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Keywords:

  • Allee effects;
  • demographic heterogeneity;
  • demographic stochasticity;
  • extinction;
  • genetic variation;
  • growth rate;
  • population persistence;
  • population viability analysis;
  • selection;
  • small population;
  • stochastic simulation

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Population persistence has been studied in a conservation context to predict the fate of small or declining populations. Persistence models have explored effects on extinction of random demographic and environmental fluctuations, but in the face of directional environmental change they should also integrate factors affecting whether a population can adapt. Here, we examine the population-size dependence of demographic and genetic factors and their likely contributions to extinction time under scenarios of environmental change. Parameter estimates were derived from experimental populations of the rainforest species, Drosophila birchii, held in the lab for 10 generations at census sizes of 20, 100 and 1000, and later exposed to five generations of heat-knockdown selection. Under a model of directional change in the thermal environment, rapid extinction of populations of size 20 was caused by a combination of low growth rate (r) and high stochasticity in r. Populations of 100 had significantly higher reproductive output, lower stochasticity in r and more additive genetic variance (VA) than populations of 20, but they were predicted to persist less well than the largest size class. Even populations of 1000 persisted only a few hundred generations under realistic estimates of environmental change because of low VA for heat-knockdown resistance. The experimental results document population-size dependence of demographic and adaptability factors. The simulations illustrate a threshold influence of demographic factors on population persistence, while genetic variance has a more elastic impact on persistence under environmental change.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Organisms live in environments that fluctuate or change in a directional manner. Hence, the ability to adapt is a relentless challenge, and failure to do so results in fitness decline and eventual local extinction. Models of population persistence have commonly considered environmental change as a stochastic force causing fluctuations in vital rates (Boyce et al., 2006). The most prominent type of such analysis, population viability analysis, incorporates the adverse effects of demographic and environmental stochasticity on population persistence, and – more rarely – the genetic problems associated with small census size (Reed et al., 2002). However, in the face of directional environmental change such as global climate change, models of population persistence also need to account for whether a population can adapt (Stockwell et al., 2003). While evolutionary models of population persistence have incorporated parameters representing the ability to adapt and the costs of selective deaths (Lynch & Lande, 1993), they have neglected the special demographics of small, isolated populations. Both demographics and adaptability should be combined to predict population persistence, particularly in the context of climate change or any other short- or long-term directional environmental change (Hoffmann & Willi, 2008).

Lynch & Lande (1993) were the first to develop a quantitative genetic model of population persistence. Their model predicts the growth rate of a sexual population of finite size in a changing environment by taking into account four types of load. The first results from phenotypic variation that arises during development, which leads to a net loss of mean fitness because of the existence of nonoptimal phenotypes. The second load, termed the lag load, refers to how much a population lags behind the moving selection optimum. The lag load is large if the environment changes quickly or genetic variation is low. These first two types of load are well established in population genetics theory, but so far have received little attention from conservation biologists. In contrast, the other two types of load, caused by genetic drift and stochasticity in the selection environment, have long been part of conservation genetics theory (Frankham et al., 2003, p. 178 and pp. 247–248). Genetic drift is important because it causes deviations of realized phenotypes from the expected phenotype, particularly in small populations. The strength of drift is inversely proportional to Ne (Kimura, 1955). Stochasticity in the selection environment causes phenotypes to further depart from the current selective optimum. Lynch and Lande discounted the maximum growth rate by these four loads to predict the realized long-term growth rate of the population.

Lynch & Lande (1993) used their model to define the critical rate of environmental change that a population can handle without going extinct. In other words, they investigated how fast the environment can change so that the population growth rate remains at least 0. In a later study, Bürger & Lynch (1995) declared this model too deterministic because it implies that populations either live forever or go extinct, depending on their predicted growth rate. They argued that any population can go extinct at any time because of the stochastic nature of genetic variation, demography and the environment, even though small size makes extinction more likely. The alternative proposed by Bürger and Lynch placed more emphasis on the stochastic nature of population processes and included a simple form of density dependence (carrying capacity). Their model predicted the expected mean time to the extinction of a population.

Conservation biologists have acquired good evidence for several further types of load, which were not explicitly included in Lynch & Lande (1993) or Bürger & Lynch (1995). These loads are direct consequences of small population size. They include inbreeding depression due to biparental inbreeding, the accumulation and fixation of deleterious mutations, and demographic Allee effects and increased variation in reproductive output due to the stochastic nature of vital rates (Lande, 1988; Lynch et al., 1995). Convincing evidence for inbreeding depression has been found in laboratory experiments, wild populations and artificial breeding (Crnokrak & Roff, 1999; Crnokrak & Barrett, 2002; Keller & Waller, 2002; Kristensen & Sørensen, 2005; Kristensen et al., 2007). Mutation accumulation due to genetic drift has been documented in natural populations (e.g. Roelke et al., 1993; Willi et al., 2005). These two types of load can substantially diminish mean fitness, as illustrated by studies where propagules sampled in natural populations of varying size were raised under common environmental conditions (e.g. Willi & Fischer, 2005) or when populations were bottlenecked in lab studies (e.g. Fowler & Whitlock, 1999). Demographic Allee effects result from disturbed ecological processes, such as when low density or small census size causes pollen limitation (Groom, 1998; Knight, 2003). Furthermore, the extinction risk of small populations is predicted to be enhanced due to four categories of stochasticity affecting demography: stochastic variation in vital rates among individuals (demographic stochasticity), variation in vital rates among populations (environmental stochasticity), biased sex ratio, and condition-dependent variation in vital rates among individuals (demographic heterogeneity) (Melbourne & Hastings, 2008).

In this study, we estimated relationships between population size and several sources of load in experimental populations of the rainforest fruit fly Drosophila birchii, and explored their effect on population persistence in a stochastic simulation model. We held populations at three size classes – 20, 100 and 1000 individuals – for 10 generations, and then estimated quantitative genetic variation by imposing selection for increased heat-knockdown resistance. We chose heat-knockdown resistance because of its likely relevance under climate change (Reusch & Wood, 2007), and because it does not vary clinally in D. birchii and is unaffected by laboratory culture (Griffiths et al., 2005). We then used our parameter estimates to explore population persistence under scenarios of environmental change, integrating the genetic and demographic problems that small populations face. Our main goals were to investigate the rate of environmental change a population can survive without going extinct (Lynch & Lande, 1993), and to predict the time until extinction using a stochastic simulation model based on Bürger & Lynch (1995).

Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Experimental study

Set-up of experimental populations

We chose D. birchii to study the demographic and genetic factors contributing to population persistence because it is a habitat specialist species limited to tropical rainforests of northeastern Australia, with a short generation time and the potential to be raised in the lab. From mid-March to mid-April 2005, we caught D. birchii at six locations in the area of Cairns, Australia, separated by at least 7 km from one another. In the lab, field-inseminated females were set up in individual vials to establish isofemale lines. After three generations in the lab, we founded 28 experimental populations of three sizes: 20 (18 replicates), 100 (eight replicates) and 1000 (two replicates) individuals. The two smallest size classes were designed to achieve a slight-to-moderate accumulated effect of genetic drift by the end of the experiment, after 10 generations.

For all populations, we combined flies from many isofemale lines to boost the initial genetic variation. For each site of origin, flies of 15 randomly chosen isofemale lines per site were merged to create populations of 20 (two per site of origin) or 100 (one per site of origin) so that all lines were equally represented and the sex ratio was completely balanced. Further populations of 20, 100 and 1000 were founded by mixing flies from different origins, from at least 20 isofemale lines that had been randomly chosen from a total of 105 isofemale lines. In the statistical analysis, we took account of this design by creating the random factor of ‘origin’ that included the six sampling sites and site mixtures, totalling seven ‘origin’ levels. Flies were kept in vials at equal densities of 20 individuals for all lines. Hence, at any time, each population of size 20 was kept in a single 40-mL glass vial, each population of 100 was distributed among five vials and each population of 1000 was in 50 vials. When the number of flies dropped under the capacity size, all available flies were used to produce the next generation, and (usually) one vial per line had < 20 flies.

To initiate each generation, adult flies of peak egg-laying age were placed onto fresh medium for two consecutive 2-day periods to allow oviposition. Eclosing flies of a population were collected and pooled until no new flies appeared. This allowed adults to mate freely before we enforced the carrying capacity treatment. Flies were allowed to age until the youngest were at least 3 days old before we chose the appropriate number of flies randomly and distributed them over the sets of vials to produce the next generation. Flies were counted out in numbers of 20 without regard to sex and put in 40-mL vials with 12 mL of fresh medium. The medium consisted of 1.9% freeze-dried potato powder, 4.7% sugar, 5.3% agar, 8.3% yeast and 79.8% water (by weight), and small amounts of tegosept, propionic acid and phosphoric acid to prevent microbial growth.

Productivity

We assessed the intrinsic rate of natural increase (r) for each population beginning at generation 4, when differences among population-size classes in reproductive output became obvious. r is defined as ln(R0) in organisms with nonoverlapping generations (Begon et al., 1986, p. 150), where R0 is the mean number of offspring produced per individual (Begon et al., 1986, p. 136). Offspring were frozen and counted individually for the smaller two size classes, and for the 1000 size class fly numbers were determined by weight. During these 10 generations and subsequent flushing, 12 populations of size 20 went extinct (i.e. 0 or 1 fly emerged in the generation of extinction). Because reproductive output can vary with the quality of the food and other generation-specific environmental conditions, we corrected r of each population and generation for differences caused by the particular environment experienced by all populations and vials within a given generation. We then analysed whether population mean r and within-population variation in r, expressed as the standard deviation (SD) of mean r, depended on population size. We hypothesized that small populations would show reduced growth rates, indicating genetic problems, and that they would have a higher SD of r across generations, indicating increased stochasticity in r. This measure of stochasticity possibly integrated demographic stochasticity (sensuMelbourne & Hastings, 2008), biased sex ratio and demographic heterogeneity caused by among-vial variation in conditions. Mixed models tested for the fixed effect of population size on r and the SD in r, with ‘origin’ included as a random effect and the number of vials included as weights (MIXED procedure in sas; SAS Institute Inc., 2002).

Realized heritability for increased heat-knockdown resistance

After 10 generations of maintenance at sizes of 20, 100 or 1000, we assessed the ability of populations to respond to directional selection. First, the smaller populations were flushed to at least 200 flies during five (10 populations) or six (six populations) generations. Flushing time was set at five generations to minimize linkage disequilibrium caused by inbreeding and subsequent flushing. Next, the populations were selected for increased heat-knockdown resistance over four to five generations. This trait is ecologically relevant for a tropical drosophilid, easy to score, and well studied in other Drosophila (Huey et al., 1992; McColl et al., 1996). Heat-knockdown resistance was assessed by placing groups of 200 flies of similar age (eclosed over 3 subsequent days) at the top of a vertical plexiglas column (inebriometer) with a double wall of circulating water maintained at 40 °C (McColl et al., 1996). Resistance was recorded as time until a fly was incapacitated and fell into the bottom of the column. Flies were sexed and counted under CO2, and the most resistant 50% of females were transferred into vials where they oviposited. Males that fell at the same time as the selected females were also transferred to provide a stimulus for females to lay eggs. Flies were kept at densities of 20 individuals per vial. Because females had already had ample opportunity to mate prior to selection, we assumed that selection acted only on females. Selection continued for a total of five or four generations (depending on flushing). For each selected population, we also kept an unselected control line of ≥ 200 individuals for which the heat-knockdown was also assessed during the last three generations.

For each population and selection round, we calculated the selection intensity i by the approximation: = 0.8 + 0.41 × ln(1/p − 1), where p is the proportion of females selected (Smith, 1969). We then calculated the selection differential S by multiplying the selection intensity by the phenotypic SD of female heat-knockdown time (SDP), times 0.5 because selection acted only on females (Falconer & Mackay, 1996, pp. 188–191). For the last three rounds of selection, we estimated accumulated selection response by subtracting the mean resistance of the control line from that of the selected line. Realized heritability (h2) of each population was revealed by regressing selection response against accumulated selection differential (over all previous generations of selection), both of which were estimated in three consecutive generations. The regression was forced through the origin. Population additive genetic variance (VA) was calculated by multiplying h2 by the mean phenotypic variance (VP) of both sexes assessed in the control lines over three generations.

Modelling component

Critical rate of change

We estimated the maximal rate of environmental change, kc, under which each of our initial 28 experimental populations could achieve a growth rate (r) of at least zero (Lynch & Lande, 1993). kc is expressed in units of change in the optimum of the trait per time, which in our case is minutes of increased heat-knockdown resistance per generation, adjusted for an environmental variance (VE) in the trait of 1. The model assumes that the trait is under stabilizing selection, and the trait optimum moves unidirectionally as the environment changes. Our calculation neglected stochasticity in the selection environment, one of the four sources of load considered by Lynch and Lande. We assumed that maximum growth rate in the absence of selection, r*, was r assessed in the absence of heat-knockdown selection; r* therefore includes adverse effects of genetic drift such as inbreeding depression. Estimates of VA and VP, scaled so that VE = 1, were obtained separately for each population. The width of the fitness function (VW) of the trait under stabilizing selection was set to 20. This value has been justified by Turelli (1984) based on a dozen empirical data sets listed in Johnson (1976, p. 178). A high value of VW reflects weak selection, under which individuals with phenotypes far from the fitness optimum enjoy relatively high fitness. Furthermore, we assumed that the ratio of effective population size (Ne) to census size (N) was 0.1, an average value for drosophilids (Frankham, 1995).

The formula derived from Lynch & Lande (1993) is:

  • image(1)
Simulating time to extinction

We simulated the time to extinction for the three population census sizes by combining Lynch & Lande’s (1993) formula of growth rate with Bürger & Lynch’s (1995) difference equations for expected mean phenotype and its variance:

  • image(2)

where

  • image(3)

and where

  • image(4)

Equation 2 predicts population growth rate under stabilizing selection with a mean phenotype inline image, an optimum phenotype θ and phenotypic variance VP. We assumed that the optimum phenotype θ was 0 at the onset of the simulation and increased thereafter at the rate of k per generation.Equation 3 predicts the expected mean phenotype under a lag load that depends on the rate of environmental change, k, and a measure of the strength of selection, VA/(VP + VW). Equation 4 predicts the variance in the mean phenotype due to drift-induced deviations from the expected phenotype and due to stochasticity in the selection environment, inline image (which we set equal to zero). Our simulations followed the population size and the mean and variance of the phenotype. For each size class (20, 100 and 1000), simulations were run for 2000 populations (Fig. 2) or 1000 populations (Fig. 3) and for a maximum of 300 generations. Before the first generation started, a population was assigned values of VA, VP and mean r specific to its population size class. These parameters were sampled from normal distributions with (least squared) means and SD derived from the analysis of the empirical data (Table 1). Ne was set to N × 0.1. In every generation, a deviation from mean r due to a combination of demographic stochasticity, unequal sex ratio and demographic heterogeneity was sampled from a population size class-specific distribution, which came from the empirical data (SD r in Table 1). Then, the expected mean phenotype and its variance were calculated from eqns 3 and 4, and the realized mean phenotype in a given generation was drawn from a normal distribution defined by the two values. We calculated growth rate after selection according to eqn 2 and determined the number of offspring by N × er. Finally, before the onset of the next generation, we enforced the carrying capacity (20, 100 or 1000, depending on the initial census size). When the number of offspring was below the carrying capacity, all survivors entered the next generation and N– but not Ne– was adjusted; N could be a noninteger. The population was considered extinct when < 2. There was no density dependence below the carrying capacity.

image

Figure 2.  Median number of generations to extinction related to the rate of environmental change (k), as revealed by stochastic simulation incorporating demographic and genetic data from experimental populations of Drosophila birchii. Predicted time to extinction was about nine generations for the populations of 20 flies, regardless of the rate of environmental change, and fewer than about 170 generations for the populations of 100 flies. Only populations of 1000 flies were predicted to persist for long periods when the rate of environmental change was < 0.05.

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image

Figure 3.  Contour plots presenting median number of generations to extinction as a function of additive genetic variance (VA) of the trait under selection, mean intrinsic rate of natural increase (r) and stochasticity in growth rate (SD of r) for populations of size 20, 100 and 1000. Panels (a) and (b) are based on simulations incorporating parameter estimates derived from the size 20 treatment, (c) and (d) from the 100 treatment, and (d) and (e) from the 1000 treatment. Two parameters were kept fixed: rate of environmental change (k) was 0.1 and the width of the fitness function (VW) was 20. The highest value of VA (1.0) corresponds to h2 = 0.5. The white dots indicate the parameter combination estimated in experimental populations of that size class. Median extinction time of population size 20 was below 50 generations for most parameter combinations. Populations of size 100 persisted for longer periods only if r was large and VA was high, and when stochasticity in r was low and VA was high. Populations of 1000 flies were predicted to persist well within the approximate ranges of > 0.5, stochasticity in < 1.5 and VA > 0.4 (h2 > 0.29).

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Table 1.   Effect of population size on demographic and adaptability parameters.
SourceMean rSD rRealized h2VPVAkc
d.f.Numd.f.DenFPd.f.DenFpd.f.DenFPd.f.DenFPd.f.DenFPd.f.DenFP
  1. We investigated the effect of census population size (20 vs. 100 vs. 1000) on the population mean intrinsic rate of natural increase (r) across generations, the standard deviation (SD) of r across generations as well as the three parameters of realized heritability (h2), phenotypic variance (VP) and additive genetic variance (VA) in heat-knockdown resistance. Based on estimates of r, h2 and VP, we calculated the critical rate of environmental change that a population can cope with without going extinct (kc) according to Lynch & Lande (1993). The generalized linear mixed models included the random effect of ‘origin’ and used restricted maximum likelihood. The denominator degrees of freedom (d.f.Den) for testing the fixed effects were estimated by Satterthwaite’s approximation. P-values < 0.05 are printed in bold. n for testing r and kc was 28; for SD r 27; and for h2, VP and VA 16.

Fixed effect
Population size217.215.6< 0.00120.921.51< 0.001133.570.058132.910.090135.770.01624.17.270.003
t- and P-values of contrasts
20 vs. 100  −4.70< 0.001 5.06< 0.001 −2.610.022 1.370.195 −3.280.006 −3.81< 0.001
20 vs. 1000  −5.36< 0.001 6.53< 0.001 −0.450.661 2.360.035 −0.430.676 −0.540.597
100 vs. 1000  −1.240.231 1.850.081 1.320.210 1.500.157 1.800.095 1.540.137

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Experimental study

Productivity

Populations of size 20 had significantly lower mean growth rate (r) across generations than populations of size 100 or 1000 (Table 1, Fig. 1a). However, populations of 100 did not have significantly lower growth rates than those of 1000. The results indicate that flies in the smallest populations suffered from problems caused by genetic drift (independent of environmental change). Furthermore, populations of size 20 had more variable r across generations compared with those of 100 and 1000 individuals, and populations of 100 tended to have higher variability in reproductive output than those of 1000 (Table 1, Fig. 1b). The population class of 20 was more prone to random demographic effects than populations with 100 or 1000 individuals. The 12 lines that went extinct during the 10 generation experiment and subsequent flushing were all of size class 20. This further illustrates the genetic problems and stochasticity problems experienced by the smallest population size class.

image

Figure 1.  Adaptability of 28 experimental populations of Drosophila birchii flies kept at 20, 100 and 1000 individuals for 10 generations. For each population, we assessed the mean intrinsic rate of natural increase (r) for seven generations (a), the SD of r among generations (b) and additive genetic variance (VA) for heat-knockdown resistance (c). (d) Based on these values, we calculated the critical rate of environmental change that a population can sustain without going extinct, kc, following Lynch & Lande (1993). Each symbol reflects one replicate population. The dashed lines connect least square means for the three population-size classes, and different letters indicate significant differences between size classes (see Table 1). Populations of 20 flies had a significantly lower mean growth rate than populations of 100 and 1000 flies, they were significantly more affected by stochasticity in growth rate and they had a 70% extinction rate before the end of the experiment. VA was lower in populations of 20 than 100 flies, but the size classes of 20 and 1000 did not significantly differ in VA. Compared with the size class of 1000 flies, those of 100 flies tended to have more stochasticity in growth rate, but also more VA, so that the predicted ability of these larger two size classes to cope with environmental change was not significantly different.

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Realized heritability for increased heat-knockdown resistance

Realized heritability for heat-knockdown resistance was low, and smaller in the lines of size 20 than in the lines of 100 (Table 1; least square means ± standard error (SE) for populations of size 20, 100 and 1000: 0.056 ± 0.060, 0.263 ± 0.052 and 0.110 ± 0.104). However, contrary to our expectation, lines of 1000 flies did not have significantly higher realized heritability than lines of size 20 and 100. Phenotypic variance of the nonselected lines significantly differed between the treatments of 20 and 1000 individuals, with increased phenotypic variance in the treatments of 20 (Table 1; least square means ± SE for populations of size 20, 100 and 1000: 12.4 ± 1.0, 10.7 ± 0.8 and 7.9 ± 1.7). For additive genetic variance, the populations of size 20 had significantly lower values than the populations of 100 (Table 1; Fig. 1c). Lines of size 1000 had intermediate levels of genetic variance, which were not significantly different from those of size 20 or 100.

Modelling study

Critical rate of change

The critical rate of environmental change above which extinction is inevitable, kc, was calculated without including either stochasticity in reproductive output or stochasticity in the moving optimum. kc was significantly smaller for the treatment of 20 than for the treatment of 100 (Table 1, Fig. 1d). In fact, the smallest populations were predicted to be almost entirely unable to cope with increasing heat stress. The size classes of 20 and 1000 did not significantly differ in kc, and their estimated kc values were not significantly different from 0 (least square means ± SE for populations of size 20, 100 and 1000: 0.01 ± 0.02, 0.16 ± 0.03 and 0.04 ± 0.07).

Simulating time to extinction

Simulations based on the model incorporating stochasticity in r revealed that median time to extinction for the populations of 20 flies was around nine generations, even when there was no environmental change (Fig. 2). This result illustrates that mean reproductive rate and stochasticity in r dominated in their effect on the smallest populations. Populations of 100 flies persisted for intermediate durations, with median extinction times of 30–170 generations, and shorter persistence with increasing directional environmental change. The median time to extinction of populations of 1000 flies exceeded our simulation limit of 300 generations when the rate of environmental change was below 0.05, but dropped to a similar level for populations of 100 individuals at very high rates of environmental change.

Figure 3 illustrates the interactions among genetic variation, mean r and stochasticity in r on median time to extinction. The rate of environmental change in these simulations (= 0.1), averaged over the three population census size classes, was equivalent to 0.29 min of increased heat-knockdown resistance per generation (assuming mean SDP = 3.2, or mean SDP = 1.1 when VE = 1). This value of k was 6% of the average heat resistance of 4.5 min of the unselected controls of the three size classes. Populations of 20 flies were predicted to go extinct within less than a few dozen generations independent of how high-reproductive output and VA were, because they experienced very high stochasticity in r (Fig. 3a). Similarly, extinction time was short for populations of 20 for all combinations of stochasticity in r and VA (Fig. 3b). Interestingly, when VA was very low in populations of 20, persistence time increased slightly because drift load was reduced (Fig. 3a). For populations of 100 individuals, demographic parameters had threshold effects on persistence. When mean r was high and stochasticity in r was low, VA came into play; higher VA then led to longer persistence. The persistence of populations of 1000 was generally better than that of the 100 and more broadly affected by the level of VA. When a minimal r was realized and a relative high value of stochasticity not exceeded, persistence increased with VA. At the parameter values observed in our experiment, the rank order of predicted population persistence under environmental change was 1000 > 100 > 20 (Fig. 3).

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

The goal of our study was to simultaneously estimate demographic and adaptability parameters of replicate Drosophila lines varying in census size and to investigate the impact of these parameters on population persistence under environmental change by stochastic simulation. The empirical study revealed low growth rate (r) and high stochasticity in r for the smallest population size class of 20. Populations of 100 had significantly higher reproductive output, lower stochasticity in r and more additive genetic variance (VA) than populations of 20. Populations of 1000 tended to be affected even less by stochasticity in reproductive output than population of 100, while their VA for heat-knockdown resistance tended to be lower. The simulations showed that very small populations are likely to go extinct within a few generations because their potential to adapt is severely compromised by reduced mean reproductive output and heightened stochasticity in reproductive output compared with larger population size classes. These factors reduce population growth rates even in the absence of a changing environment. Populations of intermediate size (100 individuals) tended to be negatively affected by somewhat heightened stochasticity and increased drift load for the trait under directional selection, reducing their evolutionary potential despite heightened levels of genetic variance. Finally, even large populations with high reproductive output and low stochasticity were prone to extinction when levels of additive genetic variance for ecologically relevant traits are low and the response to selection limited. This set of results implies that evolutionary models of population persistence should include genetic and demographic features and consider deterministic and stochastic elements, particularly when the focus is on small populations.

Our experimental results, simulations and previous studies reveal important relationships between population size and factors influencing adaptability. First, the mean reproductive rate of populations was critically important in both the deterministic and stochastic models used in this study because the smallest size class suffered from a 50% reduction in population mean fitness compared with the larger two size classes. Similar fitness reductions have been observed in natural populations of plants and animals. Reed (2005) used 11 studies of plant populations to derive the relationship between relative fitness and population census size; a positive slope was attributed to inbreeding in small populations. Reed’s results suggest that populations of size 20 experience a mean fitness reduction of 54% compared to populations of 1000. Similarly, O’Grady et al. (2006) found very high inbreeding loads segregating in wild populations of mammals and birds, such that even populations with an effective size of 100 (for 10 generations) suffered from a 41% fitness decline relative to populations of 1000. Hence, the fitness reductions revealed by our study are in the range observed in nature.

A second factor affecting adaptive potential was stochasticity in r. Our estimate of stochasticity in reproductive output combined true demographic stochasticity, due to variation in vital rates among individuals within populations (Melbourne & Hastings, 2008), with possible variation arising from biased sex ratio and heterogeneity among vials in reproductive output. This integrative estimate of stochasticity in reproductive output was negatively related to population size in our experiment. Stochasticity was probably particularly high because of variance in female reproductive output (Frankham, 1995) and low carrying capacity (Pimm et al., 1993; Belovsky et al., 1999; Drake, 2005). The simulation results revealed that stochasticity in reproductive output indeed strongly influenced the time to extinction. The deterministic model, which included observed levels of population growth rate and genetic variation, predicted that a population of 100 could cope about equally well with environmental change as a population of 1000 (Fig. 1d). However, the stochastic simulation study – also accounting for stochasticity – revealed that populations of a census size of 100 were generally more prone to going extinct compared with the larger size class (Fig. 2).

A third factor affecting adaptive potential is the level of additive genetic variance. Quantitative genetics theory assuming additive gene effects predicts a monotonic decline in genetic variance with decreasing population size (reviewed in Willi et al., 2006). While lab experiments have confirmed this pattern for morphological traits, they do not support it for life-history traits associated with fitness, which are more influenced by nonadditive gene effects (Roff & Emerson, 2006; Van Buskirk & Willi, 2006). Outside the lab, the relationship between population size and genetic variance is not well supported by available empirical data, although only few studies have estimated VA or narrow-sense heritability in natural populations over a large range of census population sizes (reviewed in Willi et al., 2006). Willi et al. (2007) estimated VA for seven morphological and life-history traits in 13 plant populations varying in census size over about 2 orders of magnitude, and discovered a positive relationship between census size and genetic variance.

Gene frequency perturbations due to genetic drift may explain our observation that populations of 20 had significantly lower VA for heat resistance than populations of 100, but that of 1000 were intermediate. Studies on the impact of drift on additive genetic variance have usually shown that VA can increase for traits with some nonadditive genetic basis (Van Buskirk & Willi, 2006). Indeed, in a rainforest fly species related to D. birchii, desiccation resistance has been shown to gain VA following bottlenecking, suggesting that stress resistance traits are influenced by nonadditive variation (van Heerwaarden et al., 2008). Hence, although the somewhat heightened VA in some populations of 100 compared to those of 1000 may reflect an artefact of small sample size, the pattern could also have been caused by genetic drift. In populations of 20, there may have been a similar initial drift-induced rise in VA, which was then eroded by 10 generations of small size.

Our model of population persistence integrated one quantitative genetic and two demographic factors to assess population persistence under environmental change. The stochastic simulations revealed that demographic and quantitative genetic parameters behave differently in determining population persistence (Bürger & Lynch, 1995). Both the intrinsic rate of natural increase, r, and stochasticity in r showed threshold effects on population persistence (Fig. 3). For example, if stochasticity in r was too high relative to the longer term mean r, populations did not persist for long, independent of genetic variation. Populations of size 20 were in the extreme situation of having no evolutionary potential, not because of a lack of genetic variation but because they did not meet the threshold levels of reproductive rate and the combined measure of demographic stochasticity and demographic heterogeneity. Figure 2 shows that they had the same time to extinction under all rates of environment change. Populations of size 100 barely exceeded the thresholds for mean reproductive output and stochasticity in reproductive output and had levels of genetic variance that were not high enough to adapt in response to a realistic rate of environmental change. In contract, populations of 1000 individuals had levels of mean reproductive output and stochasticity beyond critical thresholds, but population persistence was ultimately limited by low genetic variance. Exploration of the parameter space for growth rate, stochasticity in growth rate and genetic variance showed that populations of 100 individuals had lower persistence potential than those of 1000 even when their vital rates were similar (Fig. 3). The basic problem for intermediate-sized populations is that their potential to follow environmental change is negatively affected by stochasticity.

Several different modelling approaches have been used to anticipate the effects of directional global climate change, including ecological niche models, metapopulation models and population viability analysis (PVA; e.g. DeWoody et al., 2005; Meyer et al., 2007; Morin et al., 2007). Their focus is on predicting persistence based on habitat requirements, ecological tolerances and/or demographic parameters under scenarios of spatial and temporal structure of suitable habitat. However, all these approaches ignore evolutionary factors affecting persistence. Lynch & Lande’s (1993) model was therefore welcome because it explicitly considered how population persistence depends on genetic variation and natural selection. However, a more realistic model of adaptive potential – especially in a conservation context – must combine factors shown to be important in these different approaches (Gomulkiewicz & Holt, 1995; Boulding & Hay, 2001). Our study is the first to integrate the three parameters of population-size-dependent mean growth rate, stochasticity in growth rate and levels of genetic variance for ecologically relevant traits to predict population persistence under longer-term environmental change, and it demonstrates that the three factors are predicted to have biologically meaningful impacts. Nevertheless, we also caution that more experimental and natural population data are necessary to confirm the interactive effects of demographics and genetic variation on population persistence.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

We thank Torsten Nygaard Kristensen, Jane Leslie, Alan Rako, Lea Rako, Rhonda Rawlinson, Jennifer Shirriffs and Josh Van Buskirk for their support with the fly work; Josh Van Buskirk for advice with the simulation and for critical comments on the manuscript; and Tadeusz Kawecki and two anonymous reviewers for helpful comments that further improved this manuscript. We were supported by the Swiss National Science Foundation (PBZHA-108498) and the Australian Research Council.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References