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Journal of Experimental Botany, Vol. 50, No. 340, pp. 1635–1645, November 1999 Assessing the ecological significance of molecular diversity data in natural plant populations N. McRoberts1,4, R.P. Finch1,5, W. Sinclair1, A. Meikle1, G. Marshall1, G. Squire2 and J. McNicol3 1 Plant Biology Department, SAC Auchincruive, Ayr KA6 5HW, UK 2 Scottish Crop Research Institute (SCRI), Invergowrie, Dundee DD2 5DA, UK 3 Biomathematics and Statistics Scotland (BioSS), SCRI, Invergowrie, Dundee DD2 5DA, UK Received 25 January 1999; Accepted 6 August 1999 Abstract Despite extensive research for several decades, there remains a lack of understanding of the processes that determine the dynamics of natural plant communities. In this paper some current concepts in vegetation dynamics are reviewed and an attempt is made to provide a perspective of the way in which data for molecular diversity might be used to help in developing an understanding of population processes. It is proposed that data from assessments of general population diversity, and specific ecophysiological traits can be used to assess the potential for individual species to compete and substitute for each other in a community. Key words: Natural plant communities, dynamics, molecular diversity, population diversity, ecophysiological traits. Introduction Understanding the relationships between species richness, species diversity and community stability remains a key area of interest in vegetation ecology. At the theoretical level a great deal of attention has been given to how the processes of competition and reproduction determine interactions amongst plant species in communities. Maintaining stability in natural or managed vegetation is important for practical reasons relating to habitat and species preservation and rural sustainability. There is thus a motivation to bring theoretical results into practical use and, as a result, a considerable amount of research has been conducted in both the theoretical and applied aspects of vegetation ecology. Recent developments in molecular methods for assessing diversity, particularly the analysis of randomly amplified polymorphic DNA fragments, have made it possible to obtain estimates of intra- and inter-specific diversity from nuclear genomes of natural plant populations with relative ease. However, methods for applying the results of such analyses to improve our understanding of the ecology of natural vegetation are still relatively poorly developed. This is due, in part, to the difficulties which arise in relating molecular marker data to important ecophysiological traits in natural plant populations. The relationship between the traits displayed by individual species and their role in the ecological community is a further poorly researched subject. Recent publications (Aerts, 1999; Grime et al., 1997; Wardle et al., 1998) have shown that insights into plant community structure can be obtained from careful study of the ecophysiology of individual species. However, it appears that a general, theoretical framework for this aspect of vegetation ecology is only just being constructed. In this paper the authors draw on their own findings from a study of species-rich grassland in Scotland, as well as the work of others, to illustrate connections between community structure, ecophysiology and molecular diversity in plant communities. Some issues of methodology in the use of RAPD markers for the assessment of molecular diversity and trait variation in natural plant populations are also addressed. Ecological background Stability, complexity and diversity Relationships between stability and diversity are a central theme in standard, modern ecology texts (Begon et al., 4 To whom correspondence should be addressed. Fax: +44 1292 525314. E-mail: [email protected] 5 Present address: Royal College of Obstetricians and Gynaecologists, 27 Sussex Place, Regent’s Park, London NW1 4RG, UK. © Oxford University Press 1999 1636 McRoberts et al. 1996) and are an important issue in current ecological theory (Southwood, 1996). It is now commonly accepted that the stability of complex biological systems (such as species-rich vegetation) does not derive per se from these systems containing a large number of interacting species. Computational and analytical results generated over 25 years ago (Gardner and Ashby, 1970; May, 1974) illustrate that, if interactions between species in model ecosystems occur in a purely random way, the stability of the system declines with increasing species numbers for a given level of interaction (or connectance). Similarly, in systems containing a fixed number of species, stability declines as the level of interaction (connectance) in the system increases. Two additional implications of these theoretical analyses have been noted (May, 1974): (1) if a system contains a large number of interacting species, the individual interactions will tend to be rather weak, and; (2) a system containing a large number of species is more likely to be stable if it is ‘organized’ into a set of subsystems between which there is no interaction. Both of these points are relevant to the discussion which will follow. Prior to these analyses it had been proposed (for example, Elton, 1958; Pimentel, 1961) that the presence of many species within a habitat conferred stability directly through the buffering effects of the individual species on each other against the effects of sources of instability. This proposal is supported by observational evidence and appears, superficially, to contradict the theoretical results described above. However, as already noted (May, 1974), natural systems are not randomly constructed. It is very likely that the stability of complex natural systems results from the particular subset of the possible interactions between species that actually occurs, and the structure of the environment in which the interactions take place. Similar points have been made by several other authors (Southwood and Way, 1970; Shmida and Ellner, 1984; Tilman, 1994; Southwood, 1996). There is also empirical evidence for a positive correlation between diversity and stability in plant communities (Frank and McNaughton, 1991; Tilman and Downing, 1994). Contrary to the results mentioned above, in a community of plants such as that studied at Cedar Creek by Tilman, one might expect that interspecific competition for resources would be greatest where numbers of species were highest, and hence that diversity would decline over time as stronger competitors excluded weaker ones. This is the basic premise of the familiar competitive exclusion principle (May, 1974). If competition is to be accepted as an important driving force in community ecology, one might ask whether competitive exclusion (as conceived in theory) occurs in the sort of grassland community which has been observed by Tilman and others. A summary of results from the Minnesota grassland experiments ( Tilman, 1994) illus- trates the ability of Schizachyrium scoparium ( little bluestem) rapidly and competitively to exclude other species under experimental conditions, where competition is predominantly for nitrogen only. However, in natural conditions, where competition is also mainly for nitrogen, little bluestem may co-exist with over 100 other species for many years, before eventually becoming dominant. Taking these observations together with the theoretical results on connectance, it might be surmised that very strong competitive effects are avoided or suppressed in the communities studied. The spatial patterns of competing species and interspecific trade-offs in relation to ecological traits have been highlighted as mechanisms by which strong competition might be avoided in multi-species communities (Crawley and May, 1987; Shmida and Ellner, 1984; Tilman, 1994). If different species have different and partially uncorrelated spatial patterns, the less competitive may be able to persist by occupying patches that are not occupied by the more competitive species. In order to maintain the dynamic equilibrium which is suggested by this model, it is necessary that there are interspecific trade-offs with respect to traits determining competitive and reproductive behaviour. A poor competitor will persist provided that it allocates resources to producing large numbers of propagules and that these disperse readily, allowing rapid colonization of empty patches. Large-scale screening of plant species in the British flora has revealed that such trade-offs between competitive and reproductive traits do indeed exist (Grime et al., 1997). While much of the theoretical work on community structure has been concerned with analytical models of interactions amongst species, competition in the real world occurs between individuals, or groups of individuals of each species. In attempting to model interactions at the level of the individual a simulation approach is often more appropriate than an analytical approach. While simulation models lack the generality that is provided by analytical models, they do tend to focus on the mechanisms by which competition operates between individuals (Benjamin, 1996) and thus to consider the traits involved in the interspecific trade-offs discussed by other authors ( Tilman, 1994; Marshall and Squire, 1996; Grime et al., 1997; Aerts, 1999). Competition between ecophysiological traits The general theory of community structure which has developed in the last 25 years proposes that the number of competing species which can co-exist in a habitat is a function of the range of the available resources, the differences between the preferred or optimum part of the available resource that each species uses, and the stability of the environment. The theory contends that an environment which is relatively stable over time (such as that The ecological significance of molecular diversity data 1637 found in a tropical rainforest) allows a large number of species to adapt to specialized niches (i.e. gain certain sets of required traits), avoid direct competition, and thus co-exist. The alternative, and less popular, energydiversity hypothesis proposes that species numbers are determined not by the stability of the environment, but by available energy. In simple terms, this theory suggest that a large amount of available energy allows a large number of species, which in turn forces each species into having a narrow niche. Thus, ‘. . . tropical species have extremely narrow niches because so many of them are crammed into the forest!’ ( Turner, 1992). Drawing on the ‘stability-diversity’ and ‘energydiversity’ theories outlined above, one could consider that the traits which a species expresses determine its function in the community, or that the available roles in the community determine the traits that a species is allowed to express. In either case, by examining ecophysiological traits in species that differ in behaviour it might be possible to understand how competition operates in complex communities. In turn, this might allow an understanding of how the communities themselves are constructed and the factors which are important in their long-term stability ( Tilman, 1994; Wardle et al., 1998; Aerts, 1999). The relationship between plant communities and their environments has been shown to be more subtle than is implied by the simple interpretations of the stabilitydiversity and energy-diversity theories given above ( Tilman, 1994; Aerts, 1999). In particular it has been shown that feedback between plants and their environment through soil processes can have a significant role in changing the environment to suit species expressing particular sets of traits (Aerts, 1999). When considering competition among species in terms of traits it is useful to consider the interactions as taking place in a trait-space in which each species occupies a certain region determined by the values of each trait that its members express. A simple bivariate example of a trait-space is presented in Fig. 1 (based on data presented by Wardle et al., 1998). Examination of Fig. 1a makes apparent the fact that some areas of the trait-space defined by specific leaf area and leaf nitrogen content are, for the 20 species examined, more densely occupied than others. If a large number of traits is examined, data reduction methods can be used to project the multidimensional trait-space onto a small number of composite axes (dimensions). The technical details of these multivariate methods have been described ( Krzanowski, 1990) and a clear account of their application to ecological data has been given (Digby and Kempton, 1987). Figure 1b shows the results of applying principal coordinates analysis (PCO) to data for 12 traits from Tables 1, 4 and 6 in Wardle et al. ( Wardle et al., 1998) and gives an impression of the way in which the 20 species occupy the Fig. 1. (a) The distribution of 20 herbaceous plant species in a bivariate trait-space: Leaf nitrogen content is plotted against specific leaf area from the data of Wardle et al. ( Wardle et al., 1998). The error bars are the standard errors reported by the original authors. (b) An ordination of 20 herbaceous plant species in two principal co-ordinates derived from data taken from Wardle et al. ( Wardle et al., 1998). Numbers next to the data points identify individual species: 1, Achillea millefolium; 2, Anthemis cotula; 3, Brassica rapa; 4, Carduus tenuifolius; 5, Cerastium glomeratum; 6, Chrysanthemum leucanthemum; 7, Cirsium arvense; 8, Crepis capillaris; 9, Daucus carota; 10, Hypochaeris radicata; 11, Leontodon taraxicoides; 12, Plantago lanceolata; 13, Ranunculus sardous; 14, Rumex obtusifolius; 15, Rumex pulcher; 16, Silene gallica; 17, Sisymbrium officinale; 18, Spergula arvensis; 19, Stellaria medea; 20, Taraxacum officinale. Some of the numbers have been omitted from (a) for clarity. 1638 McRoberts et al. trait-space defined by those 12 traits. As in the simpler two-trait example in Fig. 1a, certain regions of the traitspace in Fig. 1b are more densely occupied than others, suggesting that certain combinations of traits are more common among the species examined by Wardle et al. than others ( Wardle et al., 1998). Considering the long-term stability of communities and their ability to recover from periods of extreme environmental conditions, species which share similar traits should be able to substitute for one another in the community as a whole. Thus, the degree of potential competition between two species might also be viewed as their potential for mutual substitution. The most direct and long-term competition is likely to occur between species which behave in similar ways (i.e. display similar sets of traits and are closest in trait-space). Although experiments of the type conducted by Wardle et al. ( Wardle et al., 1998) provide useful insights into the mechanisms through which competition occurs, and the interspecific trade-offs which exist, some caution is required in extrapolating from the experimental situation to the natural multi-species community. It remains unclear exactly the extent to which the expression of ecophysiological traits might differ under natural and experimental conditions. Molecular versus phenotypic variation So far, diversity has been considered from a predominantly phenotypic point of view. The problems which can be encountered in trying to relate phenotypic variation to underlying genotypic variation in natural plant populations have already been discussed (Bachmann, 1994). Certainly one should expect to find considerable phenotypic variation in some species, even for populations with an apparently narrow genetic base. Moreover, there is good evidence that mean values of ecologically significant traits change over time in competing plant species (Gray, 1987) and, given this, one might expect to find that the level of underlying genetic variation will also change over time. In the context of habitat management and maintenance, the phenotypic plasticity of plants introduces the question of how much underlying genetic diversity it is necessary to conserve in order to safeguard the survival of individual species or communities. Given the potential practical and fundamental value of reliable genetic diversity data, it is not surprising that methods for the analysis of molecular diversity have been used increasingly to study natural plant populations (Bachmann, 1994). In the following section the authors draw on their own analyses of molecular variation in natural plant populations to illustrate how correlations between diversity and competition can be made with reference to the ecological theory outlined above. Molecular analysis of diversity Reproducibility and reliability of RAPDs A number of methods are available for analysing molecular diversity in plant populations. Recent reviews (Bachmann, 1994; Karp et al., 1996) have discussed the relative merits of these methods. This study will be concerned with issues arising from the use of RAPD (randomly amplified polymorphic DNA) markers ( Welsh and McClelland, 1990; Williams et al. 1990). One frequently cited limitation of RAPDs, in a variety of applications in molecular genetics, is a lack of reproducibility in the fingerprints which they produce (see, for example, He et al., 1994; Brown and Kresovich, 1996; Karp et al., 1996). Experience with Agrostis capillaris, Festuca rubra, and Rumex acetosa has shown that it is possible to generate reproducible RAPD fingerprints (Fig. 2), but only by placing great importance on careful repetition of robust, experimental protocols. Even with reproducible fingerprints, however, it must be remembered that the presence of co-migrating non-homologous markers is a possibility ( Williams et al., 1993). Developments of the basic RAPD approach such as SCARs (sequence-characterized amplified regions) increase the reproducibility of PCR-based marker systems and avoid the occurrence of nonhomologous markers of equal molecular weight (Paran and Michelmore, 1993). However, increases in the complexity of the basic RAPD method reduce its ease of use and its practicality in handling large numbers of samples. Despite the potential problems mentioned above, the use of RAPDs in assessing diversity and population structure in natural plant populations is now commonplace (Gabrielsen et al., 1997; Le Corre et al., 1997; Martin et al., 1997). In some cases where direct comparisons have been made between RAPDs and other types of Fig. 2. Examples of RAPD markers from Festuca rubra plants. Lanes 1 and 14 are molecular weight markers. Lanes 2–5, 6–9 and 10–13 are, respectively, four-replicate samples of three different F. rubra plants; i.e. the template DNA in each lane was derived from one of four different vegetative shoots for each plant. The markers were generated by primer AB2–13 (5∞-CCCGATTCGG-3∞) using 5 ng DNA and 5 pmol of primer. Amplification conditions were: 5 min at 94 °C, then 45 cycles of (i) 94 °C for 1 min, (ii) 41 °C for 1 min, and (iii) 72 °C for 2 min. Samples were then held at 72 °C for 5 min, then cooled to, and held at, 4 °C prior to electrophoresis. The ecological significance of molecular diversity data 1639 marker, comparable estimates of genetic diversity have been obtained (Finch et al., 1997; Le Corre et al., 1997; Sydes and Peakall, 1998; Buso et al., 1998). General analyses of intraspecific diversity Ignoring for the moment the more difficult question of how to use molecular diversity data as indicators of potential phenotypic diversity, the relatively simple question of how to gather the molecular data can be addressed. The examples used are drawn mainly from a five-year study of the dynamics of mixed species plant communities on unimproved upland grazing at two sites in Scotland; Kirkton near Crianlarich in Perthshire, and Cleish, in Fife. At each site samples were collected from a plot 50×40 m by sampling 11 randomly selected loci along 5 transects 10 m apart. The nearest plant of each species to each sampling point was selected for analysis. In common with analyses of genetic variation in other natural plant populations (Bachmann, 1994, Martin et al., 1997), these analyses have revealed high levels of diversity in RAPD markers in the three species which were examined. Figure 3 illustrates typical results from PCO of similarity matrices generated from small data sets for A. capillaris, F. rubra and R. acetosa. In all three cases, similarities among the individuals, estimated using Jaccard’s coefficient, are relatively low (typically between 20% and 80%). When average similarities within and between sites are considered ( Table 1) it can be seen that although mean between-site similarities are lower than within-site similarities, the differences are small, suggesting that there is as much variation within sites as between sites. Note that in the plots presented in Fig. 3 the PCO axes have been chosen to illustrate the presence of inter-site variability in the data. The high level of variability detected among individuals of the three species that were examined generally results in the dominant axes of the PCO capturing a low proportion of the variation in the similarity matrix. Comparable studies on apomictic species (Palacios and GonzàlezCandelas, 1998) and inbreeding species (Buso et al., 1998) have shown that interpopulation (i.e. intersite) differences can readily be identified by this method when they are sufficiently large, in comparison with within-population differences. Returning to the data sets illustrated in Fig. 3, the first five principal coordinates in total in each case accounted for: 61% (A. capillaris), 53% (F. rubra) and 49% (R. acetosa) of the variation. Multivariate analysis of variance (MANOVA) conducted on the PCO scores for the plants along the sets of five axes suggested that a significant difference existed between sites only in the case of F. rubra ( Table 1). These results were corroborated by examining the sources of variance within the original similarity matrices. The between-sites to within-sites variance ratios ( Table 2) were small in all three cases, but Fig. 3. Ordinations of approximately 20 individuals from two sites of (a) Agrostis capillaris, (b) Festuca rubra and (c) Rumex acetosa following principal coordinates analysis of similarity matrices constructed from RAPD marker data using Jaccard’s coefficient. (&) Plants from Kirkton, Perthshire; (#) plants from Cleish, Fife. Table 1. Mean intra- and inter-site similarities for three plant species sampled at two different sites Samples are of approximately 20 individuals in each case and similarities were calculated using Jaccard’s coefficient on 50–100 RAPD markers. Kirkton Cleish A. capillaris F. rubra 45.5 43.5 Kirkton 40.8 36.9 Kirkton 47.9 Cleish R. acetosa 37.1 Cleish 42.9 42.4 Kirkton 44.8 Cleish 1640 McRoberts et al. Table 2. Within and between site variances based on similarity matrices generated from RAPD profiles and the results from MANOVA of the first five principal coordinates of each similarity matrix Per cent variance within sitesa Per cent variance between sitesa Per cent variancea accounted for in first five PCO axes F statisticb A. capillaris F. rubra R. acetosa 49 51 61 2.92 (5, 13 d.f.) 46 54 53 6.99 (5,12 d.f.) 56 44 49 1.66 (5,12 d.f.) aVariances of inter-individual similarity matrix. bApproximate F statistic from MANOVA of differences between sites for first five PCO axes. slightly larger in the case of F. rubra than with the other species. Prior to analysis of the marker data it had been expected that greater levels of variation might be observed in R. acetosa (an obligate outbreeder) than in A. capillaris and F. rubra. In the A. capillaris and F. rubra, it was expected that genetic diversity might be relatively low as a result of either inbreeding, in the case of F. rubra, or suppression of sexual reproduction in both species by grazing. However, in all three species, no evidence of clonal development was observed in the samples of plants collected in the first year of the study. It is possible that the relatively large inter-sample distance used in the first year of sampling reduced the probability of detecting clones in any of the species. Indeed, data collected for R. obtusifolius suggested that clonal development over periods of up to 5 years would be unlikely to extend beyond 1 m from the initial seedling (Pino et al., 1995). In subsequent years of this study a range of sampling distances have been employed in order to determine whether clonal development is present in any of the species. Sampling among and within genomes Although levels of molecular variation within sites are as high as between sites, between-site differences can still be detected as a source of variation in the RAPD data. It is possible to determine which markers, and therefore which primers, are most closely associated with inter-site variation. Reanalysis of data for those primers alone can increase discrimination between sites (results not shown). Such judicious use of particular RAPD primers for the analysis of diversity and population structure in buffalograss was reported (Huff et al., 1995). Note that the process of selecting primers that are particularly associated with inter-site differences makes explicit the fact that some regions of the genome appear to differ among sites while others do not. Parallel observations can be made at a lower spatial scale. For example, it is possible to identify primers which generate similarity matrices that show significant correlations with matrices of physical distance between individuals within a site. Table 3 gives a set of results for 13 primers which were tested on F. rubra plants from Kirkton. Of the primers Table 3. Mantel test statistics and associated probabilities for the significance of correlations between genetic distance matrices and the physical distance matrix for a set of Festuca rubra plants sampled at Kirkton, Perthshire Correlations significant at P≤0.05 are shown in bold. Primer Mantel statistic (m) Probability (M≥m) AB207 AB208 AB209 AB210 AB211 AB212 AB213 AB214 AB215 AB216 AB217 AB218 AB219 0.3533 −0.2831 −0.1951 0.2164 0.7035 −0.4195 0.6853 −0.1273 0.6281 −0.2970 0.6364 −0.2744 −0.4390 0.4000 0.7853 0.6750 0.2750 0.0333 0.8583 0.0417 0.7000 0.0333 0.6833 0.0500 0.7853 0.9000 examined, four (AB211, AB213, AB125, and AB217) produced matrices of genetic distance (distance=1–similarity) which showed significant positive correlations with the matrix of physical distances among the plants. It follows from the observations above that, by chance, it is possible to select different sets of primers which give very different estimates of molecular diversity both within and between sites. Similarly, for a given set of primers, the variation which is detected will depend on the particular sample of plants that is used for analysis. In part, both of these potential problems can be overcome by maximizing the number of individuals sampled and the number of primers used. However, it should be noted that in making inferences about diversity in natural plant populations at least two sources of sampling variation occur. The genotypes which are assessed are a sample of the available population and the molecular markers examined are a sample of all potential markers in the genome. These sources of variation may individually, or in conjunction, introduce as much uncertainty into the use of RAPDs for the analysis of molecular diversity as the reported lack of reproducibility in marker profiles; however, they are issues which are not often discussed in detail in published analyses. In cases where a primary objective is to examine The ecological significance of molecular diversity data 1641 differences in diversity, genotype incidence or evolutionary history among a set of distinct populations (Dawson et al., 1993; Huff et al., 1995; Peakall et al., 1995; Gillies et al., 1997; Buso et al., 1998), or to examine the variation of RAPD markers with physical separation (Graham et al., 1997), at least one level of stratification (that of populations) is imposed on the sampling of individuals. Within each population the aim should be to collect a representative selection of genotypes. Irrespective of whether the sampling within populations is conducted according to a predetermined sampling protocol, or is random, or arbitrary, the assumption most commonly made, for the purposes of statistical inference, is that the resulting sample is random. These issues were discussed in relation to sampling from small populations of Limomium dufourii species on the Iberian Peninsula., and also provided a method for assessing the reproducibility of RAPD markers (Palacios and Gonzàlez-Candelas, 1998). In selecting the primers that will be used to generate the molecular marker data, care is required if estimates of diversity within populations are not to be biased. Some preliminary screening of primers may be needed to identify those which give reproducible marker profiles. However, this step introduces the possibility of unintentional selection either of primers which produce a relatively high, or a relatively low, proportion of polymorphic bands. In a recent study of diversity in wild rice, Buso et al. (Buso et al., 1998) explicitly addressed ways in which pre-selecting biased primers can be avoided (as did Palacios and Gonzàlez-Candelas, 1998), but the issue is not commonly dealt with in such a manner in similar studies. The difficulty in extrapolating from estimates of diversity based on DNA marker data to estimates of diversity in adaptive characters was highlighted (Bachmann, 1994). As he pointed out, in order to use RAPD data to make inferences about diversity in functional genes, it is necessary to assume that levels of variation revealed by RAPDs are representative of the genome as a whole. The fact that RAPD markers may be distributed preferentially in certain regions of the genome (Noli et al., 1997), and may therefor provide estimates of diversity which vary in their accuracy across the genome, should make one cautious in drawing inferences about levels of diversity in functional genes on the basis of RAPD data. The issues of obtaining representative samples from the plant population and unbiased estimates of marker variation from those samples are also of key importance in any effort to relate markers to particular traits. Associating markers with ecophysiological traits In cultivated species, associations between RAPD markers and traits can be established by QTL (Quantitative Trait Locus) analysis. Essentially, the co-segregation of markers, or groups of markers and quantitative traits in controlled crosses is studied through the use of variance analysis or regression techniques (Lebowitz et al., 1987; Lander and Botstein, 1989; Paterson, 1996). In trying to study natural plant populations in situ, there are considerable difficulties in following a standard QTL approach. First, it is difficult to establish parent–offspring relationships among groups of plants sampled in such populations. Secondly, many traits are difficult to assess in a non-destructive way. One partial solution to these problems is to assess plants which have been removed from their natural habitats and grown under controlled conditions. This approach, of course, suffers from the weakness that one cannot be certain of functional significance of the traits in the wild, when studying their variation in controlled experimental conditions. This problem notwithstanding, it has been possible to demonstrate correlations (not formal linkages) between RAPD markers and relative root growth rate in F. rubra and R. acetosa plants. In fact, given a sample of plants for which both RAPD marker data and quantitative trait data are available, it is straightforward to obtain initial tests for associations between the presence of each marker and expression of the trait. The first step in identifying associations between markers and traits is to select an appropriate method for screening the large number of RAPD markers which will be examined. The approach outlined below was found to be useful, because it employs a graphical method and allows explicit examination of the distribution of the trait value in the sample of plants under study; several other methods based around commonly available statistical tests (e.g. t-tests, or Mann-Whitney tests) would produce similar results. To give a description of the method, consider a single polymorphic RAPD marker, the incidence of which has been determined in a sample of plants for which quantitative trait data are also available. The incidence of the RAPD marker can be used to divide the sample of plants into two groups, those which have the marker present and those which do not. For each of these groups it is possible to plot a frequency distribution of the number of individuals against values of the trait. If the presence of the marker is correlated with expression of the trait, then the frequency distributions of the two groups of individuals will tend to overlap to a smaller degree than they would if there was no correlation between marker and trait. A hypothetical example is shown in Fig. 4. Taking any value of the trait from the region in which the two groups of individuals overlap (indicated by the vertical line in Fig. 4), two further groups can be defined. Those that have the marker and that have values of the trait greater than the chosen threshold value, are referred to as the true positive proportion ( TPP). Those that do 1642 McRoberts et al. Fig. 4. A hypothetical example of trait frequency distributions for individuals which either have (above the x-axis) or do not have (below the x-axis) a particular RAPD marker. In both cases the trait is assumed to be Normally distributed in the sample. Presence of the marker is partly, and positively, correlated with higher values of the trait. not have the marker and which have values of the trait less than or equal to the threshold are referred to as the true negative proportion ( TNP). In medical diagnostic scales testing, from where the technique and terminology outlined here are borrowed, the TPP is known as the specificity (of the diagnostic) and the value (1–TNP) is known as the sensitivity. If the threshold value of the trait is varied across many points in its measured range, and at each point the specificity and sensitivity is recorded, by plotting sensitivity against (1–specificity) a graphical display of the degree of association of the marker with the trait is generated (for example, Fig. 5c). This type of plot is known as the Receiver Operating Characteristic (ROC ) curve (Metz, 1978; Zweig and Campbell, 1993). A detailed account of the method in relation the assessment of ecological indicators has been given (Murtaugh, 1996). If marker incidence is particularly well correlated with expression of the trait, the marker will discriminate well between two groups of individuals in the population and the ROC curve associated with it will tend to be bowed toward the top left-hand corner of the plot. A marker which has no particular association with the trait will tend to generate a ROC curve which follows the straight diagonal from the bottom left to top right hand corner of the plot (as in Fig. 5f ). As an example, consider a preliminary study of RAPD markers associated with root growth in R. acetosa. Root length (mm) was assessed in pot-grown R. acetosa plants over a period of 9 weeks from March to May 1997. Relative root growth was calculated as the difference in root length between the start date and end date divided by root length at the start date. Figure 6 shows ROCs from six RAPD markers which were generated in the analysis of diversity in R. acetosa described above. The first five ROC curves ( Fig. 5a–e) are for markers which were identified as positively correlated with expression of the trait. The sixth ROC curve, included for comparison, is from a marker not associated with the trait. Of 114 markers screened, 11 generated ROC curves that suggested they were correlated with the trait. The association between this set of 11 markers and the trait was examined further by multiple regression analysis. Two multiple regression models were identified that included the five markers identified in Fig. 5a–e. The more complex model, which accounted for 81% of the variation in relative root growth, included markers m106, m60, m46, and m14. The simpler model which included only m2 and m14 accounted for 64% of the variation in relative root growth. The sources of the markers and their approximate molecular weights are given in Table 4. Note that two of the markers were generated by the same primer (AB4–08). Before proceeding with the isolation and sequencing of the markers identified in R. acetosa, their association with root growth will be tested on a larger sample of plants in order to eliminate the possibility that the results reported here are a sampling effect. Discussion It has been shown that, in a particular class of competition model, that specifically accounts for allele frequencies in both intra- and interspecific competition, the effect of increasing competition between genotypes is to reduce fluctuations in gene frequencies (Clarke and Beaumont, 1992). Thus, at least theoretically, competition can buffer species from the loss of genes; i.e. it can help to maintain diversity. Clarke and Beaumont note that their findings are due to the structure of the model which they investi- Table 4. Summaries of RAPD markers correlated with root growth in pot-grown Rumex acetosa plants Primer Primer sequence Marker identity Marker molecular weight (base pairs) AB4-08 5∞-CCTCCAGTGT-3∞ AB2-19 AB4-09 AB5-18 5∞-ACGGCGTATG-3∞ 5∞-TCCCACGCAA-3∞ 5∞-GATGCCAGAC-3∞ m2 m14 m46 m60 m106 2400 1000 250 1500 930 The ecological significance of molecular diversity data 1643 Fig. 5. ROC curves for six RAPD markers and relative root growth in Rumex acetosa. (a–e) The markers are positively correlated with the trait. (f ) The ROC curve is included for comparison and is for a marker not correlated with the trait. gated, and that there are obvious cases where competition will not act to preserve diversity (Clarke and Beaumont, 1992). Nonetheless, their work does suggest that there need not be a contradiction between the existence of competition and diversity within plant communities. Continued investigation of the links between molecular diversity and the expression of ecologically significant traits in plant communities should allow us a better understanding of the processes that stabilize communities over time. 1644 McRoberts et al. However, the stochastic nature of both the trait data and the molecular data that are collected for such purposes should be kept in mind. There is a contradiction in the way in which molecular data appear to be viewed in molecular ecology. In order to establish indices of diversity or to relate marker incidence to traits, it is necessary that there should be variation in marker incidence among individuals in a population. However, the very existence of this variation means that estimates of diversity, or associations between markers and traits derived from samples of populations and samples of markers of those individuals, are subject to uncertainty. In molecular ecology, as in other areas of population biology (Turner, 1992), it might be wise not to ignore the impact that this stochasticity might have on our models of population processes, particularly when dealing with small populations. The above reservations notwithstanding, careful manipulative experiments as advocated previously (Crawley, 1990), in conjunction with observational studies, will provide detailed information on the competitive interactions between natural plants species, and on the expression of ecologically significant traits relating to physiology and reproduction. The identification of markers associated with expression of such traits (Luo, 1998) offers the possibility of extending our analysis of natural populations in situ even further, provided care is taken in extrapolating from the results of controlled experiments to natural conditions. 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