How general are positive relationships between plant population size, fitness and genetic variation?

Summary

• 1

  Relationships between plant population size, fitness and within-population genetic diversity are fundamental for plant ecology, evolution and conservation. We conducted meta-analyses of studies published between 1987 and 2005 to test whether these relationships are generally positive, whether they are sensitive to methodological differences among studies, whether they differ between species of different life span, mating system or rarity and whether they depend on the size ranges of the studied populations.

• 2

  Mean correlations between population size, fitness and genetic variation were all significantly positive. The positive correlation between population size and female fitness tended to be stronger in field studies than in common garden studies, and the positive correlation between genetic variation and fitness was significantly stronger in DNA than in isoenzyme studies.

• 3

  The strength and direction of correlations between population size, fitness and genetic variation were independent of plant life span and the size range of the studied populations. The mean correlations tended to be stronger for the rare species than for common species.

• 4

  Expected heterozygosity, the number of alleles and the number or proportion of polymorphic loci significantly increased with population size, but the level of inbreeding F_IS was independent of population size. The positive relationship between population size and the number of alleles and the number or proportion of polymorphic loci was stronger in self-incompatible than in self-compatible species. Furthermore, fitness and genetic variation were positively correlated in self-incompatible species, but independent of each other in self-compatible species.

• 5

  The close relationships between population size, genetic variation and fitness suggest that population size should always be taken into account in multipopulation studies of plant fitness or genetic variation.

• 6

  The observed generality of the positive relationships between population size, plant fitness and genetic diversity implies that the negative effects of habitat fragmentation on plant fitness and genetic variation are common. Moreover, the stronger positive associations observed in self-incompatible species and to some degree in rare species, suggest that these species are most prone to the negative effects of habitat fragmentation.

Introduction

The relationships between plant population size, fitness and genetic diversity are of fundamental importance in plant ecology, evolution and conservation. Although many plant populations are naturally isolated and small, populations of numerous plant species have become more isolated and further decreased in size due to the recent anthropogenic fragmentation of habitats. Small populations are predicted to face the negative genetic consequences of increased inbreeding and reduced genetic variation caused by genetic drift, founder effects and accumulation of deleterious mutations (Lynch et al. 1995; Young et al. 1996). In the long run, reduced genetic diversity, mutation accumulation and increased inbreeding, decrease the evolutionary potential of species to adapt to changing environments, and in the short run they may reduce fitness, especially in small populations (Ellstrand & Elam 1993). In addition to the genetic mechanisms, ecological mechanisms, such as pollinator limitation, may further reduce fitness in small populations (e.g. Ågren 1996).

Positive relationships between population size, genetic variation and fitness may come about for two reasons. On the one hand, such associations may indicate an extinction vortex where reductions in population size decrease genetic variation. If this reduction leads to inbreeding depression or reduced mate availability, it will consequently reduce plant fitness and lead to a further decrease in population size (Ellstrand & Elam 1993). On the other hand, such positive relationships may arise if plant fitness differs between populations due to differences in habitat quality. This will result in variation in population sizes and may consequently also influence the level and distribution of genetic variation. These two different causal backgrounds can be distinguished by comparing field studies with experimental common garden studies that examine plant fitness. This reveals whether the associations between population size or genetic variation and plant fitness observed in the field are due to underlying differences in habitat quality (Fischer & Matthies 1998).

During the past two decades, a number of studies examined relationships between plant population size, measures of fitness and genetic variation (Oostermeijer et al. 2003). Although positive relationships were reported in some studies, non-significant or even negative relationships were reported in others (see Appendix S1 in Supplementary Material). Hence, it is not clear whether these relationships are overall positive, and how strong they are. Because most studies have been conducted in the field and only very few in common environments, it is not clear whether the reported relationships are due to the effects of population size per se or due to confounding habitat differences. Moreover, it is not known whether the different methods used to measure genetic variation affect the observed relationships. Most studies used near-neutral isoenzyme or DNA-markers to determine the level of genetic variation, although variation for such neutral markers may correlate poorly with traits under selection and does not necessarily reflect the evolutionary potential of a population (Reed & Frankham 2001). Moreover, the relationship between population size and genetic variation has been suggested to be strongest for neutral genetic markers and weakest for the most strongly selected markers (Frankham 1996). Unfortunately, studies on quantitative genetic variation of fitness-related traits in natural populations are still very scarce.

The strength and direction of the relationships between plant population size, fitness and genetic variation may depend on different plant characteristics, especially life span, mating system and rarity. Short-lived plants may be more prone to the negative genetic consequences of reduced population size. The more generations passed during a given time span, the stronger will be the effect of genetic drift (Hartl & Clark 1989). Therefore, drift is likely to have greater impact on short-lived species with generally shorter generation times compared with long-lived species (Hamrick et al. 1979). Moreover, short-lived species are likely to be more vulnerable to the ecological consequences of small population size, such as increased pollinator limitation, or increased demographic stochasticity in recruitment, which is essential for short-lived species because they are mainly semelparous.

Associations between population size, genetic variation and plant fitness can be stronger in self-compatible species because in these species inbreeding depression may be expressed more readily. However, genetic load may have been purged in populations of self-compatible plants. Thus, especially in populations with a long history of inbreeding, self-compatible plants could also be less vulnerable to inbreeding depression and therefore less susceptible to the negative effects of small population size (Busch 2005). In self-compatible species, genetic variation resides largely between populations, whereas in self-incompatible species it resides rather within populations (Hamrick & Godt 1989). Therefore, variation in population size may have a greater impact on within-population genetic variation in self-incompatible species. Self-incompatibility may also break down in small and isolated populations, especially after population bottlenecks (Porcher & Lande 2005), which can consequently erase the differences in the strength of associations of population size, genetic variation and fitness between self-incompatible and self-compatible species.

Species rarity may also affect the relationships between population size, genetic variation and fitness. Rare species are typically considered to be genetically less variable than common and widespread species (Karron 1987; Hamrick & Godt 1989; Ellstrand & Elam 1993; Spielman, Brook & Frankham 2004). This indicates that the level of genetic variation might be less strongly associated with population size in rare plants compared with common plants. This is because genetic variation is likely to be low in all populations of rare plants and higher in all populations of common plants regardless of the size of the populations. However, hybridization, recent speciation, multiple origins or recent population bottlenecks may result in high levels of genetic variation also in rare species (Lewis & Crawford 1995; Purdy & Bayer 1995; Friar et al. 1996; Smith & Pham 1996). Moreover, when differences between rare and common species are considered the exact definition of rarity has to be taken into account (Rabinowitz 1981). For example, in contrast to a widespread assumption, rare species do not always have small population sizes (Rabinowitz 1981; Gitzendanner & Soltis 2000).

Finally, whether positive associations of population size, genetic variation and fitness become apparent may depend on the size of the populations in a study. Although these associations may be strong at low population sizes, they may be less strong or absent for larger populations.

In this review, we use meta-analysis to examine the relationships between plant population size, genetic variation and fitness reported in studies published between 1987 and 2005. Meta-analysis allows us to combine the results of independent studies addressing the same research question, to estimate the mean effect size, and to identify the factors that influence the strength and sign of the effect (Gurevitch & Hedges 2001). One of the advantages of meta-analysis is that effects may be detected across studies even for cases where individual studies report non-significant effects because of lack of statistical power. In particular, we examined: (i) whether the relationships between plant population size, fitness and genetic variation are generally positive; (ii) whether they differ between field and common environment studies of plant fitness, or between genetic studies using isoenzymes or DNA-based analyses; (iii) whether they differ between annual/biennial and perennial species, self-compatible and self-incompatible species, or between rare and common species; and (iv) whether they depend on the actual size range of the studied populations.

Methods

data acquisition

We conducted key word searches in the Web of Science (ISI) electronic bibliographic data base to find plant studies on the relationships between population size and fitness, between population size and genetic variation, and between genetic variation and fitness. Using combinations of the key-words ‘population size’, ‘fitness’, ‘reproductive success’, ‘genetic variation’ and ‘genetic diversity’ we obtained three data sets. The first set included 45 studies of the relationship between population size and fitness measures in 34 plant species, the second set consisted of 46 studies of relationships between plant population size and genetic variation in 41 plant species, and the third set included 14 studies of the relationship between fitness and genetic variation in 12 plant species (see Appendix S1 and S2). These studies were published in 20 journals between 1987 and 2005.

Based on the information given in the articles, we classified the species according to their longevity (annual/biennial or perennial), mating system (self-incompatible (SI) or self-compatible (SC)), and rarity (rare or common, Table 1), and then tested for differences between these classes of species in the strength and direction of the correlations.

Table 1. Characteristics of the plant species and populations included in the analyses. SC = self-compatible, SI = self-incompatible. For references see Appendix S2 in Supplementary Material

Species	Family	Longevity	Rarity	Mating system	Geometric mean of population size	Size of smallest population	Size of largest population	Reference
Allium stellatum	Liliaceae	Perennial		SC	39.1	3	1125	Molano-Flores et al. (1999)
Anacamptis palustris	Orchidaceae	Perennial	Rare		821.9	100	5000	Cozzolino et al. (2003)
Anacamptis pyramidalis	Orchidaceae	Perennial	Rare	SC	72.6	11	400	Fritz & Nilsson (1994)
Antirrhinum charidemi	Scrophulariaceae		Rare	SI	50.4	23	150	Mateu-Andres & Segarra-Moragues (2000)
Arnica montana	Asteraceae	Perennial	Rare	SI	21.1	2	690	Luijten et al. (2000)
Asclepias meadii	Asclepiadaceae	Perennial	Rare	SI	42.4	5	400	Tecic et al. (1998)
Asclepias verticillata	Asclepiadaceae	Perennial	Rare	SI	47.3	11	80	Fore & Guttman (1996)
Austromyrtus bidwillii	Myrtaceae	Perennial	Common	SI	15.1	8	20	Shapcott & Playford (1996)
Austromyrtus hillii	Myrtaceae	Perennial	Common	SI	16.0	7	41	Shapcott & Playford (1996)
Banksia goodii	Proteaceae	Perennial	Rare	SI	34.3	8	150	Lamont et al. (1993)
Brassica kaber	Brassicaceae	Annual	Common	SI	15.2	3	78	Kunin (1997)
Calypso bulbosa	Orchidaceae	Perennial	Rare	SC	134.7	101	178	Alexandersson & Ågren (1996)
Centaurea scabiosa	Asteraceae	Perennial	Common	SI	141.9	27	650	Ehlers (1999)
Cestrum parqui	Solanaceae	Perennial	Common	SI				Aguilar et al. (2004)
Cochlearia bavarica	Brassicaceae	Perennial	Rare	SI	67.4	10	4850	Fischer et al. (2003)
Cochlearia bavarica	Brassicaceae	Perennial	Rare	SI	87.8	8	3215	Paschke et al. (2002)
Dactylorhiza majalis	Orchidaceae	Perennial	Common	SI	286.0	24	1700	Hansen & Olesen (1999)
Eryngium alpinum	Apiaceae	Perennial	Rare	SC	797.1	35	100000	Gaudeul et al. (2000)
Eucalyptus albens	Eucalyptaceae	Perennial	Rare		199.1	14	10000	Prober & Brown (1994)
Festuca ovina	Poaceae	Perennial	Common	SI	149.3	15	980	Berge et al. (1998)
Gentiana lutea	Gentianaceae	Perennial	Rare	SI				Kéry et al. (2000)
Gentiana pneumonanthe	Gentianaceae	Perennial	Rare	SC	121.7	5	50000	Oostermeijer et al. (1994)
Gentiana pneumonanthe	Gentianaceae	Perennial	Rare	SC	165.6	5	50000	Oostermeijer et al. (1998)
Gentiana pneumonanthe	Gentianaceae	Perennial	Rare	SC	238.0	8	100000	Raijmann et al. (1994)
Gentianella austriaca	Gentianaceae	Biennial	Rare	SC	172.3	15	1000	Greimler & Dobes (2000)
Gentianella germanica	Gentianaceae	Biennial	Rare	SC	428.6	40	5000	Fischer & Matthies (1998)
Grevillea caleyi	Proteaceae	Perennial	Rare	SC	175.7	9	2000	Llorens et al. (2004)
Halocarpus bidwillii	Podocarpaceae	Perennial	Rare	SI	948.6	20	400000	Billington (1991)
Iris atrofusca	Iridaceae	Perennial	Rare	SI	244.9	15	10000	Arafeh et al. (2002)
Leucochrysum albicans	Asteraceae	Perennial	Rare	SI	1554.7	74	50000	Costin et al. (2001)
Lupinus sulphureus ssp. kincaidii	Fabaceae	Perennial	Rare	SC	3245.7	805	7928	Severns (2003)
Lychnis viscaria	Caryophyllaceae	Perennial	Common	SC	52.4	10	680	Berge et al. (1998)
Lychnis viscaria	Caryophyllaceae	Perennial	Rare	SC	143.7	7	1000	Lammi et al. (1999)
Lythrum salicaria	Lythraceae	Perennial	Common	SI	93.0	1	8680	Waites & Ågren (2004)
Lythrum salicaria	Lythraceae	Perennial	Common	SI	42.3	1	19100	Ågren (1996)
Microseris lanceolata	Asteraceae	Perennial	Rare	SI	2267.3	87	140000	Prober, S. M. et al.
Narcissus longispathus	Amaryllidaceae	Perennial	Rare	SC	208.0	40	600	Barrett et al. (2004)
Nepeta cataria	Scrophulariaceae	Perennial	Common	SI				Sih & Baltus (1987)
Orchis palustris	Orchidaceae	Perennial	Rare	SC	153.9	26	2325	Fritz & Nilsson (1994)
Orchis spitzelii	Orchidaceae	Perennial	Rare	SC	36.0	3	1000	Fritz & Nilsson (1994)
Parnassia palustris	Saxifragaceae	Perennial	Rare	SC	1251.3	140	10000	Bonnin et al. (2002)
Pedicularis palustris	Scrophulariaceae	Biennial	Rare	SC	149.2	3	28500	Schmidt & Jensen (2000)
Phaseolus lunatus	Fabaceae	Biennial	Rare	SC	8.1	3	60	Bi et al. (2003)
Primula elatior	Primulaceae	Perennial	Common	SI	81.7	13	2273	Jacquemyn et al. (2004)
Primula elatior	Primulaceae	Perennial	Common	SI	170.2	20	1000	Van Rossum et al. (2002)
Primula veris	Primulaceae	Perennial	Rare	SI				Brys et al. (2003)
Primula veris	Primulaceae	Perennial	Rare	SI				Kéry et al.
Primula veris	Primulaceae	Perennial	Common	SI				Van Rossum et al. (2004)
Primula vulgaris	Primulaceae	Perennial	Rare	SI	45.8	1	700	Brys et al. (2004)
Rutidosis leptorrhynchoides	Asteraceae	Perennial	Rare	SI	284.0	13	5419	Morgan (1998)
Rutidosis leptorrhynchoides	Asteraceae	Perennial	Rare	SI	789.6	5	95240	Young et al. (1999)
Salvia pratensis	Lamiaceae	Perennial	Rare	SI	97.6	23	350	Ouborg & Van Treuren (1995)
Salvia pratensis	Lamiaceae	Perennial	Rare	SI	96.5	5	1500	Van Treuren et al. (1991)
Salvia pratensis	Lamiaceae	Perennial	Rare	SC	174.3	22	1500	Van Treuren et al. (1993)
Sarracenia rubra ssp. alabamensis	Sarraceniaceae	Perennial	Rare	SC	176.0	30	1600	Godt & Hamrick (1998)
Scabiosa columbaria	Dipsacaceae	Perennial	Rare	SI	360.2	9	2000	Pluess & Stöcklin (2004)
Scabiosa columbaria	Dipsacaceae	Perennial	Rare	SI	789.4	14	100000	Van Treuren et al.
Scabiosa columbaria	Dipsacaceae	Perennial	Rare	SI	990.6	35	100000	Van Treuren et al. (1993)
Scorzonera humilis	Asteraceae	Perennial	Rare	SI				Colling & Matthies (2004)
Scutellaria montana	Scrophulariaceae	Perennial	Rare	SC	91.2	10	500	Cruzan (2001)
Sesleria albicans	Poaceae	Perennial	Common	SI	370.1	5	50000	Reisch et al. (2002)
Silene latifolia	Caryophyllaceae	Perennial	Common	SI	11.3	6	19	Richards et al. (2003)
Spiranthes sinensis	Orchidaceae	Perennial	Rare	SC	14.3	3	98	Sun (1996)
Succisa pratensis	Dipsacaceae	Perennial	Common	SC				P. Vergeer et al.
Swainsona recta	Fabaceae	Perennial	Rare	SI	59.9	1	430	Buza et al. (2000)
Swertia perennis	Gentianaceae	Perennial	Rare	SC	2394.3	7	118500	Lienert et al. (2002)
Taxus baccata	Taxaceae	Perennial	Common	SI	191.9	21	2500	Hilfiker et al. (2004)
Tetratheca juncea	Tremandraceae	Perennial	Rare	SI				Gross et al. (2003)
Trillium camschatcense	Trilliaceae	Perennial	Rare	SI	2588.4	46	153600	Tomimatsu & Ohara (2003)
Trollius europaeus	Ranunculaceae	Perennial		SI	536.4	50	1500	Despres et al. (2002)
Vincetoxicum hirundinaria	Asclepiadaceae	Perennial	Common	SC	541.0	32	5200	Leimu & Mutikainen (2005)
Viscaria vulgaris	Caryophyllaceae	Perennial	Common	SC	387.1	227	660	Jennersten & Nilsson (1993)

Because relationships between population size, fitness and genetic variation were reported as r in most studies, we used Pearson product-moment correlation coefficients r as a measure of effect size. For studies not reporting r-values we calculated them from the population mean values of measures of fitness and genetic variation and estimates of population size given in tables or figures. To obtain data from figures, we enlarged graphs and digitized data manually. From studies using regression analysis we obtained r as square root of the coefficient of the determination (r²).

Most studies reported several fitness measures, and overall 19 different fitness measures were reported. For the meta-analysis of the relationship between population size and plant fitness, we used the number of flowers, fruit set, seed set, the number of seeds or the number of fruits (female fitness), and pollinator visitation rates and pollen removal (male fitness), because these were most frequently reported and because at least one of them was used in each of the selected studies.

For the meta-analysis of the relationship between population size and genetic variation, we considered expected heterozygosity (H_EXP), observed heterozygosity (H_OBS), the number or percentage of polymorphic loci (P), the number of alleles (A), and for PCR studies molecular variance.

For the meta-analysis of the relationship between genetic variation and fitness, we considered the number of flowers, fruit set, seed set, the number of seeds or the number of fruits, and, for studies not providing a measure of reproductive output, biomass, as fitness measures, and expected heterozygosity (H_EXP), observed heterozygosity (H_OBS), the number or percentage of polymorphic loci (P), the number of alleles (A), or molecular variance (PCR), as measures of genetic variation. In addition, we tested the relationship between population size and the level of inbreeding (F_IS).

meta-analysis

We performed all meta-analyses with Meta Win 2.0 (Rosenberg et al. 2000). We z-transformed individual correlation coefficients and weighted them by their sample size, i.e. by the number of studied populations. Across studies we combined the transformed coefficients with the mixed effects model, i.e. we assumed that differences among studies are due to both sampling error and random variation, which is the rule for ecological data (Gurevitch & Hedges 2001).

To test whether effect sizes differed statistically significantly from zero, we used bias-corrected 95% bootstrap confidence intervals (Adams et al. 1997) of the mean z-transformed correlation coefficients from 4999 iterations. We considered overall relationships as significant if the confidence interval did not include zero.

To analyse the relationship between population size and fitness, we first calculated mean effect sizes for each species and study over the different measures of fitness (female and male), and then used these data to calculate the overall effect size and confidence intervals. To analyse the relationship between population size and genetic variation, we first calculated mean effect size for each species and study over expected heterozygosity (H_EXP), observed heterozygosity (H_OBS), the number or percentage of polymorphic loci (P), and the number of alleles (A), and then used these data to calculate the overall effect size and confidence interval. If several species were examined in one study we calculated mean effect size for each of the species separately. To analyse the relationship between genetic variation and fitness, we calculated mean effect size by study and by species and used these pooled data to calculate overall mean effect size and confidence intervals.

The number and proportion of alleles and polymorphic loci depend on the number of individuals sampled and different sample sizes, i.e. number of plants in different studies might influence the results. Moreover, a small sample size may bias the estimates of average heterozygosity (Nei 1978). Therefore, we tested whether the number of plants sampled influences the strengths of the associations between population size and genetic variation, and between genetic variation and fitness. The strength of the effects turned out to be independent of the number of plants sampled. Furthermore, the strength of the associations between genetic variation and population size or fitness, did not differ between studies correcting measures of genetic variation for sample size and studies that did not (data not shown).

To examine the effects of potential sources of variation, including differences in methods or plant species characteristics, on the strength of the relationships between population size, genetic variation and plant fitness, we examined between-group heterogeneity with the chi-square test statistic Q_b (Rosenberg et al. 2000). In all analyses, we pooled the data by study and in cases where several species were examined in the same study, also by species. Because some studies examined same species, we also ran the analyses using a data pooled by species. The results did not differ depending on whether the data were pooled by study or by species, indicating that the results are not influenced by double counting of some species, and thus we only present the results obtained using the data pooled by study.

We tested whether the strength of the relationship between population size and fitness differed between female and male fitness, and between field studies and those conducted in a common environment. Moreover, we examined whether the strength and direction of relationships between population size, fitness and genetic variation differed between species of different life span, mating system or rarity. We also studied the associations between the geometric mean of the population sizes and the mean effect size in each study to examine the effects of the size range of the populations. Moreover, to test whether the sizes of the studied populations were confounded with plant characteristics, we tested whether the geometric mean of population size, or the size of the smallest or largest population included in a study, differs between rare and common species, between self-compatible and self-incompatible species, or between annual, biennial or perennial species. Population sizes or size ranges were not statistically significantly affected by any of these plant characteristics (Table 1; results not shown). For the relationships that involved genetic diversity, we examined whether the strength of the relationships between genetic variation and population size or plant fitness differed between isoenzyme and DNA-PCR studies. To compare relationships for the different measures H_EXP, P and A, and for the inbreeding coefficient (F_IS), for which the expected relationship with population size is negative, we also carried out separate analyses for each of these measures.

Using the funnel plot technique (Light & Pillemer 1984; Palmer 1999), we found no evidence for publication bias among the selected studies. Furthermore, effect sizes were independent of sample size, i.e. of the number of populations in a study, for the associations between population size and fitness (r = 0.299, P = 0.064), population size and genetic variation (r = 0.082, P = 0. 578), and genetic variation and fitness (r = 0.306, P = 0.287), which also indicates lack of publication bias (Palmer 2000).

Results

relationship between population size and fitness

Overall, population size and fitness were significantly positively correlated (Fig. 1). The strength and direction of this correlation did not differ between rare and common species (Q_b = 0.7770, d.f. = 1, P = 0.391), or between perennials and annuals/biennials (Q_b = 0.2226, d.f. = 1, P = 0.642), self-incompatible and self-compatible species (Q_b = 0.0019, d.f. = 1, P = 0.964), or between field studies and common environment studies (Q_b = 2.118, d.f. = 1, P = 0.158) (Fig. 2). Furthermore, the strength and direction of the effect were independent of the geometric mean of the population sizes in the different studies (Q_b = 0.426, d.f. = 1, P = 0.514).

Figure 1

Mean correlations (r) between population size, female fitness and genetic variation. In all figures, bars denote 95% confidence intervals obtained by bootstrapping, and sample size N denotes the number of independent studies included in meta-analysis. The relationships are considered significant if the confidence intervals do not include zero.

Figure 2

Mean correlations (r) between (a) female and (b) male fitness and population size according to plant life span, mating system, rarity and type of study.

A significant positive correlation was found between population size and female fitness (Fig. 2a), whereas the correlation was non-significant for male fitness (Fig. 2b). The strength and direction of the correlation between population size and female fitness did not, however, differ from that between population size and male fitness (Q_b = 0.1004, d.f. = 1, P = 0.752). The positive association between population size and male fitness did not differ significantly between rare and common species (Q_b = 0.4072, d.f. = 1, P = 0.561), although the association was significant only for rare species (Fig. 2).

relationship between population size and genetic variation

Overall, the mean correlation between population size and genetic variation was significantly positive (Fig. 3), and independent of the genetic method used (isoenzymes vs. DNA-PCR) (Q_b = 0.3450, d.f. = 1, P = 0.567; Fig. 3). The strength and direction of this correlation did not differ between rare and common species (Q_b = 0.7454, d.f. = 1, P = 0.404; Fig. 3), between perennial and annual/biennial plants (Q_b = 0.0529, d.f. = 1, P = 0.817; Fig. 3), or between self-compatible and self-incompatible species (Q_b = 1.5240, d.f. = 1, P = 0.226; Fig. 3). Moreover, the strength and direction of the correlation were independent of the geometric mean of the sizes of the study populations (Q_b = 0.976, d.f. = 1, P = 0.323).

Figure 3

Mean correlations (r) between genetic variation and population size according to plant life span, mating system, rarity and method used to assess genetic variation.

When the different measures of genetic variation were analysed separately, the correlation between genetic variation and population size was significantly positive for expected heterozygosity (H_EXP), the number or proportion of polymorphic loci (P), and the mean number of alleles (A) (r₊ = 0.317, r₊ = 0.465, r₊ = 0.481, respectively), but not for the inbreeding coefficient F_IS (r₊ = 0.054). For all measures of genetic variation (H_EXP, P, A or F_IS), the correlation between population size and genetic variation was independent of plant longevity, rarity, and the method used to assess genetic variation (data not shown). The correlation between population size and genetic variation was significantly greater in self-incompatible species than in self-compatible species when genetic variation was measured as the mean number of alleles (Q_b = 6.528, d.f. = 1, P = 0.016) or as the number or proportion of polymorphic loci (Q_b = 4.906, d.f. = 1, P = 0.036), but not as expected heterozygosity (Q_b = 1.549, d.f. = 1, P = 0.234), although the mean correlation between population size and heterozygosity was significant only in self-incompatible plants (Fig. 4). While the level of inbreeding (F_IS) increased significantly with population size in self-incompatible species, it tended to decrease in self-compatible species (Fig. 4).

Figure 4

Mean correlations (r) between genetic variation and population size in self-incompatible (black symbols) and self-compatible (grey symbols) species for different measures of genetic variation. Heterozygosity denotes expected heterozygosity.

relationship between genetic variation and fitness

Overall, the mean correlation between genetic variation and fitness was significantly positive (Fig. 5). The magnitude and direction of the correlation was not significantly influenced by plant rarity (Q_b = 0.1585, d.f. = 1, P = 0.713), or longevity (Q_b = 0.3275, d.f. = 1, P = 0.561) (Fig. 5). The association between genetic variation and fitness was, however, significantly influenced by plant mating system (Q_b = 5.9872, d.f. = 1, P = 0.038). Fitness increased with genetic variation in self-incompatible species, but not in self-compatible species (Fig. 5). The association between genetic variation and fitness also differed between isoenzyme and DNA studies (Q_b = 7. 1842, d.f. = 1, P = 0.023). While fitness increased with genetic variation in studies using PCR (AFLP or RAPD), no significant association was found in studies using isoenzyme electrophoresis (Fig. 5).

Figure 5

Mean correlations (r) between genetic variation and fitness according to plant life span, mating system, rarity and method of assessing genetic variation.

Discussion

generality of the overall relationships

Our meta-analyses clearly demonstrated that the relationships between population size, plant fitness and genetic diversity are generally significantly positive (1, 2). The positive relationship between fitness and population size did not differ significantly between field and common garden studies. This suggests that this association arises due to the negative effects of small population size on genetic variation and plant fitness, rather than due to the effects of habitat quality on plant fitness, which would subsequently reduce population size and genetic variation. Thus, our findings support the idea of an extinction vortex of interdependently ever decreasing population size, genetic variation and fitness. However, the statistically non-significant, but large, difference between field and common garden studies in the strength of the mean correlation between population size and fitness, suggests that reduced fitness in small populations results not only from reduced genetic variation or increased inbreeding, but potentially also from environmental factors, demographic stochasticity and biotic interactions. Undoubtedly, more studies conducted in common environments are needed to resolve this question.

Associations between population size, genetic variation and fitness may be mediated by differences in the demographic structure of plant populations, e.g. if small plant populations only consist of old plants that no longer contribute to offspring recruitment (Oostermeijer et al. 1994). Because data on the demographic structure of population was rarely provided, we were not able to consider the role of demographic population structure in our meta-analysis. However, even if the observed relationships between population size, genetic variation and fitness would have been mediated by the demographic structure of the populations, this would not reduce their high biological importance.

Population size has been suggested to be the most important variable explaining differences in allozyme variation between populations (Frankham 1996). Although population size and genetic variation were positively associated and no significant differences were found in the strength of the association irrespective of whether DNA-markers or isoenzymes were used to assess genetic variation, a significantly positive correlation between the level of genetic variation and fitness was found only for DNA studies. The latter suggests that DNA methods should be favoured in this context, most likely due to the higher resolution of DNA methods compared with isoenzyme analysis.

According to theory, loss of rare alleles is a primary consequence of small population size, whereas heterozygosity is reduced significantly only after the population has been small for several generations (Barrett & Kohn 1991). Although expected heterozygosity and the number of alleles and polymorphic loci all decreased with population size in our meta-analyses, this decrease tended to be greater for the number of alleles and polymorphic loci than for expected heterozygosity. This suggests that in general genetic drift, rather than direct or biparental inbreeding, causes the observed reduction in genetic variation in small populations (e.g. Oostermeijer et al. 2003). This is further supported by the finding that the inbreeding coefficient F_IS, which measures within-population inbreeding, was not related to population size. At the same time, the independence of F_IS from population size suggests that in general there are no differences in population substructure between small and large populations.

In accordance with our results, a recent meta-analysis by Reed & Frankham (2003) on 10 animal and 12 plant species reported a positive mean association between genetic diversity and fitness. Reduced genetic variation in small populations may lead to reduced fitness for several reasons. First, increased homozygosity may lead to increased expression of inbreeding load. Secondly, higher fixed mutation load may further decrease plant fitness in small populations. Because only a few studies have examined the association between heterozygosity and fitness or experimentally separated the two possibilities (Willi et al. 2005), we cannot distinguish between these two possibilities in our meta-analyses. Furthermore, because the number of marker loci is far smaller than the total number of loci in a genome, finding a relationship between fitness and marker heterozygosity is highly unlikely (Mitton & Pierce 1980).

effects of species characteristics

Contrary to our prediction, our meta-analysis indicates that short-lived species are in general as prone to the negative effects of small population size as long-lived species. Possibly, differences between short-lived and perennial plants will turn out to be more pronounced than reported here once more data become available on shrubs or trees that were hardly represented in the reviewed literature.

The positive relationships between plant population size, genetic variation and fitness tended to be stronger for rare than for common species (2, 3, 5), but these differences were not significant. Possibly, differences between rare and common species will only become apparent when more studies are available, which would also increase the statistical power for meta-analysis. Nevertheless, male fitness, measured as pollinator visitation and pollen removal, was significantly reduced in smaller populations of rare, but not of common, species. This suggests that reduced pollinator activity generally contributes to reduced fitness of plants in small populations of rare species. However, in general the variation in the positive associations between population size, genetic variation and fitness among the study species was low. Therefore, a more fine-grained classification of species according to the different categories of rarity is not very likely to reveal further differences in these associations between rare and common species. Because populations of rare plants are not necessarily smaller (Rabinowitz et al. 1986) or have lower levels of genetic variation within or between populations (Gitzendanner & Soltis 2000) than common plants, these populations do not necessarily have to be expected to be more prone to the negative effects of small population size. Accordingly, the sizes or size ranges of populations of the studies included in our analyses did not differ between rare and common species (Table 1).

The negative effects of habitat fragmentation may be especially pronounced for formerly more common and recently declining species and populations, than for naturally rare species and populations (Huenneke 1991). Unfortunately, such historical information is hardly available for species and populations in the published studies and could therefore not be considered in our analyses. If published studies focused on formerly common species, which have declined because of anthropogenic habitat fragmentation, our meta-analyses might possibly have overestimated the mean strength of relationships between population size, genetic variation and fitness. However, this would make our data even more relevant from a conservation point of view, where species declining due to anthropogenic fragmentation are of greatest interest and priority.

We found that male fitness tends to decrease more strongly in small populations of self-incompatible species than in self-compatible species, which suggests higher pollinator limitation in small populations of self-incompatible species. Unfortunately, the interesting comparison between insect-pollinated and wind-pollinated species was not possible because the examined plant species included in our data were primarily insect-pollinated and data from wind-pollinated species were lacking almost completely.

The strength of the association between population size and heterozygosity did not differ between self-compatible and self-incompatible species, but the numbers of alleles and polymorphic loci decreased more strongly in small populations of self-incompatible species. Inbreeding within populations, estimated as the inbreeding coefficient F_IS, increased, however, with population size in self-incompatible species, but not in self-compatible species. These findings may possibly be explained by lower ratios of effective genetic population sizes to census population sizes in self-incompatible species than in self-compatible species. Such differences in the ratios between effective and census population size could be caused by larger annual fluctuations in the sizes of self-incompatible species due to unreliable pollination in some years, or by higher genetic substructuring of large populations of self-incompatible species (Frankham 1995). However, published information is not sufficient to test these hypotheses.

A positive association between fitness and the mean level of genetic variation was found in self-incompatible but not in self-compatible species. This may reflect decreased availability of suitable mating partners in small populations of self-incompatible plants due to reduced genetic variation at the self-incompatibility loci (Fischer et al. 2003; Willi et al. 2005). Moreover, because in self-compatible species inbreeding could be high in all populations irrespective of their size, the level of direct and biparental inbreeding may not increase as much in small populations of self-compatible species compared with self-incompatible species. Consequently, if fitness is associated with genetic variation, this association should be stronger for self-incompatible than for self-compatible species. Self-compatible species may also be less susceptible to the negative effects of small population size if a long history of inbreeding has enabled purging of the genetic load (Busch 2005). Our results suggest that in general the negative effects of small population size are indeed less detrimental in self-compatible species. Furthermore, our results are in contrast to the idea that the breakdown of self-incompatibility in small populations would erase the differences in the strength of the associations of population size, genetic variation and plant fitness between self-compatible and self-incompatible species.

Conclusions

The close relationships between population size, genetic variation and fitness imply that population size should be taken into account in any multipopulation study of plant fitness or genetic variation.

The observed generality of positive relationships between population size, plant fitness and genetic diversity clearly implies that the negative effects of habitat fragmentation on plant fitness and genetic variation are common. Moreover, the stronger positive associations observed in self-incompatible species and, to some degree, also in rare species suggest that these species are most prone to the negative effects of habitat fragmentation.

The small and sometimes unequal sample sizes in some of our analyses suggest that the according results and conclusions, especially on the relationship between plant fitness and genetic variation within populations, should be considered preliminary. At the same time this indicates a need for future research. Our study revealed a number of further gaps in our knowledge of relationships between population size, genetic variation and fitness. In addition to observational studies, experiments should address the relative importance of the potential causal genetic and ecological mechanisms underlying the relationships between population size, genetic variation and fitness. Therefore, field studies should increasingly be complemented by common environments. Moreover, studies that also consider population history will be highly valuable. Furthermore, quantitative genetic variation in addition to neutral molecular markers should be measured.

Acknowledgements

We thank H. Prentice, L. Haddon and three anonymous reviewers for constructive comments. This study was supported financially by the Academy of Finland.