Coalescent patterns in diploid exchangeable population models

A class of two-sex population models is considered with N females and equal number N of males constituting each generation. Reproduction is assumed to undergo three stages: 1) random mating, 2) exchangeable reproduction, 3) random sex assignment. Treating individuals as pairs of genes at a certain locus we introduce the diploid ancestral process (the past genealogical tree) for n such genes sampled in the current generation. Neither mutation nor selection are assumed. A convergence criterium for the diploid ancestral process is proved as N goes to infinity while n remains unchanged. Conditions are specified when the limiting process (coalescent) is the Kingman coalescent and situations are discussed when the coalescent allows for multiple mergers of ancestral lines.Work supported by the Bank of Sweden Tercentenary Foundation.Mathematics Subject Classification (2000):Primary 92F25, 60J70; Secondary 92D15, 60F17     

The mean and variance of the number of segregating sites since the last hitchhiking event

 Tight linkage may cause a reduction of nucleotide diversity in a chromosomal region if an advantageous mutation appears in that region which is driven to fixation by directional selection. This process is usually called genetic hitchhiking. If selection is strong, the entire process takes place during a time period of length 2s ln (2N) that is very short relative to 2N generations [s is the selection coefficient of the advantageous mutation and N the effective diploid population size]. On the time scale of 2N generations, which is characteristic for neutral evolution, we may therefore call this process a hitchhiking event. Using coalescent methods, we analyzed a model in which a hitchhiking event occurred in a chromosomal region of zero-recombination in the past at time x. Such a hitchhiking “catastrophe” wipes out completely genetic variation that existed in a population before that time. Standing variation observed at present must therefore be due to mutations that have arisen since time point x. Assuming that all newly arising mutations are neutral, we derived expressions for the expectation, variance and also for the higher moments of the number of nucleotide sites segregating in a sample of n genes as a function of x. The result for the first moment is then used to estimate the time back to the last hitchhiking event based on DNA polymorphism data from Drosophila. Assuming that directional selection is the sole determinant of the level of genetic variation in the gene regions surveyed, we obtained estimates of x that were typically in the order of 0.1N generations. Received 14 May 1996; received in revised form 26 August 1996     

When and where was the most recent common ancestor?

 The structured coalescent is investigated for single-locus, digenic samples in the diffusion limit of the unidimensional stepping-stone model for homogeneous, isotropic migration and random genetic drift. Let T denote the scaled time to the most recent common ancestor (MRCA) of the two genes, and let Z designate the scaled deviation of the position of the MRCA from the average position of the two genes. The joint probability density of T and Z is evaluated explicitly. Both the marginal and conditional distributions of T have infinite expectation, as does the marginal distribution of Z. Conditioned on T = τ, the distribution of Z is Gaussian with mean zero and variance 2τ. The main results are extended to anisotropic migration. The results establish the existence of and define in the diffusion limit a retrospective stochastic process for digenic samples in one spatial dimension. Received: 1 May 2001 / Revised version: 2 September 2001 / Published online: 8 February 2002     

Simulation of ‘hitch-hiking’ genealogies

An ancestral influence graph is derived, an analogue of the coalescent and a composite of Griffiths' (1991) two-locus ancestral graph and Krone and Neuhauser's (1997) ancestral selection graph. This generalizes their use of branching-coalescing random graphs so as to incorporate both selection and recombination into gene genealogies. Qualitative understanding of a ‘hitch-hiking’ effect on genealogies is pursued via diagrammatic representation of the genealogical process in a two-locus, two-allele haploid model. Extending the simulation technique of Griffiths and Tavaré (1996), computational estimation of expected times to the most recent common ancestor of samples of n genes under recombination and selection in two-locus, two-allele haploid and diploid models are presented. Such times are conditional on sample configuration. Monte Carlo simulations show that ‘hitch-hiking’ is a subtle effect that alters the conditional expected depth of the genealogy at the linked neutral locus depending on a mutation-selection-recombination balance. Received: 21 July 2000 / Published online: 5 December 2000     

Chloroplast phylogeography and evolution of highly polymorphic microsatellites in lodgepole pine ( Pinus contorta)

We employed a novel set of six highly polymophic chloroplastic simple sequence repeat (cpSSR) loci to investigate the phylogeography of lodgepole pine (Pinus contorta Dougl. Ex. Loud.), and to examine aspects of the evolutionary process operating on these repetitive DNA sequences. Chloroplast haplotypes of 500 trees, sampled throughout the range of lodgepole pine, were determined. We found a marked association of genetic distance with physical distance within the scale of 0 to 1,000 km, but no association beyond that range. Likewise, geographic clustering was observed only among recent clades in a dendrogram. These phylogeographic patterns are consistant with a rapid rangewide expansion (”big-bang”) followed by recent, local population differentiation (”galaxy formation”). In support of this expansion, coalescent simulations of the genealogical process gave a long-term effective population size in the low thousands, and a time to common ancestry of about 1,500 generations (12,000 years), consistent with a post-Pleistocene population expansion as documented by previous pollen-sediment analyses. Two lines of evidence (mapping mutational events onto a phylogeny, and evaluation of observed versus expected gene diversity) suggest that five of the cpSSR loci evolve primarily by a stepwise model of evolution of single repeat changes (but with a small proportion of changes involving two or more repeats), and the coalescent simulations point to a mutation rate of about 10^–3. Received: 7 December 2000 / Accepted: 17 May 2001     

In vitro propagation of endangered Lippia filifolia mart. and schauer ex schauer

Summary This work describes an efficient micropropagation protocol of Lippia filifolia. Nodal segments cultivation in MS medium supplemented with 6-benzylaminopurine (4.5 μM)/α-naphthaleneacetic acid (NAA; 54nM) induced multiple shoots (in average 27 shoots per explant). Elongated shoots were rooted with NAA (0.11 μM) and they maintained ploidy level of the in vitro produced explants. The basic chromosome number were 2n=2x=24. Regenerated rooted shoots were successfully acclimatized under shading house conditions. This is the first report involving the establishment of a protocol for shoot multiplication and rooting for endangered L. filifolia, contributing for germplasm preservation of this species.     

Current progress of the biological single-ion microbeam at FUDAN

A biological microbeam for precisely positioned single-ion/single cell irradiation is built in the Institute of Modern Physics in Fudan University, Shanghai, China, based on the tandem accelerator (2 × 3MV) in the laboratory. In this paper, the developing progress of the FUDAN microbeam is reported, including the newly constructed beam line, the microbeam collimator, the ion detection system, and the cell-imaging and targeting systems. Statistical models are proposed for evaluating the spatial resolution and dosage precision of the microbeam. By taking the collimated ions as a Gaussian beam, the spatial resolution can be evaluated by the full width at half maximum of the 2-D Gaussian distribution, which is determined by fitting the proportions of peripheral pits outside specific radii in the pit clusters etched on ion track detectors to a 2-D Gaussian distribution. In the preset hitting of defined ion number, by taking the real delivered number of ions as an independent identically distributed random variable (iidrv), according to the Law of Large Numbers and Central Limit Theorem, the expected value μ and standard deviation σ of the real delivered ion number in a preset N-ion hitting can be determined by approaching the normal distribution of N (μ, σ ²/n) with the proportions of the mean counts of pits in multiple pit clusters on ion track detectors. By the values of μ, σ and additional assumptions, statistical dosage precision evaluations can be made on the preset hitting. From the linear fit curve of μ(N) and the power function fit curve of σ(N) on different preset ion numbers, characteristic factors k, b, A, p can be extracted for a precision evaluation independent of the specific preset ion number.     

No BLUE among phylogenetic estimators

 Multivariate analysis is a branch of statistics that successfully exploits the powerful tools of linear algebra to obtain a fairly comprehensive theory of estimation. The purpose of this paper is to explore to what extent a linear theory of estimation can be developed in the context of coalescent models used in the analysis of DNA polymorphism. We consider a large class of coalescent models, of which the neutral infinite sites model is one example. In the process, we discover several limitations of linear estimators that are quite distinct from those in the classical theory. In particular, we prove that there does not exist a uniformly BLUE (best linear unbiased estimator) for the scaled mutation parameter, under the assumptions of the neutral model of evolution. In fact, we show that no linear estimator performs uniformly better than the Watterson (1975) method based on the total number of segregating sites. For certain coalescent models, the segregating-sites estimator is actually optimal. The general conclusion is the following. If genealogical information is useful for estimating the rate of evolution, then there is no optimal linear method. If there is an optimal linear method, then no information other than the total number of segregating sites is needed. Received: 29 July 1998 / Revised version: 9 October 1998     

Evaluation of the maximum specific growth rate of a yeast indicating non-linear growth trends in batch culture

The maximum specific growth rate (μ_max) of an ethanolic D-xylose-fermenting yeast, Pichia stipitis, showing non-linear growth trends in batch culture, was calculated using the rate equation μ₂ = (1/Δt) ln(x ₂/x ₁). The absolute error Δμ, affecting μ₂, was derived using an equation given by Borzani (1994). Based on the assumption of linearity of growth curves between two closest time points, the relation between the two rate formulae, μ₁ = (1/xˉ)dx _t /dt and μ₂ = (1/Δt) ln(x ₂/x ₁) was established. In a particular condition, when μ₁ = μ₂, an equation has been developed, the roots of which are the specific growth rates at different time points. This revised version was published online in July 2006 with corrections to the Cover Date.     

DNA ploidy level variability of some fescues (<Emphasis Type="Italic">Festuca</Emphasis> subg. <Emphasis Type="Italic">Festuca</Emphasis>, Poaceae) from Central and Southern Europe measured in fresh plants and herbarium specimens

Using flow cytometry in fresh plants and herbarium vouchers, DNA ploidy levels for 411 individuals of 44 taxa of the genus Festuca, including 4 natural hybrids, originating from 237 sites in Austria, Bulgaria, Croatia, Czech Republic, Estonia, Germany, Hungary, Italy, Poland, Romania, Slovakia, Slovenia, and Switzerland were estimated. The following taxa and DNA ploidy levels are reported: F. airoides (2n ≈ 2x), F. alpestris (2n ≈ 2x), F. alpina s.l. (2n ≈ 2x), F. amethystina subsp. amethystina (2n ≈ 4x), F. bosniaca subsp. bosniaca (2n ≈ 2x), F. brevipila (2n ≈ 6x), F. bucegiensis (2n ≈ 2x), F. carnuntina (2n ≈ 6x), F. csikhegyensis (2n ≈ 4x), F. csikhegyensis × F. eggleri (2n ≈ 4x), F. dalmatica (2n ≈ 4x), F. duvalii (2n ≈ 4x), F. eggleri (2n ≈ 2x, 4x), F. filiformis (2n ≈ 2x), F. glauca (2n ≈ 6x), F. heterophylla (2n ≈ 4x), F. inops (2n ≈ 2x), F. laevigata (2n ≈ 8x), F. laxa (2n ≈ 4x), F. lemanii (2n ≈ 6x), F. norica (2n ≈ 2x), F. ovina subsp. ovina (2n ≈ 2x), F. ovina subsp. guesfalica (2n ≈ 4x), F. ovina × F. pallens (2n ≈ 4x), F. pallens (2n ≈ 2x, 3x), F. pallens × F. pseudodalmatica (2n ≈ 3x, 4x), F. pirinica (2n ≈ 2x), F. polesica (2n ≈ 2x), F. psammophila subsp. dominii (2n ≈ 2x), F. pseudodalmatica (2n ≈ 4x), F. pseudovina (2n ≈ 2x), F. quadriflora (2n ≈ 4x), F. rupicola (2n ≈ 6x), F. rupicola × F. vaginata (2n ≈ 3x, 4x), F. saxatilis (2n ≈ 6x), F. stricta subsp. bauzanina (2n ≈ 8x), F. supina (2n ≈ 4x), F. tatrae (2n ≈ 2x), F. valesiaca (2n ≈ 2x), F. versicolor subsp. pallidula (2n ≈ 2x), F. versicolor subsp. versicolor (2n ≈ 2x), F. violacea subsp. puccinellii (2n ≈ 2x), F. wagneri (2n ≈ 4x), F. xanthina (2n ≈ 2x). In F. pallens, up to 12-year-old herbarium specimens were proved to be suitable for DNA ploidy level measurements with flow cytometry. DNA ploidy levels of F. bucegiensis, F. bosniaca, and F. versicolor subsp. pallidula are reported here for the first time. The taxonomy of some polyploid complexes and several records of mixed ploidy level populations are briefly discussed. Festuca pseudodalmatica and its hybrid F. × krizoviensis were first recognised as native to the Czech Republic, and F. brevipila as native to Hungary. Also some new records of F. filiformis, F. brevipila, and F. wagneri from Slovakia are reported.     

Coalescent histories for discordant gene trees and species trees

Given a gene tree and a species tree, a coalescent history is a list of the branches of the species tree on which coalescences in the gene tree take place. Each pair consisting of a gene tree topology and a species tree topology has some number of possible coalescent histories. Here we show that, for each n≥7, there exist a species tree topology S and a gene tree topology G≠S, both with n leaves, for which the number of coalescent histories exceeds the corresponding number of coalescent histories when the species tree topology is S and the gene tree topology is also S. This result has the interpretation that the gene tree topology G discordant with the species tree topology S can be produced by the evolutionary process in more ways than can the gene tree topology that matches the species tree topology, providing further insight into the surprising combinatorial properties of gene trees that arise from their joint consideration with species trees.     

In vitro induction of autotetraploids from diploid yellow passion fruit mediated by colchicine and oryzalin

In vitro chromosome doubling from hypocotyl segments of yellow passion fruit (Passiflora edulis Sims.) was carried out in the presence of either colchicine (0, 25, 250 and 1,250 μM) or oryzalin (0, 5, 15 and 30 μM). Murashige and Skoog (in Physiol Plant 15:473–497, 1962)(MS)-based regeneration medium containing 250 or 1,250 μM colchicine markedly affected explant development leading to browning and death of the hypocotyl segments. Oryzalin has similar effect to colchicine in inducing polyploidy. In vitro regenerated autotetraploid plants induced by 25 μM colchicine or 15 μM oryzalin were further acclimatized and cultivated in hydroponics system in greenhouse. Autotetraploids plants were more vigorous than the control diploids. The chromosome number of diploid plants was 2n = 2x = 18, whereas that found on autotetraploid plants were 2n = 4x = 36. The stomata sizes of the autotetraploids were significantly larger than those on the diploid counterparts, while the frequency of stomata was significantly reduced. Similarly, the chloroplast number of guard cells of autotetraploid plants increased significantly. Two albino plants (4%) were generated in medium with 25 μM colchicine, indicating phytotoxic effects. These plants are being grown to full maturity in order to test their potential to use in a breeding program.     

Two types of P2x-purinoceptors in neurons of the guinea pig ileum submucous plexus

Effects of exogenous adenosine 5′-triphosphate (ATP) on dissociated guinea pig ileum submucous neurons were studied using a conventional whole-cell patch-clamp technique. With the holding potential of −50 mV, application of 50–1,000 μM ATP evoked an inward current (ATP-induced current) in most (90%) of the tested neurons (n-35). ATP-induced currents were observed regardless of whether or not guanosine 5′-triphosphate (GTP, 0.2 mM) and ATP (2 mM) were present in the intracellular solution, or GTP was replaced with equimolar concentration of guanosine 5′-O-3-thiotriphosphate (n-5). In 26 of 29 neurons studied, which responded to ATP, applications of 50–1,000 μM ATP induced slowly declining currents. ATP receptors did not appear to be completely desensitized during a long pulse (up to 4 min) of 200 μM ATP. Suramin (200 μM) accelerated an increase to peak of the current induced by 200 μM ATP without affecting the maximum response amplitude (n−4_. In about 10% of the neuronsn−3), 50 μM ATP evoked rapidly declining (about 1 sec) currents. Application of 100 μM α,β-Me-ATP to these neurons evoked similar responses. The above results suggest that submucous neurons express two specific subtypes of ionotropic P_2x-purinoceptors, which might be involved in distinct excitatory processes in these neurons.     

Testing hypotheses for genealogical discordance in a rainforest lizard

Genealogical discordance, or when different genes tell distinct stories although they evolved under a shared history, often emerges from either coalescent stochasticity or introgression. In this study, we present a strong case of mito‐nuclear genealogical discordance in the Australian rainforest lizard species complex of Saproscincus basiliscus and S. lewisi. One of the lineages that comprises this complex, the Southern S. basiliscus lineage, is deeply divergent at the mitochondrial genome but shows markedly less divergence at the nuclear genome. By placing our results in a comparative context and reconstructing the lineages' demography via multilocus and coalescent‐based approximate Bayesian computation methods, we test hypotheses for how coalescent variance and introgression contribute to this pattern. These analyses suggest that the observed genealogical discordance likely results from introgression. Further, to generate such strong discordance, introgression probably acted in concert with other factors promoting asymmetric gene flow between the mitochondrial and nuclear genomes, such as selection or sex‐biased dispersal. This study offers a framework for testing sources of genealogical discordance and suggests that historical introgression can be an important force shaping the genetic diversity of species and their populations.     

Species abundance distributions in neutral models with immigration or mutation and general lifetimes

We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth independently at constant rate λ. Thus, the population size is a homogeneous, binary Crump–Mode–Jagers process (which is not necessarily a Markov process). We assume that types are clonally inherited. We consider two classes of speciation models in this setting. In the immigration model, new individuals of an entirely new species singly enter the population at constant rate μ (e.g., from the mainland into the island). In the mutation model, each individual independently experiences point mutations in its germ line, at constant rate θ. We are interested in the species abundance distribution, i.e., in the numbers, denoted I _n (k) in the immigration model and A _n (k) in the mutation model, of species represented by k individuals, k = 1, 2, . . . , n, when there are n individuals in the total population. In the immigration model, we prove that the numbers (I _t (k); k ≥ 1) of species represented by k individuals at time t, are independent Poisson variables with parameters as in Fisher’s log-series. When conditioning on the total size of the population to equal n, this results in species abundance distributions given by Ewens’ sampling formula. In particular, I _n (k) converges as n → ∞ to a Poisson r.v. with mean γ/k, where γ : = μ/λ. In the mutation model, as n → ∞, we obtain the almost sure convergence of n ⁻¹ A _n (k) to a nonrandom explicit constant. In the case of a critical, linear birth–death process, this constant is given by Fisher’s log-series, namely n ⁻¹ A _n (k) converges to α ^k /k, where α : = λ/(λ + θ). In both models, the abundances of the most abundant species are briefly discussed.     

The shapes of neutral gene genealogies in two species: probabilities of monophyly,paraphyly, and polyphyly in a coalescent model

Abstract.— The genealogies of samples of orthologous regions from multiple species can be classified by their shapes. Using a neutral coalescent model of two species, I give exact probabilities of each of four possible genealogical shapes: reciprocal monophyly, two types of paraphyly, and polyphyly. After the divergence that forms two species, each of which has population size N , polyphyly is the most likely genealogical shape for the lineages of the two species. At ∼ 1.300 N generations after divergence, paraphyly becomes most likely, and reciprocal monophyly becomes most likely at ∼1.665 N generations. For a given species, the time at which 99% of its loci acquire monophyletic genealogies is ∼5.298 N generations, assuming all loci in its sister species are monophyletic. The probability that all lineages of two species are reciprocally monophyletic given that a sample from the two species has a reciprocally monophyletic genealogy increases rapidly with sample size, as does the probability that the most recent common ancestor (MRCA) for a sample is also the MRCA for all lineages from the two species. The results have potential applications for the testing of evolutionary hypotheses.     

Convergence time to the Ewens sampling formula in the infinite alleles Moran model

In this paper, we establish an upper bound for time to convergence to stationarity for the discrete time infinite alleles Moran model. If M is the population size and μ is the mutation rate, this bound gives a cutoff time of log(M μ)/μ generations. The stationary distribution for this process in the case of sampling without replacement is the Ewens sampling formula. We show that the bound for the total variation distance from the generation t distribution to the Ewens sampling formula is well approximated by one of the extreme value distributions, namely, a standard Gumbel distribution. Beginning with the card shuffling examples of Aldous and Diaconis and extending the ideas of Donnelly and Rodrigues for the two allele model, this model adds to the list of Markov chains that show evidence for the cutoff phenomenon. Because of the broad use of infinite alleles models, this cutoff sets the time scale of applicability for statistical tests based on the Ewens sampling formula and other tests of neutrality in a number of population genetic studies.     

Protocol for in vitro propagation of Excoecaria agallocha L., a medicinally important mangrove species

An in vitro propagation protocol has been developed for Excoecaria agallocha L. (Euphorbiaceae), a mangrove species. Nodal segments were used for axillary shoot proliferation. One shoot from each node of binodal explants was observed 3 weeks after inoculation. The best axillary sprouting was seen on a newly formulated medium containing BA, Zeatin and IBA in concentrations of 13.3 μM, 4.65 μM and 1.23 μM, respectively. The new medium, first used in this study, has a specific composition of major nutrients, MS micronutrients and iron compounds. Nodal segments from rooted cuttings and seedlings responded better than those of mature tree explants. Multiple shoot induction was complemented with efficient shoot elongation, and repeated subculture of binodal segments from axillary shoots resulted in 10–12 shoots per explant in 3 months. Rooting was achieved by growing shoots in the new medium with 0.23 μM IBA. Regenerated plants were successfully acclimatized to the natural environment, and about 85% of plantlets survived under ex vitro conditions. This is the first report of micropropagation in the genus Excoecaria and also in mangrove tree species. Received: 11 August 1997 / Revision received: 10 February 1998 / Accepted: 2 March 1998     

Okadaic acid and trifluoperazine enhance <Emphasis Type="Italic">Agrobacterium</Emphasis>-mediated transformation in eastern white pine

Mature zygotic embryos of recalcitrant Christmas tree species eastern white pine (Pinus strobus L.) were used as explants for Agrobacterium tumefaciens strain GV3101-mediated transformation using the uidA (β-Glucuronidase) gene as a reporter. Influence of the time of sonication and the concentrations of protein phosphatase inhibitor (okadaic acid) and kinase inhibitor (trifluoperazine) on Agrobacterium-mediated transformation have been evaluated. A high transformation frequency was obtained after embryos were sonicated for 45–50 s, or treated with 1.5–2.0 μM okadaic acid or treated with 100–200 μM trifluoperazine, respectively. Protein phosphatase and kinase inhibitors enhance Agrobacterium-mediated transformation in eastern white pine. A 2–3.5-fold higher rate of hygromycin-resistant callus was obtained with an addition of 2 μM okadaic acid or 150 μM trifluoperazine or sonicated embryos for 45 s. Stable integration of the uidA gene in the plant genome of eastern white pine was confirmed by polymerase chain reaction (PCR), Southern and northern blot analyses. These results demonstrated that a stable and enhanced transformation system has been established in eastern white pine and this system would provide an opportunity to transfer economically important genes into this Christmas tree species. Communicated by W. H. Wu     

High Dietary Intake of Sodium Selenite Does Not Affect Gene Mutation Frequency in Rat Colon and Liver

Our previous studies have shown that selenium (Se) is protective against dimethylhydrazine (DMH)-induced preneoplastic colon cancer lesions, and protection against DNA damage has been hypothesized to be one mechanism for the anticancer effect of Se. The present study was designed to determine whether dietary selenite affects somatic mutation frequency in vivo. We used the Big Blue transgenic model to evaluate the in vivo mutation frequency of the cII gene in rats fed either a Se-deficient (0 μg Se/g diet) or Se-supplemented diet (0.2 or 2 μg Se/g diet; n = 3 rats/diet in experiment 1 and n = 5 rats/group in experiment 2) and injected with DMH (25 mg/kg body weight, i.p.). There were no significant differences in body weight between the Se-deficient and Se-supplemented (0.2 or 2 μg Se/g diet) rats, but the activities of liver glutathione peroxidase and thioredoxin reductase and concentration of liver Se were significantly lower (p < 0.0001) in Se-deficient rats compared to rats supplemented with Se. We found no effect of dietary Se on liver 8-hydroxy-2′-deoxyguanosine. Gene mutation frequency was significantly lower in liver (p < 0.001) than that of colon regardless of dietary Se. However, there were no differences in gene mutation frequency in DNA from colon mucosa or liver from rats fed the Se-deficient diet compared to those fed the Se-supplemented (0.2 or 2 μg Se/g diet) diet. Although gene mutations have been implicated in the etiology of cancer, our data suggest that decreasing gene mutation is not likely a key mechanism through which dietary selenite exerts its anticancer action against DMH-induced preneoplastic colon cancer lesions in a Big Blue transgenic rat model. The US Department of Agriculture, Agricultural Research Service, Northern Plains Area, is an equal opportunity/affirmative action employer and all agency services are available without discrimination. Mention of a trademark or proprietary product does not constitute a guarantee or warranty of the product by the US Department of Agriculture and does not imply its approval to the exclusion of other products that may also be suitable. This work was supported by the US Department of Agriculture and National Cancer Institute.