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Published online 1 March 2007
Published in Crop Sci 47:861-866 (2007)
© 2007 Crop Science Society of America
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PLANT GENETIC RESOURCES

Probabilistic Models for Collecting Genetic Diversity: Comparisons, Caveats, and Limitations

Dale R. Lockwooda,c, Christopher M. Richardsb,* and Gayle M. Volkb

a Program for Interdisciplinary Mathematics, Ecology and Statistics; Dep. of Mathematics, Colorado State Univ., Fort Collins, CO 80523
b USDA, National Center for Genetic Resources Preservation, 1111 South Mason St., Fort Collins, CO 80521
c The research of D.R.L. is partially supported by the National Science Foundation through grant DGE-0221595

* Corresponding author (Chris.Richards{at}colostate.edu).


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 THE STRATEGIES
 COMPARISON OF STRATEGY OUTCOMES
 HOW MANY POPULATIONS?
 DISCUSSION
 REFERENCES
 
Methods for collecting genetic diversity from in situ populations are important tools for plant conservation. Many quantitative collection strategies for sampling populations without a priori information regarding the ecology, reproductive biology, or population genetic structure of the taxa have been proposed, but their different assumptions regarding the collection scale and the basis for diversity often make them difficult to compare. Understanding the limitations of the different strategies enables collectors to make more informed choices when implementing conservation and restoration projects or collecting for germplasm improvement. We compare two genetically based strategies under a common set of assumptions and extend the probabilistic arguments of the strategies to accommodate rare alleles, multiple loci, and multiple populations. The recommendations of many models are based on a single locus, but larger numbers of individuals must be collected to assure with a high probability (>0.95) the acquisition of alleles at multiple independent loci within a population. Sampling from multiple populations linked by gene flow may offset this increase. Additionally, the likelihood of capturing rare alleles remains high when sampling for multiple loci or across multiple populations. Comparison of the models provides germplasm collectors with a basis to evaluate risks of over- and undersampling to capture genetic diversity within a species.

Abbreviations: LMD • Lawrence–Marshall–Davies • MB, Marshall–Brown


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
THE STRATEGIES
 COMPARISON OF STRATEGY OUTCOMES
 HOW MANY POPULATIONS?
 DISCUSSION
 REFERENCES
 
COLLECTING FROM plant populations to obtain genetic diversity is an integral part of conservation of genetic resources to support agriculture (Hawkes et al., 2000), conservation biology (Maunder et al., 2004), restoration ecology (Stanley Price et al., 2004), and many areas of basic and applied research (Frankel et al., 1995). Diversity can be measured at a single locus or across multiple loci, whether within an individual or a population or across a species. The choice of the measure of diversity influences the sampling strategy used to collect it. Any sampling of genetic material comes with associated costs in exploration and storage, thus the adage of "more is better" is balanced by the realities of available resources.

Numerous quantitative sampling strategies have been proposed to effectively collect plant material for ex situ storage (see Lockwood et al., 2007 for a review). In general, these strategies all make the assumption that the taxa to be collected are not fully characterized. Specifically, many of the strategies assume that the breeding system, dispersal characteristics, and pollination processes are unknown. Importantly, these strategies also assume that no population genetic structure is known. With the absence of marker data, no information regarding the genetics of these plant populations exists before the first collection. These assumptions are well aligned with the reality of most plant collecting expeditions. The strategies range from collecting 100 phenotypically diverse specimens per location (Bogyo et al., 1980) to collecting based on economically derived success functions that factor the costs of collecting directly into the strategy (Yonezawa, 1985). The Marshall–Brown (MB) strategy (Marshall and Brown, 1975) develops a quantitative model that specifies the number of plants that should be collected within a site. Additionally the strategy develops an argument to address the number and distribution of sites required to acquire a substantial proportion of the species' diversity. In plant conservation, the MB strategy is the most widely cited strategy when sampling protocols are designed (Center for Plant Conservation, 1991; Kew, 2001; Engels and Visser, 2003; Guerrant et al., 2004; Rogers and Montalvo, 2004; BLM, 2005). The MB strategy has been the basis for more specific strategies (Brown, 1978; Marshall and Brown, 1983; Brown and Briggs, 1991; Brown and Marshall, 1995; Brown and Hardner, 2000). As an alternative, the Lawrence–Marshall–Davies (LMD) strategy (Lawrence et al., 1995) employs a probabilistic model of multilocus variation within a population to estimate the number of individuals to be collected. Both the MB and LMD strategies effectively capture common alleles but result in very different numbers of individuals to collect.

The strengths and limitations in the MB and LMD strategies have not been directly addressed in a common framework. Understanding the limitations that each strategy imposes on the sampling process better informs collectors about the overall use of the strategies in practical collection expeditions. We compare the MB and LMD strategies under a common set of assumptions and extend the basic strategies to accommodate rare alleles, multiple loci, and multiple populations.


   THE STRATEGIES
TOP
 ABSTRACT
 INTRODUCTION
 THE STRATEGIES
COMPARISON OF STRATEGY OUTCOMES
 HOW MANY POPULATIONS?
 DISCUSSION
 REFERENCES
 
The MB and LMD strategies are based on a general probabilistic argument. This is stated as the probability of obtaining, from a pool composed of elements from two classes (i.e., two alleles from a single locus), at least one element from Class A in n trials; this probability can be determined as one minus the probability of not obtaining an element from Class A in n t rials. Both models make critical assumptions about the frequency of alleles in populations. Alleles are classified as either rare or common (other terms used to describe the frequency of alleles can be found in Table 1), with an arbitrary frequency selected to define rarity. In addition, alleles are either local (occurring in a single or a few populations) or widespread (occurring in many populations in the target areas). Precise definitions of "local" and "widespread" vary by model and are listed in Table 1.


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  		Table 1. Classifications of allelic frequencies and their spatial distributions used in ex situ collection strategies.

 
Marshall–Brown Strategy
The MB strategy focuses on collecting locally common alleles, i.e., alleles occurring in only a single population with a frequency of 0.05 or greater. The strategy considers both neutral alleles and overdominant alleles and ignores rare alleles because they are assumed to be either deleterious or new mutations. Widespread common alleles are obtained easily. Rare alleles are considered too difficult to collect and may be deleterious and are assumed to be collected by chance.

The MB strategy determines the number of individuals to be randomly collected per site. It considers a single locus with two alleles, A1 and A2, occurring with frequencies p1 and p2, respectively. The strategy separates alleles into two classes, common and rare, where the frequency pi, of allele Ai, can take on any value 0 < pi ≤ 1. The probability, P, of obtaining at least one copy of each allele (A1 and A2) when sampling gametes or homozygous individuals is expressed as

Formula 1[1]
where n is the number of individuals collected. Equation [1] assumes collecting with replacement, which implies that the population is sufficiently large so that sampling does not alter the overall gene frequencies. Equation [1] allows consideration of the probability of capturing two alleles from a group of more than two alleles at each locus with the last term on the right-hand side.

Marshall and Brown extend the strategy to four alleles and compute the number of individuals sampled based on five different allelic distributions. For these distributions, the number of individuals sampled increases as the smallest frequency decreases to ensure capture of infrequent alleles. When considering the various allelic distributions, 50 to 100 individuals capture with 0.95 probability the alleles with frequencies greater than 0.05 in the population.

The MB strategy suggests collecting among different populations or sites, but gene flow among populations is not part of the analytical model considered by Marshall and Brown. In the MB model, sites are considered independent sampling trials, mathematically implying that populations contain mutually exclusive sets of alleles. The MB strategy also considers the number of sites required to maximize the collection of genetic variation within the target area as constrained by an economic cost function. A simple linear relationship is derived between the total effort (measured in units of time), the number of sites sampled, and the number of individuals collected per site. While the economic model serves as a practical guide to collecting among sites, there is no attempt to consider how genetic diversity is distributed among sites.

The MB strategy concludes that 50 to 100 individuals should be collected per site. Additionally it recommends collecting from as many sites as possible over a broad environmental range.

Lawrence–Marshall–Davies Strategy
The LMD strategy determines the minimum number of plants to be collected randomly from a population that results in a high probability of capturing at least one copy of each allele with frequencies ≥0.05, at a number of loci. The basic model assumes a single diallelic locus, with the probability, P, of capturing both alleles given as

Formula 2[2]
where n is the number of plants collected and P11 and P22 are the respective genotypic frequencies of the homozygotes. Genotypic frequencies allow the LMD strategy to include the effects of nonrandom mating. The genotypic frequencies for P11 and P22 are p12+p1p2fe and p22+p1p2fe, respectively, with an inbreeding coefficient, fe, and allelic frequencies p1 and p2. Assuming dynamic equilibrium in the population and assuming the modeled variation in mating is limited to the proportion of selfing in the population results in fe = s/(2 – s), with s, the selfing coefficient, ranging from 0 (complete outcrossing) to 1 (complete selfing). The number of individuals required to capture alleles that occur with frequencies of ≥0.05 is computed with P set to 0.95, 0.99, 0.999, and 0.9999 and s set to 1 or 0. A total of 172 individuals is needed to ensure a 0.9999 probability of collecting at least one copy each of A1 and A2.

Lawrence, Marshall, and Davies (1995) expand the basic model to include up to four alleles at a locus. The probability of capturing all alleles is computed for a range of allelic frequencies, while the number of individuals collected is held to 172. The probability of capturing all alleles is lowest when the distribution of alleles is skewed, which is demonstrated with allelic frequencies of 0.85, 0.05, 0.05, and 0.05 (see Gregorius [1980] for a detailed analysis of the relationship of the relative frequencies of alleles).

Lawrence, Marshall, and Davies (1995) then expand the model to k loci, and although a probability of success of 0.9999 is excessive for a single locus, when multiplied across many independent loci the probability of success remains high (P = 0.90 for k = 1000 loci). When all k loci have two alleles with the same frequencies, the probability of acquiring at least one of each of the 2k alleles is

Formula 3[3]
If P is near 1 then Pk should be near unity, even for relatively large values of k. Using the best available information at the time, Lawrence, Marshall, and Davies developed estimates of k based on the then current estimate of the number of the functional mammalian genes (40000) and the assumption that 50% of these genes are polymorphic.

Although the single-locus computations consider the lower-frequency allele to have a frequency as low as 0.05, the multilocus case considers 0.1 as the smallest allelic frequency. The LMD strategy uses Eq. [3] to determine that 0.9997 is the probability of acquiring at least one of each of the pair of alleles at each locus when k = 20 000, n = 172, p1 = 0.1, and s = 1. If the value of p1 is set to 0.05, the probability of success drops to 0.05. The strategy's general applicability is limited when a fully selfing species (s = 1) is considered since there is a low probability of success for small values of p1 coupled with high selfing rates. Outcrossing and variability in the frequency of rare alleles across loci improve the probability that all alleles are collected.

The LMD strategy seeks to capture the genetic diversity of the species, not of individual populations; thus, the authors argue that collecting should be done on the taxonomic species level, and intraspecific structure should be disregarded. The 172 individuals to be collected are equally divided among populations to address spatial structure. For example, if there are 10 populations, collecting 17 or 18 individuals from each population is considered sufficient. The LMD strategy suggests that alleles at low frequency specieswide will be captured when they occur at a "relatively high frequency in a minority of populations."

Like the MB strategy, the LMD strategy concludes that rare alleles in the population are of no practical importance and that including them would increase the number of individuals collected substantially. It is also argued that collecting coadapted gene complexes may provide important adaptive variation. Lawrence and colleagues consider it impractical to collect individual genotypes from wild populations for ex situ conservation.


   COMPARISON OF STRATEGY OUTCOMES
TOP
 ABSTRACT
 INTRODUCTION
 THE STRATEGIES
 COMPARISON OF STRATEGY OUTCOMES
HOW MANY POPULATIONS?
 DISCUSSION
 REFERENCES
 
Both the MB and LMD strategies share a common theoretical framework but result in different numbers of individuals that are needed to capture genetic diversity for ex situ collections. By assuming a single locus with exactly two alleles in a fully homozygous (fe = 1) population, Eqs. [1] and [2] become identical. The assumption of selfing is conservative as it doubles the number of individuals collected with respect to populations that are fully outcrossing (Lawrence et al., 1995). The probability of capturing both alleles over a set of k loci in linkage equilibrium is

Formula 4[4]
Equation [4] allows for a direct comparison of the MB and LMD strategies. We maintain a conservative approach by restricting the model to assume the same allelic frequencies at all loci, with the smaller frequency allele set to the minimum frequency intended to be sampled.

Neither the MB nor the LMD equations directly address population structure. As described previously, in the MB model, populations (or sites) are considered independent sampling units. The LMD model treats the species as a single sampling unit, and fine-scale variation at the level of the population is discounted. The spatial distribution of sampling is therefore incidental to the goal of species level collections.

Using Eq. [4], we generated the probability distributions (Fig. 1 ) for the successful acquisition of alleles with the rarer of two alleles present at a range of frequencies (x axis). The right vertical axis of Fig. 1 divides 172 individuals into multiple equally sized populations, as described by the LMD strategy.


Figure 1
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  		Figure 1. The four panels represent collecting based on 1, 10, 100, and 1000 loci. The x axis is the frequency of the less common allele in a diallelic population across all loci. The left-hand y axis is the number of individuals sampled from a single population. The right-hand y axis is the number of populations as given in the Lawrence–Marshall–Davies (LMD) strategy. The y axes are correlated since the total sample size of 172 is distributed evenly among the populations. For example, a single sample of 172 is given for one population, and if there are two populations (right hand axis), the sampling per population is 86 (left-hand axis). In each panel, probability isoclines representing 0.9999, 0.95, and 0.5 are plotted. These values represent the probability of acquiring two alleles at each locus based on the frequency of the less common allele (x axis). The vertical dashed line is the 5% allelic frequency, which is the cutoff for common alleles (Table 1). The horizontal dashed line represents the 50 individuals suggested from the Marshall–Brown strategy, and the dotted line represents the 172 individuals suggested from the LMD strategy (left axis).

 
Single Locus, Single Population
The two models are identical for diallelic loci and can be directly compared under the assumptions that the allelic frequencies are constant across all populations and the populations are fully selfing. The only major difference between the models is the value used for the probability of success. Figure 1 (one locus) demonstrates that for a single locus, both models capture the alleles close to the probabilities that are targeted in each strategy (0.95 in MB and 0.9999 in LMD). In the MB strategy, collecting 50 individuals results in a 92% probability of success and collecting 58 individuals results in a 95% probability of success when the rarer allele occurs at a frequency of 0.05. In both the LMD and MB strategies, there is a diminishing return of captured alleles as the number of individuals collected increases (Fig. 1). As alleles become increasingly rare, the number of individuals required to capture those alleles increases exponentially.

Multiple Loci, Single Population
A major difference between the two strategies is apparent when multiple loci are studied. We consider two alleles at 10, 100, or 1000 loci for a single population (Fig. 1). The probability of success, for a fixed allelic frequency, declines as the number of loci increases. At 10 loci, with 50 individuals collected (MB strategy) and the rare allele set at a frequency of 0.05, the probability of success is 0.5. An alternative way to view the relationship between loci and probability of capture is to consider that, for 10 loci, collecting 50 individuals captures all alleles with a frequency of 0.10 or greater with a probability of 0.95. Likewise for 1000 loci this strategy captures all alleles with a frequency of 0.18 or greater. For 10000 loci (not shown in Fig. 1) the minimum allelic frequency becomes 0.22.

Capturing alleles across multiple loci is the primary focus of the LMD strategy. The strategy points out the difficulty of retaining low-frequency alleles by demonstrating that for a minimum allelic frequency of 0.05, the alleles at 20 000 loci have only about a 5% probability of complete capture. By collecting 172 individuals for 1000 loci, well below the target number used by the LMD strategy, the probability of success declines to 86% for loci each with an allele with a frequency of 0.05 (Fig. 1, 1000 loci).

Single Locus, Multiple Populations
The two strategies differ greatly in their approaches to multiple populations; the MB strategy recommends collecting 50 individuals from each population, and the LMD strategy divides the 172 individuals among all the populations surveyed.

In the MB strategy, collecting 50 to 100 individuals from each population is intended to capture locally common alleles (alleles that exist at a frequency of at least 0.05 within only a single population). Populations are rarely completely isolated from other populations within a species. The definition of "locally common" does not preclude the gene from existing in other populations at frequencies defined to be rare. Repeated collecting from other populations will necessarily increase the probability of capture of rare alleles. Given m populations, the total probability of success in acquiring an allele at a single locus becomes

Formula 5[5]
where n is the number of individuals collected per population and iP1 is the frequency of the A1 allele at the locus in population i. If the allele is uniformly rare across all populations, then the result is equivalent to a single population with a sample size of m x n, as pointed out by Crossa et al. (1993). Equation [5] can be used as a basis for estimating the increased probability of sampling alleles that are locally common and globally rare. This increase in probability of sampling an allele (Es) can be expressed as the difference between Eqs. [5] and [1],

Formula 6[6]
assuming population 1 contains A1 at a frequency of 0.05 or greater and populations 2 through m contain A1 only at a rare level (below a frequency of 0.05). If an allele occurs in one population at a frequency of 0.05 and in four other populations at a frequency of 0.01, the probability of acquiring the allele increases to 0.99 (Table 2). If any other population has the allele present at a frequency below but near 0.05, the allele will be acquired with near certainty (Table 2, last row of the first column).


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  		Table 2. Realized cumulative sampling success for single alleles.{dagger}

 
With the LMD strategy of collecting 172 individuals, we consider the effect of subdivided sampling for alleles that are restricted to a single population. For a single locus with the lower-frequency allele at 0.05 and four populations, the probability of success of obtaining both the high- and low-frequency alleles is 0.89 (Fig. 2 ). The subdivision of the species into populations and the concomitant division of the number of individuals collected per population imparts a restriction on the number of populations that can be collected. When one population has two alleles occurring with equal frequency, collecting from more than 30 populations will reduce the probability of capturing the two alleles below 0.95 (Fig. 2). The lowest allelic frequency captured within a population is 0.2 with 10 populations and an expected probability of success of 0.95. The lowest-frequency allele has a global frequency of 0.02, below the level that LMD strategy considers useful.


Figure 2
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  		Figure 2. For the Lawrence–Marshall–Davies strategy, the isoclines represent the probability of acquiring both alleles at a single locus based on the frequency of the lower-frequency allele. It is assumed that the alleles occur in only one population. The number of individuals per population is 172 divided by the number of populations.

 
Rare Alleles
Rare alleles have been discounted on the grounds that they are likely deleterious (Marshall and Brown, 1975; National Research Council, 1993; Brown and Hardner, 2000) or that the increase in collection effort is not worth the benefit (Lawrence et al., 1995; Brown and Hardner, 2000). The probability of acquiring rare alleles is not addressed by either the MB or the LMD strategies. However, both Eqs. [1] and [2] address the probability of acquiring rare alleles found in a single population. Figure 1 shows that the number of individuals collected must increase to acquire rare alleles. Equation [5] can be used to determine the probability of acquiring widespread rare alleles.

If an allele occurs in more than one population, the probability of acquiring the allele increases as more populations containing the allele are sampled. Alleles that are very rare within any one population have a high probability of being collected if they occur within 10 populations. To highlight this effect, we considered 2, 10, and 50 populations, each with a low-frequency allele with a maximum value between 0.0001 to 0.025. Each point on the curves in Fig. 3 represents the mean probability of capture considering 10000 random selected frequencies, each of which is no greater than the value at the point. When an allele exists at a frequency of ≤0.01 in 10 populations of 50 individuals, there is a 0.90 probability of capturing it. When the allele has a frequency of ≤0.002 in 50 populations of 50 individuals, there is a 0.90 probability of capturing it. The variance in sampling success decreases with the number of populations, but this is an effect of the potential amount of variation among populations more than an effect of the sampling strategy.


Figure 3
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  		Figure 3. The probability of capturing a rare allele that occurs in multiple populations by either the Marshall–Brown (MB) strategy or the Lawrence–Marshall–Davies (LMD) strategy. The x axis represents the maximum value for the distribution of the low-frequency alleles over 10000 randomly selected low allelic frequencies. Curves A, B, and D represent the MB strategy with 50, 10, and 2 populations, respectively. Curve C represents the LMD strategy applied to 50 populations. Curves A through D represent the mean values of the results of Eq. [4] applied to the set of random frequencies. The error bars are at one standard deviation.

 
The LMD strategy divides the 172 individuals among all the populations, thus the capture of widespread rare alleles remains relatively constant as the number of populations changes. The collection of rare alleles is limited by constraining the total number of individuals to 172 (Fig. 3). The LMD strategy, subdivided over 50 populations, captures alleles with a frequency of >0.026 among all populations, with the probability of success of 0.90 (not shown in Fig. 3).


   HOW MANY POPULATIONS?
TOP
 ABSTRACT
 INTRODUCTION
 THE STRATEGIES
 COMPARISON OF STRATEGY OUTCOMES
 HOW MANY POPULATIONS?
DISCUSSION
 REFERENCES
 
It is widely known that genetic diversity in plant species is heterogeneously distributed. The challenge for conservation is that there are few recommendations for collecting among populations (Neel and Cummings, 2003). The definition of a site given by a collector using environmental characteristics is often quite different from the genetic definition of a population, which is the spatial scale at which panmixia occurs. Gene flow, migration, and colonization/extinction processes can confound population structure defined by locality with population history defined by genealogy. In other words, sites selected on habitat variation may not reflect the independent populations referred to in the sampling strategies. The among-population recommendations include sampling from 5 populations for rare species (Brown and Briggs, 1991; Center for Plant Conservation, 1991) and up to 50 populations (Brown and Marshall, 1995). Empirically, Neel and Cummings (2003) show that for four endemic threatened species, between 53 and 100% of the populations must be sampled to capture all alleles for frequencies > 0.05.

Both sampling strategies depend critically on an adequate definition of a sampling unit. This has led to some widespread confusion when applied to collection expeditions. Without a priori knowledge about the scale of genetic differentiation either by direct genetic evidence or ecological parameters such as dispersal distance and breeding system, an optimal strategy for deciding the number of collection sites cannot be defined. The number of sites collected in an initial collection trip is more a function of logistics (see Yonezawa [1985] for an approach based on logistics). Neither the MB nor the LMD stategy gives quantitative recommendations on the number of populations to sample. This is not surprising given the idiosyncratic nature of population structure and gene flow. One can more accurately target differentiation that can be defined to some degree among sites when a modest number of genetic analyses are performed after the initial collection. These data can be used to determine key conservation sites and can help narrow the sampling targets in future collection efforts. This allows the detection of sites of conservation interest and guides recollection efforts. This iterative process (Bennett, 1970) is the most efficient sampling strategy for capturing representative genetic variation among sites (Ceska et al., 1997; Jin et al., 2003; Caujape-Castells and Pedrola-Monfort, 2004; Richards et al., 2006).


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 THE STRATEGIES
 COMPARISON OF STRATEGY OUTCOMES
 HOW MANY POPULATIONS?
 DISCUSSION
REFERENCES
 
Sampling for allelic richness is important for conservation and in the development of genetic resource collections. The MB strategy was motivated by conservation and breeding interests. The LMD strategy was developed to conserve wild relatives or progenitors of cultivated species threatened with extinction. Restoration ecologists are often concerned with representing alleles in proportion to their distribution in the original natural population. Brown and Hardner (2000) argue that the LMD strategy is not suited to conservation or restoration needs because it targets the species level and fails to adequately capture fine-scale variation. Lawrence (2002) argues that the strategy of Brown and Hardner (2000), which is based on the MB strategy, does not collect sufficient allelic variation at multiple loci within a population, implying that the target of the sampling is not adequately conserved. Neither strategy addresses the question of whether the distribution of alleles within a collected sample matches the distribution found in the population, since both strategies aim to maximize allelic richness.

Both the MB and LMD strategies will undersample a population, depending on the target diversity and the implementation of the strategies. Marshall and Brown (1975) do not consider variation at multiple loci. When a single population has many independent loci, collecting 50 individuals will likely miss much of the variation across loci (Fig. 1). Collecting from populations connected by gene flow will increase the probability of capturing the common alleles at multiple loci (Table 2). The LMD strategy undersamples local diversity when the number of individuals collected is divided among several populations (Figs. 1 and 2). It is well suited for a species with a very homogeneous genetic distribution. However, as populations diverge, the local diversity will not be captured. Lawrence (2002) suggests that as an alternative, 172 individuals can be collected from every population, which then places the strategy in a similar format to the MB strategy, albeit with a tripling of the total collection size.

Practical limitations on the maintenance of the collection must be considered when the number of populations increases and when more individuals are collected per population. Lawrence et al. (1995) state that if the individuals collected cannot be maintained, the end result is wasted resources and effort.

Rare alleles may be detrimental under current conditions but may confer selective advantage under conditions not present at the time of collection (Frankel et al., 1995). Deleterious alleles also occur at low frequency; thus rare alleles potentially are a source of benefit as well as harm. Both the MB and LMD strategies discount the collection of rare alleles. We demonstrate that the MB strategy captures a substantial proportion of widespread rare alleles. When 50 populations are sampled, the MB strategy captures with near certainty alleles with a frequency an order of magnitude smaller than the minimum target value of 0.05 (Fig. 3). The LMD strategy also captures widespread rare alleles at relatively high probabilities even with collections divided among many populations.

The LMD strategy is well suited to capturing the genetic diversity of multiple loci for a single population. If the target species is an endemic with a generally panmictic dispersal, then the LMD strategy should be effective at collecting the allelic richness of the population. However, the concentration on capturing diversity at the species level does not take into account variation that may be important for some conservation goals.

The MB strategy is conservative in its approach for multiple sites. Since the sampling is designed around assuring a high probability of capturing local alleles at or above a frequency of 0.05, there is little alternative to this method. The issue of diversity as measured throughout the genome rather than at a locus as brought up by Lawrence et al. (1995) is important. This suggests that the low-end sampling figure of Marshall and Brown (1975) is likely to lead to undersampling, and a figure at or above the high end of the MB strategy, as practical, will capture more of the diversity across the genome.

Together, both strategies contribute to our understanding of collecting diversity within a population. It is difficult for a single model to include all the parameters that influence the scale and magnitude of genetic differentiation across plant species and landscapes. Collecting among multiple populations must be guided by species-specific ecology, with the realization that additional sampling may be required once the genetic diversity of the ex situ collection is determined.

Received for publication April 21, 2006.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 THE STRATEGIES
 COMPARISON OF STRATEGY OUTCOMES
 HOW MANY POPULATIONS?
 DISCUSSION
 REFERENCES
 





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