of environmental conditions can affect the genetic composition of populations, both via demographic and selective responses (Lande & Shannon, 1996; Björklund et al., 2009). Adaptation is one of the core principles in evolutionary biology and natural selection is universally regarded as the primary cause of evolutionary changes (Vermeij, 1996). The effects of rapid environmental changes, such as global warming, can cause problems particularly for small, isolated populations. Small populations may lack the genetic diversity that would allow adaptation to a new environment, and thus might risk extinction (Spielman et al., 2004). Further, genetic drift in small populations (Gilpin and Soulè, 1986) leads to loss of genetic diversity, further depressing the evolutionary potential and thereby the ability to respond to changing environments (see Lynch 1996). Additionally, in small populations the chance of mating among relatives is increased due to the limited number of individuals, which causes inbreeding and further decreases mean fitness (Spielman et al., 2004). The increased probability of mating among relatives and the accelerated rate of loss of genetic variability in populations are strongly associated with a reduction of NE which is the size of an "ideal" (stable, random mating) population that results in the same degree of genetic drift as observed in the actual population (Wright, 1931). Due to the numerous ways in which natural populations can deviate from the "ideal" population, NE may be only a fraction of the population census size (N) size (Lande and Barrowclough, 1987). The NE of a population can predict its capacity to survive in a changing environment more reliably than the census size and/or the amount of genetic variability (Nunney, 2000).

Global scale environmental change may affect the local NE in several ways that may not be entirely independent. Firstly, as environmental changes accelerate, the demand for rapid adaptation becomes more pronounced, as in the simplest case where an optimum mean trait value shifts as a result of e.g. a rise in mean temperature. This requires a certain 'standing crop' of genetic variation in order for the population to track the moving optimum. Failing to do so, the populations may suffer demographically from the load of being maladapted. Secondly, the variance of environmental conditions may increase putting its toll on genetic variance by lowering the harmonic mean (HM) through the population dynamic response to environmental fluctuations. Theoretical models predict that fluctuation in population size is one of the dominant causes of reduction of NE and the low NE/N ratios (Kalinowski and Waples, 2002). If generations are non-overlapping, NE can be approximated as the HM of the population census size N (Caballero, 1994).

The expected heterozygosity (He), a measure of genetic variability, can provide an indication of the immediate evolutionary potential of a population, but it has no necessary relationship to longer term potential (Nunney, 2000). This is particularly true when the environment of the population is changing. The notion of NE can therefore be viewed as a bridging point between ecology and genetics, with the ecological characteristics including life history traits, social structure and population dynamics determining NE and hence the rate of loss of genetic variation (Caballero, 1994). Likewise, environmental factors and changes thereof are mirrored in the genetic composition of affected populations. Moreover, recent work points to the impact of altered environmental variability on the variation of vital rates, which in turn obviously affects the demography and therefore NE (see Boyce et al., 2006 and references therein). The effective population size is therefore related to the temporal variability of the population, which is a fundamental property of the ecological system. Theoretical studies have established that both statistical and biological mechanisms have the potential to influence the temporal variability of populations (Tilman, 1999). Statistical averaging and mean variance rescaling are predominantly statistical mechanisms, while species interactions and contrasting responses of different species to environmental fluctuations are primarily biological mechanisms. These mechanisms may very well be interdependent, and some have both statistical and biological elements (Tilman, 1999).

Possible Evolutionary Response to Global Change – Evolutionary Rescue? 93

stochasticity affecting population viability (Drake & Lodge, 2003). An additional complication consists of considering the effect of the colour of the environmental noises (i.e. temporal environmental autocorrelation which can be negative, positive or uncorrelated) (Ranta et al., 2008; Björklund, 2010). Theoretical studies, however, have produced conflicting results even when predicting the sign of the effect of the different kind of noises (Halley & Inchausti, 2002), depending on interactions between the environmental noise and demographic processes (Ruokolainen et al., 2009) and on the time scale at which the

Extinction risk can also be deeply influenced by the community context (Guichard, 2005) and/or spatial structure (Engen et al., 2002). Currently, it is possible to simulate the realistic and complex population dynamics and hence quantify extinction risks (Schodelbauerova et al., 2010), and the predicted extinction risk can be a more objective measure rather than many other metrics (Fujiwara, 2007). Modelling approaches for quantifying extinction, such as population viability analyses, are however often faced with so many levels of uncertainty that their utility has been questioned by some researchers (Fieberg & Ellner, 2000). Additionally, before the analyses of the more complex models, it would be natural to understand the fate of a single local population in absence of the various possible biotic

There is a general consensus among ecologists that assuming an initial population size which is large enough for the population to avoid a rapid initial extinction, the distribution of extinction times is exponential in almost any kind of population model, including very complex individual-based models (Grimm & Wissel, 2004). Thus, in this case, the mean time to extinction is a sufficient proxy for predicting the full distribution of extinction times. As previously mentioned, population fluctuations also act to reduce HM of the population census size estimated over time (Pertoldi et al., 2007b). Pertoldi et al., (2007b, 2008) proposed a simple model to estimate the risk of extinction and population persistence based on a description of the HM, defined by the two parameters of the scaling equation (Pertoldi et al., 2007b). The risk of intercepting zero is highly dependent on the way the variance of the population size relates to its mean and Pertoldi et al., (2007b) demonstrated that the minimum population size required for a population not to go extinct can be determined by a scaling equation relating the variance to the arithmetic mean. Pertoldi et al., (2007b) showed that for values of *β* >2 the relation between µ and HM remains non-linear and nonmonotonic as with increasing HM first increase, followed by a domain of decreasing HM with increasing. Therefore, it can be deduced from the model that for certain values of K and *β* a population will become extinct even if its population size is sufficiently large to restrict the impact of σ2d. This description allows a separation of the domains of population persistence versus those of extinction and hence allows the identification of populations on the verge of extinction. The method also presents the estimated minimum population size required for population persistence in the presence of different levels of σ2e. To sum up, the model shows that maximizing the population size may not always reduce the extinction risk. Additionally, increasing population size is not always equivalent to an increasing NE, but may decrease and hence lower the adaptive potential critical to the evolutionary

At the same time some factors can increase *β* above 2 and therefore it would be interesting in relation to the application of the following model described below: Pertoldi et al., (2007b; 2008) has shown that environmental stochasticity either increase or reduce the amplitude of

amplitude of environmental noise is measured (Heino et al., 2000).

interactions (Hakoyama & Iwasa, 2005).

response to changing environments.

Most ecologists are familiar with the general propensity of the variance (δ2) to increase with the mean (μ) which is why ecological data are often log-transformed prior to statistical analysis. For populations experiencing constant per capita environmental variability, the regression of log δ2 versus log μ gives a line with a slope of 2 and this positive relationship between δ2 and μ can be described in terms of Taylor's power relation (Taylor, 1961),

$$
\delta^2 = \mathbb{K}\overline{\mu}^\beta \tag{1}
$$

where, *K* is a constant, and *β* is the scaling coefficient, which here is equal to 2. Larger values of *β* indicate that the variance increases more rapidly with μ than expected. Values of *β* > 2 are not uncommon, and several authors have suggested that *β* may lie anywhere in the range of 0.6 to 2.8 (Taylor and Woiwod, 1982). Taylor and Woiwod (1980) estimated *β* for 97 aphid species and for 31 of these species *β* was found to be above 2.

Several authors showed that environmental stochasticity (σ2e) can lead to a substantial extinction risk also for large populations, not merely small ones, and especially so if the population growth rate is low (Lande, 1993; Foley, 1994).

Mean time to extinction is a function of the carrying capacity (Kc) raised to the power of (Kc)ω where

$$\mathbf{a} = \frac{2\mathbf{r}}{\sigma^2 e} \cdot \mathbf{1}\_\prime$$

and where σ<sup>2</sup> e is the environmental variance due to environmental stochasticity, which is the most instantaneous effect on the risk of extinction; and r is the mean growth rate of the population, which is affecting the long-term persistence of populations, (Saltz et al., 2005). There is at the present a general accord that in a stable environment the mean time to extinction of a local population grows with the carrying capacity *K* (Lande, 1993) whereas under adequately strong, uncorrelated environmental stochasticity, the dependence is characterised by a power law (Foley 1994). Hence, large populations should practically never go extinct for the duration of ecological timescales. The main reason for the discrepancy between this prediction and reality is that real populations are also exposed to deleterious processes other than demographic stochasticity (σ<sup>2</sup> d) which with small population size, is playing a large role on the probability of extinction. Although the time to extinction is expected to increase with population size, other factors influence the dynamics of populations as e.g. mechanisms of density dependence and population growth rates (Sæther & Engen, 2003). Fluctuations in population size is a factor that strongly affects the extinction risk of a population, because larger fluctuations increase the probability that one of these excursions in population size reaches zero with extinction as a result (Boyce et al., 2006; Pertoldi et al., 2008).

Intuitively, for a given average abundance, one expects the risk of extinction to increase with temporal variability; however, many studies conducted on long-term data from natural populations have found a contradictory result (Pimm, 1993). These studies use temporal variability as a direct proxy for population vulnerability, where population variability measures are calculated from time series data as standard deviations (sd), log*N* or coefficient of variation (CV). The reasons for the discordant results obtained in these correlational studies have been the subject of a debate and the relative importance of density dependence process on population dynamics has been compared to the relative importance of environmental variability (Turchin, 1998), which is probably, the most important of

Most ecologists are familiar with the general propensity of the variance (δ2) to increase with the mean (μ) which is why ecological data are often log-transformed prior to statistical analysis. For populations experiencing constant per capita environmental variability, the regression of log δ2 versus log μ gives a line with a slope of 2 and this positive relationship

between δ2 and μ can be described in terms of Taylor's power relation (Taylor, 1961),

aphid species and for 31 of these species *β* was found to be above 2.

population growth rate is low (Lande, 1993; Foley, 1994).

(Kc)ω where

and where σ<sup>2</sup>

2006; Pertoldi et al., 2008).

<sup>2</sup> *K*

where, *K* is a constant, and *β* is the scaling coefficient, which here is equal to 2. Larger values of *β* indicate that the variance increases more rapidly with μ than expected. Values of *β* > 2 are not uncommon, and several authors have suggested that *β* may lie anywhere in the range of 0.6 to 2.8 (Taylor and Woiwod, 1982). Taylor and Woiwod (1980) estimated *β* for 97

Several authors showed that environmental stochasticity (σ2e) can lead to a substantial extinction risk also for large populations, not merely small ones, and especially so if the

Mean time to extinction is a function of the carrying capacity (Kc) raised to the power of

most instantaneous effect on the risk of extinction; and r is the mean growth rate of the population, which is affecting the long-term persistence of populations, (Saltz et al., 2005). There is at the present a general accord that in a stable environment the mean time to extinction of a local population grows with the carrying capacity *K* (Lande, 1993) whereas under adequately strong, uncorrelated environmental stochasticity, the dependence is characterised by a power law (Foley 1994). Hence, large populations should practically never go extinct for the duration of ecological timescales. The main reason for the discrepancy between this prediction and reality is that real populations are also exposed to deleterious processes other than demographic stochasticity (σ2d) which with small population size, is playing a large role on the probability of extinction. Although the time to extinction is expected to increase with population size, other factors influence the dynamics of populations as e.g. mechanisms of density dependence and population growth rates (Sæther & Engen, 2003). Fluctuations in population size is a factor that strongly affects the extinction risk of a population, because larger fluctuations increase the probability that one of these excursions in population size reaches zero with extinction as a result (Boyce et al.,

Intuitively, for a given average abundance, one expects the risk of extinction to increase with temporal variability; however, many studies conducted on long-term data from natural populations have found a contradictory result (Pimm, 1993). These studies use temporal variability as a direct proxy for population vulnerability, where population variability measures are calculated from time series data as standard deviations (sd), log*N* or coefficient of variation (CV). The reasons for the discordant results obtained in these correlational studies have been the subject of a debate and the relative importance of density dependence process on population dynamics has been compared to the relative importance of environmental variability (Turchin, 1998), which is probably, the most important of


e is the environmental variance due to environmental stochasticity, which is the

ω = 2 2r *e* (1)

stochasticity affecting population viability (Drake & Lodge, 2003). An additional complication consists of considering the effect of the colour of the environmental noises (i.e. temporal environmental autocorrelation which can be negative, positive or uncorrelated) (Ranta et al., 2008; Björklund, 2010). Theoretical studies, however, have produced conflicting results even when predicting the sign of the effect of the different kind of noises (Halley & Inchausti, 2002), depending on interactions between the environmental noise and demographic processes (Ruokolainen et al., 2009) and on the time scale at which the amplitude of environmental noise is measured (Heino et al., 2000).

Extinction risk can also be deeply influenced by the community context (Guichard, 2005) and/or spatial structure (Engen et al., 2002). Currently, it is possible to simulate the realistic and complex population dynamics and hence quantify extinction risks (Schodelbauerova et al., 2010), and the predicted extinction risk can be a more objective measure rather than many other metrics (Fujiwara, 2007). Modelling approaches for quantifying extinction, such as population viability analyses, are however often faced with so many levels of uncertainty that their utility has been questioned by some researchers (Fieberg & Ellner, 2000). Additionally, before the analyses of the more complex models, it would be natural to understand the fate of a single local population in absence of the various possible biotic interactions (Hakoyama & Iwasa, 2005).

There is a general consensus among ecologists that assuming an initial population size which is large enough for the population to avoid a rapid initial extinction, the distribution of extinction times is exponential in almost any kind of population model, including very complex individual-based models (Grimm & Wissel, 2004). Thus, in this case, the mean time to extinction is a sufficient proxy for predicting the full distribution of extinction times. As previously mentioned, population fluctuations also act to reduce HM of the population census size estimated over time (Pertoldi et al., 2007b). Pertoldi et al., (2007b, 2008) proposed a simple model to estimate the risk of extinction and population persistence based on a description of the HM, defined by the two parameters of the scaling equation (Pertoldi et al., 2007b). The risk of intercepting zero is highly dependent on the way the variance of the population size relates to its mean and Pertoldi et al., (2007b) demonstrated that the minimum population size required for a population not to go extinct can be determined by a scaling equation relating the variance to the arithmetic mean. Pertoldi et al., (2007b) showed that for values of *β* >2 the relation between µ and HM remains non-linear and nonmonotonic as with increasing HM first increase, followed by a domain of decreasing HM with increasing. Therefore, it can be deduced from the model that for certain values of K and *β* a population will become extinct even if its population size is sufficiently large to restrict the impact of σ2d. This description allows a separation of the domains of population persistence versus those of extinction and hence allows the identification of populations on the verge of extinction. The method also presents the estimated minimum population size required for population persistence in the presence of different levels of σ<sup>2</sup> e. To sum up, the model shows that maximizing the population size may not always reduce the extinction risk. Additionally, increasing population size is not always equivalent to an increasing NE, but may decrease and hence lower the adaptive potential critical to the evolutionary response to changing environments.

At the same time some factors can increase *β* above 2 and therefore it would be interesting in relation to the application of the following model described below: Pertoldi et al., (2007b; 2008) has shown that environmental stochasticity either increase or reduce the amplitude of

Possible Evolutionary Response to Global Change – Evolutionary Rescue? 95

Given that HM is mainly dominated by the minimum value reached in a fluctuating population, it must be kept in mind that even if the environmental stochasticity does not have a constant period of fluctuation (and is not synchronised with the population fluctuations), what will be important for the determination of HM is the maximum positive value of rp and/or the minimum peak of the environmental stochasticity fluctuation reached in a given time interval. More precisely it will be the maximum rp observed when

interval the population will attain its smallest value, which in turn strongly influences the HM. Without evoking the correlations between environmental noise and population fluctuations it seems rather intuitive that if the noise is positively autocorrelated (reddened), especially in the time interval where the population size is below the average of the

population size and consequently the minimum HM is increased and this phenomenon should be taken into account due to evidence that long-term ecological data sets

Temporal variability estimated using sd, logN or CV as a direct proxy for population vulnerability, could be misleading as such measures of variability only should be used if the variance scales proportionally to the square of the mean (*β* = 2), and we have illustrated how *β* often differs from 2. Consequentially, there is a call for for detecting regime shifts in the dynamic behaviour of populations as changes in the global environment begin to accelerate and it would be interesting to establish a method which allows an estimation of the importance of σ2e on the two parameters *β* and *K* and on how much alteration of the parameters will push the population towards the extinction threshold. There are, however several other complications associated with the preservation of biodiversity and/or genetic variability: An enduring debate in ecology has also been how the diversity affects the temporal stability of biological systems. The ecological consequences of biodiversity loss have gained growing attention over the past decade (Bangert et al., 2005; Reusch et al., 2005). Current theory suggests that diversity has divergent effects on the temporal stability of populations and communities (Tilman, 1996). Theoretical work suggests a paradoxical effect of diversity on the temporal stability of ecological systems: increasing diversity should result in decreased stability of populations, while the community stability enhances (Tilman, 1996). While empirical work corroborates that community stability tends to increase with diversity, investigations of the effect of diversity on populations have not exposed any clear patterns. This consideration, together with the observation that changes in vital rate may have opposing effects on growth rate and NE, is of key importance, as it can produce

It is well known that demographic instability in a population is translated into fluctuations of N and a reduced NE which is close to HM of the varying N values (Vucetich et al., 1997). Therefore, a management strategy with the goal of preserving biodiversity on the community level could theoretically lead to a reduction of NE in single populations. In the same way, the attempt of increasing growth rate in a population by modifying some of the vital rates can also produce a reduction of NE. An increase in growth rate will increase N and therefore reduce the demographic stochasticity which is related to the population's risk

Another question emerges from considering both short- and long-term adaptability in a changing environment and whether genetic variability is always beneficial. This is not

of extinction, but may simultaneously lead to a reduction of the genetic diversity.

< 0), the probability to attain the minimum value of the

< 0). In this

the population size values are below and when the first derivative is negative (fi

fluctuations and fi

is negative (fi

demonstrate reddened spectra (Halley & Inchausti, 2002).

disagreement about the optimal management strategies.

the population fluctuations depending on the sign of the correlation between population size and environmental fluctuations as:

$$\mathbf{q}\_{\rm tot} = \mathbf{q}\_{\rm e} + \mathbf{q}\_{\rm e} + 2\mathbf{r}\mathbf{p}(\mathbf{q}\mathbf{q}\_{\rm e}) \,\,\,\,\,\,\tag{2}$$

where σ2tot is the variance of the population size in the presence of environmental noise, σ2 is the variance of the population size in absence of environmental noise, σ<sup>2</sup> e is the environmental noise and r(σσe) is the covariance between the environmental noise and the population fluctuation. The covariance is given by two times the product of rp and the sd of the population size and the environmental fluctuations (σ and σe respectively). Hence, a negative correlation (rp < 0) between environmental stochasticity and population fluctuations will decrease the fluctuations of the population size, with σ2tot < σ2, whereas in case of a positive correlation (rp > 0) we will observe an increase in population fluctuations in the presence of environmental stochasticity (σ2tot > σ2). Clearly if σ2e overwhelm σ2 of the population dynamics, it will be the main determinant of the amplitude of oscillation of σ<sup>2</sup> tot whatever the correlation between σ2e and σ2 is.

Hence, a population near the carrying capacity with *β* near the value of 2 should be more prone to extinction, as when an environmental stochastic event is added *β* will become larger than 2, which means an increased risk of extinction. The fact that *β* depends on the density of the population, makes it quite evident that *β* and *K* should be considered when interpreting the fluctuations of a population. As demonstrated by Pertoldi et al., (2007b), extinction risk of populations can only increase with increasing population size only if the *β* values can reach values above 2 (*β* > 2). Pertoldi et al., (2007b) showed that for certain combinations of *β* and *K* (*β* >2 and *K* < μ(2- *<sup>β</sup>*), the following equation:

$$
\overline{\mu} - \sqrt{K \overline{\mu}^{\beta}} = 0 \tag{3}
$$

predicts the largest mean population size allowed before extinction is expected. Furthermore, Pertoldi et al., (2008) obtained after several rearrangements, the following inequality:

$$K^{\frac{1}{(2-\beta)}} < \overline{\mu} \tag{4}$$

Where μ represents the minimum viable population size necessary for the population to persist. Values of *β* > 2 are not uncommon, and several authors have suggested that *β* may lie anywhere in the range of 0.6 to 2.8 (Taylor and Woiwod, 1982). Factors increasing *β* above 2 could therefore be interesting in relation to the model. Some possible scenarios where it can be speculated that *β* values could reach values above 2 could be for example when two species interact in a predator-prey interaction, or there is a primary consumer of a resource which fluctuates with time.

Another factor potentially affecting the σ2 is temperature fluctuations and there is currently general concurrence that global warming is affecting animal and plant populations in multiple ways (Parmesan, 2006). Different degrees of σ2e and their correlation with the dynamic of the fluctuations of the population can allow the population to reach values of *β* above 2 and change the K values. Note also that the risk of *β* values above 2 is increasing when the population is approaching its carrying capacity.

the population fluctuations depending on the sign of the correlation between population

where σ2tot is the variance of the population size in the presence of environmental noise, σ2 is

environmental noise and r(σσe) is the covariance between the environmental noise and the population fluctuation. The covariance is given by two times the product of rp and the sd of the population size and the environmental fluctuations (σ and σe respectively). Hence, a negative correlation (rp < 0) between environmental stochasticity and population fluctuations will decrease the fluctuations of the population size, with σ2tot < σ2, whereas in case of a positive correlation (rp > 0) we will observe an increase in population fluctuations in the presence of environmental stochasticity (σ2tot > σ2). Clearly if σ2e overwhelm σ2 of the population dynamics, it will be the main determinant of the amplitude of oscillation of σ<sup>2</sup>

Hence, a population near the carrying capacity with *β* near the value of 2 should be more prone to extinction, as when an environmental stochastic event is added *β* will become larger than 2, which means an increased risk of extinction. The fact that *β* depends on the density of the population, makes it quite evident that *β* and *K* should be considered when interpreting the fluctuations of a population. As demonstrated by Pertoldi et al., (2007b), extinction risk of populations can only increase with increasing population size only if the *β* values can reach values above 2 (*β* > 2). Pertoldi et al., (2007b) showed that for certain

> *K* 0

 

predicts the largest mean population size allowed before extinction is expected. Furthermore, Pertoldi et al., (2008) obtained after several rearrangements, the following

> 1 (2 ) *K*

Where μ represents the minimum viable population size necessary for the population to persist. Values of *β* > 2 are not uncommon, and several authors have suggested that *β* may lie anywhere in the range of 0.6 to 2.8 (Taylor and Woiwod, 1982). Factors increasing *β* above 2 could therefore be interesting in relation to the model. Some possible scenarios where it can be speculated that *β* values could reach values above 2 could be for example when two species interact in a predator-prey interaction, or there is a primary consumer of a

Another factor potentially affecting the σ2 is temperature fluctuations and there is currently general concurrence that global warming is affecting animal and plant populations in multiple ways (Parmesan, 2006). Different degrees of σ2e and their correlation with the dynamic of the fluctuations of the population can allow the population to reach values of *β* above 2 and change the K values. Note also that the risk of *β* values above 2 is increasing

e + 2rp(σσe) , (2)

(3)

(4)

e is the

tot

σ2

combinations of *β* and *K* (*β* >2 and *K* < μ(2- *<sup>β</sup>*), the following equation:

tot = σ2 + σ<sup>2</sup>

the variance of the population size in absence of environmental noise, σ<sup>2</sup>

e and σ2 is.

size and environmental fluctuations as:

whatever the correlation between σ<sup>2</sup>

resource which fluctuates with time.

when the population is approaching its carrying capacity.

inequality:

Given that HM is mainly dominated by the minimum value reached in a fluctuating population, it must be kept in mind that even if the environmental stochasticity does not have a constant period of fluctuation (and is not synchronised with the population fluctuations), what will be important for the determination of HM is the maximum positive value of rp and/or the minimum peak of the environmental stochasticity fluctuation reached in a given time interval. More precisely it will be the maximum rp observed when the population size values are below and when the first derivative is negative (fi < 0). In this interval the population will attain its smallest value, which in turn strongly influences the HM. Without evoking the correlations between environmental noise and population fluctuations it seems rather intuitive that if the noise is positively autocorrelated (reddened), especially in the time interval where the population size is below the average of the fluctuations and fi is negative (fi < 0), the probability to attain the minimum value of the population size and consequently the minimum HM is increased and this phenomenon should be taken into account due to evidence that long-term ecological data sets demonstrate reddened spectra (Halley & Inchausti, 2002).

Temporal variability estimated using sd, logN or CV as a direct proxy for population vulnerability, could be misleading as such measures of variability only should be used if the variance scales proportionally to the square of the mean (*β* = 2), and we have illustrated how *β* often differs from 2. Consequentially, there is a call for for detecting regime shifts in the dynamic behaviour of populations as changes in the global environment begin to accelerate and it would be interesting to establish a method which allows an estimation of the importance of σ<sup>2</sup> e on the two parameters *β* and *K* and on how much alteration of the parameters will push the population towards the extinction threshold. There are, however several other complications associated with the preservation of biodiversity and/or genetic variability: An enduring debate in ecology has also been how the diversity affects the temporal stability of biological systems. The ecological consequences of biodiversity loss have gained growing attention over the past decade (Bangert et al., 2005; Reusch et al., 2005). Current theory suggests that diversity has divergent effects on the temporal stability of populations and communities (Tilman, 1996). Theoretical work suggests a paradoxical effect of diversity on the temporal stability of ecological systems: increasing diversity should result in decreased stability of populations, while the community stability enhances (Tilman, 1996). While empirical work corroborates that community stability tends to increase with diversity, investigations of the effect of diversity on populations have not exposed any clear patterns. This consideration, together with the observation that changes in vital rate may have opposing effects on growth rate and NE, is of key importance, as it can produce disagreement about the optimal management strategies.

It is well known that demographic instability in a population is translated into fluctuations of N and a reduced NE which is close to HM of the varying N values (Vucetich et al., 1997). Therefore, a management strategy with the goal of preserving biodiversity on the community level could theoretically lead to a reduction of NE in single populations. In the same way, the attempt of increasing growth rate in a population by modifying some of the vital rates can also produce a reduction of NE. An increase in growth rate will increase N and therefore reduce the demographic stochasticity which is related to the population's risk of extinction, but may simultaneously lead to a reduction of the genetic diversity.

Another question emerges from considering both short- and long-term adaptability in a changing environment and whether genetic variability is always beneficial. This is not

Possible Evolutionary Response to Global Change – Evolutionary Rescue? 97

errors due to unpredictable environmental components (for applications see Kristensen et al., 2004). Clonally reproducing strains should be used to study the extent of adaptive phenotypic plasticity, and maternal effects, including the effect of parental ageing. The use of clonal strains will allow us to exclude the genetic components and their interactions with the environment. Therefore, unbiased estimates of genetic and environmental canalization,

interpretation of the interplay between these parameters will provide important contributions to: 1) The evolutionary importance of phenotypic plasticity, maternal effects, environmental and genetic stressors. 2) The consequences of outbreeding on population fitness and phenotypic plasticity, and 3) The selective effects of fluctuating selective regimes

In order to investigate in which way environments fluctuating with different intervals can affect the mean population average fitness, and to quantify the costs and benefits of genetic variability in fluctuating environments, sexually reproducing strains ought to be utilised, creating fluctuating temperature environments and making truncated selection experiments in which the extreme phenotypes at the two tails of the phenotypic distribution are selected away. Important information could in this way be obtained about the extent of the environmental information that will be transmitted to the offspring, and to what extent it

Molecular and quantitative genetics studies should be conducted on several species with different ecological characteristics and with different demographic history, such as recent and ancient population decline or expansion. Changes in population size and range are frequent consequences of CIEC, and examples include habitat fragmentation and rapid colonization or recolonization processes. Extensive collections of several species provide the opportunity to analyse large numbers of samples on a temporal scale and directly document changes in genetic diversity. The results of these analyses will improve our understanding of the historical dimension of population change, and provide important data for the interpretation of genetic diversity studies in an ecological and evolutionary context. The possibility of amplifying ancient DNA from old museum specimen (Pertoldi et al., 2005b), should also be used. Furthermore, a phylogeographic approach should be carried out. The innovative aspect of this approach consists of the fact that different molecular and

To document the range of genetically based morphological variation within and among populations, a comparison of the degree of quantitative genetics distance (QST) with neutral genetic distance (FST) should be made (Mckay & Latta, 2002). Comparisons of morphometrical (for example, size and shape) and life-history variability (for example, longevity and fecundity) of populations and their crosses with molecular variability (using microsatellites) could present important information about the influences of environmental and genetic components in a non-genetic-equilibrium situation. Furthermore, it will provide important information about the extent to which crosses

The combination of ecological models of the distribution of the species investigated with both mitochondrial DNA (mtDNA) data and synthetic genetic maps constructed from

can enlarge the plastic response of a trait when selecting for plasticity genes.

quantitative genetics techniques should be employed simultaneously.

between different strains affect the various components of σ<sup>2</sup>

homeostasis, canalization and σ2e).

e, will be obtained. A more correct

p (plasticity, developmental

plasticity, developmental homeostasis and σ<sup>2</sup>

**6.1.2 Collection and analysis of empirical data** 

on plasticity genes.

always the case as for example in constant environments genetic variability in a quantitative character creates a segregational load each generation due to stabilizing selection against individuals that deviate from the optimum phenotype (Lande & Shannon, 1996). Consider a presumably ordinary situation where natural selection acting on quantitative characters favours intermediate phenotypes. In an intermediate-optimum model, the genetic variability may be either beneficial or detrimental, depending on the pattern of environmental change (the frequency, the amplitude and the degree of autocorrelation of the environmental oscillations) (Lande & Shannon, 1996, Björklund et al., 2011).

The genetic consequences of CIEC can be subdivided in two main categories, namely consequences in small populations and consequences in large populations:

In small populations, random genetic processes (genetic drift) lead to loss of genetic variability, which may depress the evolutionary potential and thus the ability to respond to changing environments (Pertoldi et al., 2006a). It is also anticipated that populations only persist if the rate of adaptive evolution at least matches the rate of environmental change since the evolutionary response of quantitative traits to selection necessitates the presence of genetic variability (Burger and Lynch, 1995). In fact, this is the case even in the presence significant capacity to respond plastically, including adaptations in behaviour, physiology, morphology, growth, life history and demography. The rate of loss of genetic variability in populations is associated to a reduction of NE. Reduction of NE due to amplified population fluctuations, reduce the evolutionary potential, by reducing the additive genetic variance (σ<sup>2</sup> a) and the heritability (h2) of the traits, which in turn is inversely related to σ<sup>2</sup> e.

In large populations, the regime of alternating selective pressures has the potential to increase the average population fitness, selecting for genes implicated in the expression of plasticity. Various modelling approaches have shown that to optimize fitness, phenotypic plasticity evolves by trading the adaptation to acquire resources against the costs of maintaining the potential for plasticity (Ernande & Dieckman, 2004). Plastic responses include changes in behavior, physiology, morphology, growth, life history and demography, and can be expressed either within the lifespan of an individual or across generations (Pertoldi et al., 2005; Røgilds et al., 2005). Two ways of adapting to environmental changes are therefore possible, by evolutionary or by plastic responses, including maternal transmission (trans-generational plasticity). Hence, the survival of populations relies on genetic variation and/or phenotypic plasticity. Populations with small NE and/or little genetic variability have mainly the option of adapting in a plastic way, therefore the importance of plasticity is quite evident (Pertoldi et al., 2007b).
