Homework Assignment 1 Solutions Problem 1 Understanding Components and Vectors A You would more likely give your friends a number of blocks to go east and then a number of blocks to go north. What would these two numbers be? As can be seen in the diagram below, you would tell your friend to travel 3 blocks east and 2 blocks north.
What is the x component b x of this vector? First, we need to convert our degrees into radians so it will work in the on-line answer key. What is the y component b y of this vector? Similar to part B, our y component is found using trigonometry:. This question is similar to part C. It is asking for the y component of a vector A and B are the legs and C is the hypotenuse. Problem 2 Vector Addition Suppose that you are swimming in a river while a friend watches from the shore.
HSIs of the same 26 wild accessions used above for drought trials and below for crop introgression, were compared to those of cultivated accessions spanning the range of known susceptibility and tolerance. All but three of the 26 wild accessions had HSI values at least as low as the tolerant checks Fig. Standing variation for pod borer resistance in both wild species raises the possibility of distinct alleles or mechanisms, which if true could be used to increase and stabilize pod borer resistance in the crop.
With the long-term objective of breeding with wild alleles, large-scale introgression populations were initiated. Approximately ten-thousand segregating lineages were derived from 26 diverse wild C. To correct for the confounding effect of segregating phenology, we identified a major QTL responsible for flowering time differences between the cultivated ICCV accession and wild genotypes.
The corresponding haplotype on chromosome 3 spans 3. Marker-based selection for the cultivated haplotype was sufficient to normalize the majority of phenological variation among the respective progeny. In semi-arid climates, including portions of India and Pakistan where chickpea is a vital crop, heat stress is often coincident with drought. Consistent with our genomic and ecological data, we observed variation for most phenotypes according to the identity of the wild-parent.
Thus, different wild parents contribute different trait values, which likely reflect different demographic and selection histories, and which we speculate will be of utility for chickpea improvement. Collections of wild relatives of crops will be most useful to breeding programs if they reflect the breadth of adaptations present in natural populations, which we argue is best accomplished when collections span the full geographic and environmental range of the species.
Our collection expands both the genomic diversity and environmental range of the two closest wild relatives of chickpea, increasing the size of the collection by over an order of magnitude. The variation in substrate, elevation, and climatic range encompassed by the collection increases the likelihood that the assembled germplasm contains variation in phenology, drought, heat and cold stress. Indeed, we observe phenotypes that are correlated with environmental variation in the form of seed color crypsis and responsiveness to drought, and we have identified variation in seed nutrient density, phenology, resistance to pod borer, heat tolerance, and water deficit response.
We are also actively exploring segregating variation in Fusarium wilt and Ascochyta blight resistance, nitrogen fixation and plant architecture, each of which represent traits that are of great interest for chickpea crop improvement. Our collection also highlights the need for conservation of CWRs. Rapid development in southeastern Anatolia is accompanied by the fragmentation and loss of native landscapes. Two of the populations reported here were lost or fragmented in subsequent years , , while other populations are threatened by human activities.
New sites were added based on knowledge from local shepherds and targeting similar habitats to known locations. We also made stops on an ad hoc basis. We extracted global climatic data based on GPS coordinates for each site from a global climate data set 38 in DivaGIS following a previously developed approach To characterize climate at a fine scale, we installed ibutton Maximintegrated. Data were extracted using a Matlab extraction protocol. Humidity data were normalized following Maxim protocols.
Temperature profiles were converted into cumulative degree day estimates following a previously developed procedure 15 and compared by analysis of variance ANOVA. We assessed variation in soil chemistry by analyzing variation in 18 macro and micronutrients and chemical factors. Typically five soil cores, sampling the upper 6 inches of soil, were analyzed at each site and depicted as individual samples in Fig. Analytical chemistry was performed at Dicle University in Turkey following standard protocols. PCA was conducted to reduce the number of soil chemistry variables that may differ between populations of C.
The variables were either natural logarithm transformed Zn, Fe, Ca, Mn, Na, Mg, Nitrogen, total carbon, total inorganic carbon, total sulfur, lime-CaCO3, electro conductivity, and potassium , exponential transformed pH , or not transformed. To test for species differences in principal components, one-way ANOVA was performed on each of the first two principal components. To examine the importance of particular variables, we examined loadings. The highest loadings, above 1. GBS was used to characterize genetic variation across the wild chickpea accessions. Both restriction enzymes leave a 4-bp overhang, which promotes efficient adapter ligation to insert DNA.
Two different types of adapters were used in this protocol. We used a set of 96 barcode adapters, allowing pooling 96 DNA samples into a single lane. Based on field-collected samples, plant tissue samples were prepared for GBS sequencing across 15 well plates. Illumina reads were mapped to the C. Polymorphisms were called using the GATK pipeline 41 , which considers indel realignment and base quality score recalibration, and calls variants across all samples simultaneously through the HaplotypeCaller program in GATK Initial analysis of these results confirms that 19 samples were classified as the wrong species and were subsequently discarded.
In addition, since some field samples were from the same plants collected as seed, sibling samples were removed, leaving unique samples for subsequent analysis. This SNP filtering step and the subsequent analyses were performed within and among the three species.
Given differences in polymorphism within species, the final number of polymorphic loci passing this filter step also varied: 11, loci for C. These parameters ensure that the reads are mapped to a unique place in the reference with high quality MQ , that the reads carrying both alleles are comparable in terms of mapping quality MQRankSum , that the actual variants are called with high quality QD , and that the variants are not biased towards one strand of the genome FS or towards the end of the reads ReadPosRankSum. The analysis was run for the full set of accessions and for the three species separately, with the later analyses using a set of loci polymorphic within each species.
Independent runs at the same K yielded the same clustering with similar log-likelihood values, and this consistency was taken into account by the Evanno method when assessing clustering. Agegenet 48 , 49 was used to characterize genetic diversity between individuals and between field sites. The subsequent estimates of heterozygosity were not correlated with the sample size of the population, mean coverage, or the number of loci identified in an individual accession Supplementary Fig.
Demographic analysis was performed using G-PhoCS 22 , a Bayesian inference method that estimates current and ancestral population sizes and population divergence times. Segregating sites among 24 accessions from each of the three Cicer species were identified and filtered to remove loci within genic, repeat, or assembled gap regions, similar to other work using the algorithm 22 , Each Markov chain was carried out for 1,, iterations and parameter values were sampled after a ,run burn-in period.
Diagnostic and trace plots were used to confirm convergence of log-likelihood and model parameters, as well as consistency among all MCMC runs. All G-PhoCS parameters are scaled by mutation rate and simulations are not dependent on the true value. While G-PhoCS does account for difference in population sizes across lineages, we assume this constant mutation rate for all Cicer species.
Treemix 19 was used to construct admixture graphs, fitting phylogenetic trees to the observed variance-covariance matrix of allele frequencies for 24 chickpea populations 15 C. Each of the populations had between 14 to 83 accessions. Loci with missing data were omitted, resulting in a total of 18, SNPs for the analysis. We used blocks of adjacent SNPs. Admixture graphs were first constructed without migration edges using independent replicates to assess the tree with the best likelihood, rooted with the C. Migration edges were sequentially added to this tree using the —se option for generating jackknife estimates and standard errors of the weight attributed to each migration edge.
The fitted tree with no migration events explained The addition of further migration edges brought only marginal increases in the variance explained by the fitted model. The Threepop and Fourpop programs provided within Treemix were used to calculate f 3 and f 4 statistics and their standard errors in blocks of SNPs. Z -scores with absolute value greater than 3 are considered significant A significantly negative f 3 statistic from a test of the form f 3 PX ; P 1, P 2 confirms presence of admixture in a target population PX from source populations P 1 and P 2. For the f 4 test, significant non-zero values indicate gene flow in at least one of the pairs of four tested accessions P 1, P 2, P 3, and P 4.
For tests of the form f 4 P 1, P 2; P 3, P 4 , a significantly positive value indicates gene flow between accessions P 1 and P 3 or P 2 and P 4 and a significantly negative value indicates gene flow between P 1 and P 4 or P 2 and P 3 The package relies on a Bayesian approach to model the relative contribution of geographic and ecological pairwise distances to the covariance of allele frequencies Geological coordinates and altitude values were used to construct the geographic and ecological distance matrices, respectively, and a total of independent loci called in at least one individual among 21 C.
The beta binomial model was used to account for over-dispersion. Three independent estimations ran for 5 million generations each. To assess variation in color among seeds and their source soils, we followed a previously developed protocol Seeds from plants grown in a greenhouse were used to minimize parental environmental effects on color, which we also determined to be similar to the seed obtained from the field-collected parents. Soils collected from the source habitats at the same time as seed collection were also imaged using the same dissecting microscope.
From 17 Cicer field sites, five independent soil samples were analyzed. Each session involved imaging six gray reflectance standards, 19 to 24, from the X-Rite ColorChecker.
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The six standards reflect known amounts of light equally at all wavelengths, enabling downstream adjustments in the image processing. ImageJ software was used in the digital quantification of color After separating images from their neutral backgrounds, average pixel values of RGB color channels were recorded. Gray standards were similarly treated, without the need to remove the neutral background. Potential artifacts introduced by the imaging system were removed by standardization, following well established protocols 26 , These values were further equalized according to the six gray color standards.
Both linearization and equalization steps were achieved using standard equations, yielding values in the three parts of the spectrum: Long Wave, Medium Wave, and Short Wave Red, green, and blue color measurements were recorded based on the mean of five measurements per seed and three measurements per soil. These means per line and soil sample were used in the following analyses to test whether seed and soil samples were more similar in color when compared to their native soil than foreign soils. To directly test whether seeds and soils from each site are more closely associated in color, site mean values for seeds and soils were calculated for all three colors.
These means were then used to quantify Euclidean distance in three dimensions of each seed sample to its native and all foreign site soil samples. Euclidean distance values were square-root transformed to meet assumptions of normality and homoscedasticity of ANOVA. Because of the repeated-measures of Euclidean distance per genotype, all mixed-model ANOVAs with plant genotype nested within-population were treated as a random effect, thus accounting for the non-independence of Euclidean distance measurements for population and soil comparison estimates. Containers were watered every 2—3 days, and fertilized at weekly intervals with a dilute fertilizer mix lacking in nitrogen but containing all other macro and micronutrients.
Days to first flower was recorded when the first bud reached full anthesis for each of 3—5 individual plants of each RIL. Plants that did not exhibit flowering by 10 weeks after planting were noted as late-flowering genotypes. We selected 26 wild accessions that are parents of introgression lines and four cultivated lines for common garden studies to assess differences in transpirational control in response to high VPD high vapor pressure deficit and limited soil water availability.
In the first experiment we exposed plants to high VPD. In the second, we exposed plants to dry-down conditions simulating the terminal drought typically experienced by chickpea in water limited production zones such as South Asia and East Africa, as well as most areas where chickpea is grown on residual soil moisture after a rainy season. Plants were grown in 6'' pots top diameter The experimental design was a complete randomized block design with six replicates of each genotype. The experiment was carried out over 2 days and 3 replications per genotype were tested on each of the days, on 21 April and 22 April so-called VPD1, and VPD2 , respectively.
Data for the first three replicates were recorded on 21 April , i. The afternoon before starting VPD measurements, pots were watered to saturation and allowed to drain overnight, which equilibrates the plant and soil water potentials. The following morning — a. To ensure uniformity of plant stature, a total of pots were initially planted and only those containing plants of similar size among the replicates of a same genotype were selected for the VPD and dry-down below experiments, consisting of pots for dry-down and pots for VPD.
All T data obtained from the VPD experiment consisted in pot weight losses from consecutive weighings. Transpiration was calculated both per hour and for the entire experimental time from a. Before measurement all pots were fully saturated with water and left to drain excess water overnight to reach field capacity. Leaf area was measured by digital scanning and the WinFolia program. All leaves were separated from the shoots and placed on the scanner glass for analysis. There was a close relationship between the transpiration T and the leaf area the larger the canopy the larger the transpiration.
Residual transpiration that was not explained by the leaf area was calculated as:. The purpose of calculating these residual was to investigate how much of these residual transpiration could be explained by TR differences, and especially TR differences under high VPD. The dry-down experiment was conducted 18 March to 21 May at the Dicle University glasshouse.
Plants were grown in 6'' pots filled with soil. Four seeds of each genotype were sown in each pot on 18 March Plants were thinned to two individuals per pot at 15 DAS. The experimental design was a complete randomized block design with two water treatments well-watered WW and water stressed WS as the main factors and genotypes as the sub-factors, with six replicates for per treatment.
Plants were maintained with full irrigation before beginning the dry-down phase of the experiment. The afternoon before the start of the dry-down, soil was fully saturated and the pots were allowed to drain overnight. Initial pot weight was considered to be the field capacity weight. On subsequent days, pots were weighed at to a.
Transpiration on each day was calculated as the difference in water loss between successive days plus water added to pot between the two successive weighings. WS was imposed by partial compensation of the daily water losses from plant transpiration. Thus, pots lost similar quantities of soil water each day, irrespective of differing transpiration rates, and were thus exposed to similar kinetics of water stress imposition.
Values represent the fraction of water that was available for daily transpiration and hence are an indication of the level of stress experienced by the plant Variation in selected amino acids, minerals, polyphenols, and anti-nutritional content among seeds were determined by gas chromatography GC -mass spectrometry MS , liquid chromatography LC —MS, and atomic absorption spectroscopy AA on two replicate seeds of 21 C. Thirteen amino acids alanine, glycine, serine, proline, hydroxyproline, phenylalanine, valine, leucine, isoleucine, threonine, methionine, lysine, and tryptophan were quantified by GC-MS.
P and N were determined by micro-Kjeldahl acidic digestion, followed by colorimetric flow-injection analysis. To test for species differences in seed content, means were calculated per genotype and the subsequent genotype means were used in the analyses.
Ecology and genomics of an important crop wild relative as a prelude to agricultural innovation
Because of the non-normal distribution of the data, even after transformations, we performed analysis using a generalized linear model with a single factor i. Analyses for hydroxyproline, phenylalanine, methionine, and tryptophan were performed using a normal distribution for non-transformed data. Prior to testing for species effects on each element or compound, we performed a multivariate analysis of variance MANOVA testing for a species effect on the four anti-nutrients.
Principal component analyses were performed on the amino acids, six seed elements zinc, iron, calcium, potassium, phosphorus, nitrogen , four broad classes of anti-nutritional compounds tannin, total phenolics, total flavonoids, phytic acid , carotenoid lutein and pigment carotene. To assess variation in seed mineral content in more depth, we used induced-coupled plasma mass spectrometry ICPMS following well established protocols 56 , Five replicate seeds of each genotype were analyzed for 20 different nutrients: boron, sodium, magnesium, aluminum, phosphorus, sulfur, potassium, calcium, manganese, iron, cobalt, nickel, copper, zinc, arsenic, selenium, rubidium, strontium, molybdenum, cadmium.
For each genotype, nutrients were measured on three to five samples. Prior to statistical analyses, means per genotype were calculated for each element and all analyses were conducted using genotype means. To test whether the two species C. To help meet assumptions of MANOVA and ANOVA, the following data were natural logarithm transformed: boron, sodium, aluminum, phosphorus, manganese, copper, selenium, rubidium, molybdenum, cadmium; were square-root transformed: cobalt, nickel, arsenic; or were not transformed: magnesium, sulfur, potassium, calcium, iron, zinc, strontium.
To test for species differences, we performed LSMEANS comparisons and to directly test whether cultivated genotypes differed from wild-type, we performed linear contrasts. We used a detached leaf assay, following established methods 58 , to assess pod borer Helicoverpa armigera weight gain, survival, and damage to the host plant under controlled conditions. Chickpea plants of 26 wild lines the same whole genome sequences lines above , along with a known resistant wild line IG , a resistant cultivated ICCEB and two susceptible cultivated lines ICC and ICCV were grown under greenhouse conditions.
At 30 and 60 days after seedling emergence, terminal branches 2 to 3 fully expanded leaves and a bud were bio-assayed for growth and survival impacts on neonate larvae of H. There were five replications for each accession in a completely randomized design. Ten neonate larvae of H. Observations were recorded at 6 days after initiating the experiment when the differences between the test genotypes became most apparent for branches bio-assayed at 30 days after seedling emergence, and at 5 days after initiating the experiment at the reproductive stage We created wild introgression populations to establish a resource for association mapping of climate-resilience traits and to initiate breeding with wild alleles.
Each of these cultivated regions has distinct seasonalities and accompanying biotic and abiotic factors to which both historical selection and modern breeding programs have adapted the crop. Wild parents were selected to maximize genetic diversity and the variety of source climates.
Four C. Practical considerations of seed availability and differential success in crossing, especially for certain C. Molecular phenotyping for flowering time provided a covariate for phenotyping studies in which phenology complicates analysis for example in heat tolerance analysis. The same marker provides the basis for rationale selection of population subsets for specific phenotyping tasks.
Here, we describe the utility of a flowering time marker, but a similar approach was used to reduce branching based on a marker linked to branching frequency that we identified on chromosome 1. We anticipate using the same logic for other domestication-related traits, such as pod shattering. The concept of adjusting phenotypes with known molecular markers is not novel, nor are candidate genes that we implicate.
We envision creating lineages bearing key cultivated traits, but that otherwise possess high levels of wild variation. We argue that a collection of such lineages will provide an ideal system in which to test the agronomic utility of the wild backgrounds. Such an approach could be especially powerful in the case of traits conferred by multiple loci of small effect size, for example, removing deleterious mutations that are predicted to accumulate during domestication and breeding. The majority of F2 seed were advanced to F3 seed in cultivated fields.
Population development is an ongoing activity. To conserve genetic diversity within each F2-derived lineage, we typically sow and collect seed from 10 to 20 siblings of each familial generation. Although we aim to select individual plants from each F2-derived lineage for development of pure-line recombinant inbred lines, our focus to date has been to screen multiple individuals per F2-derived lineage, which has the advantage of maintaining variation. F2 progeny were screened for phenology, biomass, growth form, sterility, yield and pod shattering, while F3 seed was characterized for seed coat color and seed weight, both of which are maternally controlled traits and thus indicative of the F2 genotype.
Plants were harvested individually as they attained maturity. For plants with shattering pods, seed was collected continuously from individual plants until maturity.
Maturity date represents the harvest date for individual plants relative to the date of germination. Plant architecture was estimated from four values: a simple constrained text based description of growth pattern upright, intermediate or prostrate; highly branching or not , and measurements of plant height, the widest point and then the axis perpendicular to the widest point. Density was estimated as the ratio of biomass to volume. At harvest, the above ground portion of individual plants was collected by cutting the plant at soil level.
Shattering was calculated as the ratio of mature seed released from or remaining within pods after drying. A total of F3 families F3 families and seven heat tolerant and sensitive cultivated genotypes were screened under field conditions during March to May To reduce the impact of phenology, the families were genotyped for the chromosome 3 early flowering FT-linked locus as described in the main text and selected to equally represent early flowering homozygotes and heterozygotes.
Based on a visual score of flower abortion and the number of filled pods per plant, genotypes were scored as tolerant to heat stress. We declare that all other data supporting the findings of this study are included in the manuscript and Supplementary Information files or is available from the corresponding author upon request.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. McCouch, S. Agriculture: feeding the future. Nature , 23—24 Dempewolf, H. Adapting agriculture to climate change: a global initiative to collect, conserve, and use crop wild relatives.
Food Syst. Hajjar, R. The use of wild relatives in crop improvement: a survey of developments over the last 20 years. Euphytica , 1—13 Ford-Lloyd, B. Crop wild relatives—undervalued, underutilized and under threat? Bioscience 61 , — Brumlop, S. Euphytica , 53—66 Maxted, N. Kawecki, T. Conceptual issues in local adaptation. Zohary, D. Oxford University Press, Varshney, R. Draft genome sequence of chickpea Cicer arietinum provides a resource for trait improvement. Abbo, S.
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