Interview Questions for Hop Breeding and Selection

Hop variety selection is a complex process aiming to identify superior genotypes based on various desirable traits. It involves a multi-step approach combining phenotypic evaluation and, increasingly, genotypic analysis.

• Phenotypic Selection: This traditional method involves evaluating plants in the field based on observable characteristics like yield, aroma, alpha acid content (bitterness), beta acid content (stability), disease resistance, and cone morphology. Experienced hop growers visually assess these traits over multiple years, selecting the best performing plants. For example, a breeder might visually assess cone size and density, noting which plants consistently produce larger, denser cones.
• Clonal Selection: High-performing individual plants are vegetatively propagated (through cuttings) to create clones. This ensures the superior genetic makeup is replicated, eliminating the need to rely on seed propagation which introduces genetic variation. This is crucial as hop is dioecious (separate male and female plants), and breeding requires controlled crosses.
• Genotypic Selection (Marker-Assisted Selection): This modern approach leverages DNA markers linked to desirable traits. It speeds up the selection process by identifying superior plants at an early stage, even before they flower and produce cones. This is particularly useful for traits like disease resistance that take longer to assess phenotypically.
• Pedigree Selection: This involves tracing the lineage of high-performing varieties to identify superior parents for future crosses. This builds upon the knowledge gained from previous generations of hop breeding.

Genetic markers play a vital role in accelerating and improving the efficiency of hop breeding programs. These markers are specific DNA sequences associated with particular traits of interest.

• Marker-Assisted Selection (MAS): MAS allows breeders to select plants possessing desirable alleles (gene variants) for traits like disease resistance, aroma compounds, or alpha acid content, even before these traits are expressed phenotypically. This saves time and resources, as only plants with the desired genetic makeup are selected for further propagation and field trials.
• Genotyping-by-Sequencing (GBS): This high-throughput technology allows simultaneous analysis of thousands of markers across numerous hop genotypes. This comprehensive dataset facilitates the identification of genetic regions associated with complex traits and improves the accuracy of selection.
• Quantitative Trait Loci (QTL) Mapping: QTL mapping is used to identify genomic regions (QTLs) that control the expression of quantitative traits (those that vary continuously, such as yield or alpha acid content). Once identified, markers linked to favorable QTLs can be used in MAS. For example, if a QTL is found to be associated with increased alpha acid content, then markers closely linked to this QTL can be used to identify superior plants early in the breeding process.

Overall, genetic markers enable breeders to make more informed decisions, resulting in faster progress towards the development of improved hop varieties.

Developing disease-resistant hop varieties is crucial for sustainable hop production. Several challenges hinder this process:

• Complexity of Disease Resistance: Disease resistance is often controlled by multiple genes, making it difficult to identify and select for effective resistance through breeding.
• Rapid Evolution of Pathogens: Hop pathogens can rapidly evolve, overcoming the resistance mechanisms developed in newly released varieties. This necessitates ongoing breeding efforts to stay ahead of pathogen adaptation.
• Environmental Factors: Environmental conditions such as temperature and humidity significantly influence disease development. A variety that exhibits good resistance in one environment may be susceptible in another.
• Limited Genetic Diversity: The genetic base of commercially grown hops is relatively narrow, limiting the range of resistance genes available for selection.
• Time-Consuming Process: Developing disease-resistant varieties takes many years, requiring extensive field testing and evaluation in diverse environments.

Addressing these challenges often involves combining traditional breeding methods with molecular techniques like MAS and the introduction of resistance genes from wild hop relatives.

Assessing the aroma and bittering properties of hop varieties involves a combination of chemical analysis and sensory evaluation.

• Chemical Analysis: High-performance liquid chromatography (HPLC) is used to quantify the levels of different aroma compounds (e.g., esters, terpenes, thiols) and bittering acids (alpha and beta acids) in hop cones. This provides an objective measurement of the aroma and bitterness potential.
• Sensory Evaluation: Trained sensory panels evaluate the aroma and taste profiles of hop varieties. They describe and rate the intensity and quality of different aroma attributes (e.g., citrusy, floral, earthy, spicy). Sensory evaluation provides a subjective assessment, adding another dimension to the evaluation process. It captures the complex interplay of various compounds contributing to the overall aroma profile.
• Comparative Analysis: Results from chemical analysis and sensory evaluation are compared to establish the relationship between the chemical composition and perceived sensory attributes. For example, high levels of certain esters might be correlated with a fruity aroma profile, as assessed by the sensory panel. This allows breeders to develop varieties with specific aroma profiles.

Climate change poses significant threats to hop cultivation, impacting yield, quality, and disease susceptibility. This necessitates adapting breeding strategies to develop more resilient varieties.

• Increased Temperatures: Higher temperatures can reduce hop yield and negatively impact the production of desirable aroma and bittering compounds. Breeding programs focus on selecting varieties with increased heat tolerance.
• Altered Precipitation Patterns: Changes in rainfall patterns, including increased droughts and extreme rainfall events, can affect hop growth and disease susceptibility. Breeders aim to select for drought tolerance and resistance to waterlogged conditions.
• Pest and Disease Pressure: Climate change can alter the distribution and severity of pests and diseases, potentially increasing the need for disease-resistant varieties. Breeding programs are incorporating resistance to emerging threats.
• Shifting Growing Regions: Climate change may make some traditional hop-growing regions less suitable for cultivation, necessitating exploration of new growing areas and the development of varieties adapted to different climatic conditions.

Adapting to these challenges involves combining traditional breeding techniques with advanced genomic tools and detailed climate modelling to predict future growing conditions and select appropriate varieties.

Hop breeding for improved yield and quality involves a multi-faceted approach aiming to enhance both the quantity and quality of hop cones.

• Yield Improvement: This focuses on selecting varieties with increased cone production per plant. Factors influencing yield include vine growth habit, cone size and density, and resistance to diseases that reduce yields. Breeding programs may employ techniques like recurrent selection or marker-assisted selection to improve yield-related traits.
• Quality Enhancement: This involves improving the concentration of desirable aroma compounds, alpha and beta acids, and other constituents that contribute to beer quality. Sensory evaluation and chemical analysis play important roles in determining the quality of hops.
• Combining Traits: Breeders strive to develop varieties that combine high yield with desirable quality attributes. This requires careful selection and crossing of superior parent plants with desirable trait combinations.
• Adaptation to Growing Conditions: Yield and quality are significantly influenced by environmental conditions. Breeding aims to improve adaptability to variations in climate, soil type, and pest pressure.

Breeding for improved yield and quality often entails a balance between these two factors, as increasing yield might compromise quality, and vice versa. Therefore, careful evaluation and selection of superior genotypes are essential.

Several breeding systems are employed for hops, each with its own advantages and limitations.

• Sexual Breeding: This involves controlled crosses between selected parent plants to create new varieties with superior traits. This is the most common approach for generating novel genetic combinations and improving multiple traits simultaneously. It is a time-consuming process, however, requiring meticulous control of pollination and selection of offspring.
• Asexual Propagation (Clonal Selection): This involves vegetatively propagating superior plants through cuttings, preserving the exact genetic makeup of the selected plants. It offers faster multiplication of superior genotypes compared to sexual breeding. However, it doesn’t create new genetic combinations and offers limited possibilities for genetic improvement.
• Somatic Hybridization: This advanced technique involves fusing protoplasts (cells with their cell walls removed) from different hop varieties to create hybrids with combined desirable traits. It allows crossing of incompatible varieties that cannot be crossed sexually. It is technologically demanding and only recently becoming more accessible.
• Genetic Transformation: This involves introducing foreign genes into hop plants to enhance specific traits like disease resistance or aroma production. This is a powerful but complex technology with regulatory challenges and some public perception barriers.

The choice of breeding system depends on the specific objectives, available resources, and time constraints. Often, a combination of these methods is employed to achieve desired improvements efficiently.

Hop propagation primarily relies on vegetative methods, as sexual reproduction (from seed) often results in significant variation and loss of desirable traits. My experience encompasses several techniques.

• Softwood Cuttings: This involves taking cuttings from young, actively growing shoots in spring. These are treated with rooting hormone and planted in a moist medium, ideally a mist propagation system to maintain high humidity. Success depends on timing and environmental conditions.
• Hardwood Cuttings: These are taken from dormant canes in late fall or winter. They require longer rooting times and are generally less successful than softwood cuttings, but are a viable option for preserving genetic material.
• Layering: This is a simple technique where a low-growing cane is bent to the ground and buried, encouraging root development at the buried portion. Once rooted, the layered section can be separated and planted as a new plant.
• Crown Division: This method involves separating established hop plants into smaller sections, each with its own root system and growing points. This is a relatively simple technique but can damage the parent plant if not done carefully.

In my work, we carefully select superior mother plants based on desirable traits like yield, alpha acid content, and disease resistance. We then propagate these plants using the most suitable method based on the available resources and the time of year. We meticulously track the performance of each propagation method to optimize our techniques and ensure consistent success in creating new planting material.

Evaluating genetic diversity in a hop breeding program is crucial for maintaining adaptability and preventing inbreeding depression. We use a multi-faceted approach:

• Morphological Characterization: Observing visible traits like cone shape, size, and color provides initial insights into the genetic variation. We carefully document these characteristics.
• Molecular Markers: We employ techniques like SSR (Simple Sequence Repeat) and SNP (Single Nucleotide Polymorphism) analysis. These molecular markers can pinpoint unique genetic variations in different hop genotypes. This gives us a far more detailed understanding of genetic diversity than morphology alone.
• Pedigree Analysis: Tracking the lineage of our hop varieties through meticulous record-keeping allows us to assess genetic relationships and identify potential bottlenecks in the gene pool. We aim to minimize genetic overlap through careful selection of parent plants.
• Genome-Wide Association Studies (GWAS): For more complex traits, we perform GWAS. This technique links specific DNA sequences to desirable traits, allowing us to identify genes responsible for yield, disease resistance, aroma compounds, etc. This can significantly guide breeding decisions.

The data obtained from these various methods is analyzed using statistical software to create comprehensive assessments of genetic diversity, allowing us to strategically manage the genetic resources within our program and maximize the chances of finding elite varieties.

Hop variety registration and intellectual property protection are essential steps to secure the rights to a newly developed variety. The process generally involves:

• Detailed Documentation: Extensive documentation of the variety’s unique characteristics, performance data, and origin is required. This usually includes detailed morphological descriptions, chemical analyses (alpha and beta acids), and yield data.
• Distinctness, Uniformity, and Stability (DUS) Testing: This rigorous testing confirms the variety’s distinctiveness from existing varieties, its uniformity within a population, and its stability over multiple generations. This is often conducted by official testing agencies.
• Variety Registration: Once DUS testing is passed, the variety is submitted for official registration with the relevant authority. In the US, this is often the Plant Variety Protection Office. Registration grants exclusive rights to the breeder for a set period (usually 18 years).
• Intellectual Property Protection: Parallel to registration, breeders often explore additional intellectual property avenues like patents to protect specific aspects of the variety or its development process, such as unique breeding techniques. Trademarks can protect the variety name.

Properly navigating this process ensures breeders can commercially exploit their new varieties, providing an incentive for continued investment in research and development. Failure to secure protection can lead to unauthorized propagation and financial losses.

Pest and disease management in hop breeding trials is critical to obtaining reliable data and protecting the genetic integrity of our promising varieties. We employ an integrated pest management (IPM) strategy, balancing preventative measures with targeted interventions:

• Resistant Cultivars: Selecting varieties with inherent resistance to major pests and diseases is our first line of defense. Genetic resistance minimizes the need for chemical interventions.
• Scouting and Monitoring: Regularly inspecting plants for signs of pests and diseases allows for early detection and prevents widespread outbreaks. We use both visual inspection and specialized traps.
• Cultural Practices: Good agricultural practices like proper spacing, irrigation, and fertilization create a healthier environment for the hops, making them less susceptible to pests and diseases. We optimize these practices for the specific needs of each variety.
• Biological Control: We explore the use of beneficial insects and microorganisms to control pests and pathogens, reducing reliance on synthetic pesticides. For example, specific insects might be used to control aphids.
• Chemical Control (Integrated Approach): In cases where other methods are insufficient, we use targeted chemical control only when absolutely necessary, following strict guidelines and prioritizing products with minimal environmental impact.

A detailed record of all interventions, including the type of pest or disease, treatment method, and its effectiveness, is crucial for future decision-making and the ongoing refinement of our IPM strategy. Our goal is always to balance crop protection with sustainability and environmental responsibility.

Hop cone quality is multifaceted and crucial for beer production. Key factors influencing it include:

• Alpha Acid Content: This is the primary determinant of bitterness in beer. Higher alpha acid content allows for less hop usage, reducing costs and improving efficiency.
• Beta Acid Content: Beta acids contribute to the overall bitterness and stability of the beer, also influencing the overall aroma profile.
• Aroma Compounds: Numerous volatile compounds contribute to the unique aroma profile of hop cones. The balance and concentration of these compounds influence the flavor and aroma characteristics of the beer.
• Cone Size and Shape: These factors influence both the yield and the ease of processing. Larger, uniform cones are generally preferred.
• Disease and Pest Resistance: Disease-free and pest-free cones are essential for high-quality hop production. Damage to the cones can affect the quality and quantity of the valuable components.
• Harvest Timing: The optimal harvest time depends on the specific variety and its desired characteristics. Early or late harvesting can negatively impact cone quality.

Our breeding program rigorously assesses these factors through detailed chemical analysis and sensory evaluations, aiming to develop varieties that consistently provide high-quality cones with desirable brewing characteristics. We use sophisticated analytical equipment and sensory panels of experienced beer professionals to evaluate the quality.

Biotechnology offers powerful tools for advancing hop breeding. Techniques we employ include:

• Marker-Assisted Selection (MAS): This technique uses DNA markers linked to desirable traits, allowing for early selection of superior individuals before they even produce cones. This speeds up the breeding cycle and increases efficiency.
• Genomic Selection (GS): GS uses genome-wide marker data to predict the breeding value of individuals. It helps in selecting the best parent combinations for higher chances of success.
• Gene Editing (CRISPR-Cas9): This technology allows for precise modification of the hop genome, potentially enhancing specific traits like disease resistance, aroma profiles, or alpha acid content. It’s a promising area but needs careful ethical and regulatory consideration.
• Tissue Culture: This technique facilitates the rapid multiplication of elite plants, enabling the large-scale propagation of superior varieties. It’s also useful for disease eradication.

While biotechnology presents incredible opportunities, we proceed cautiously, adhering to strict ethical guidelines and regulatory frameworks. We prioritize sustainability and responsible innovation in our application of these technologies. The ultimate goal is to develop superior hop varieties while maintaining biodiversity and protecting the environment.

Statistical analysis is integral to every aspect of hop breeding. We use various statistical methods to analyze data collected during trials and experiments.

• Analysis of Variance (ANOVA): This is used to compare the means of different hop varieties for various traits (e.g., yield, alpha acid content) and assess the statistical significance of the differences.
• Regression Analysis: Used to model the relationships between various factors (e.g., environmental conditions, plant characteristics) and the traits of interest. For example, we might model the relationship between fertilizer application and yield.
• Principal Component Analysis (PCA): PCA is employed to reduce the dimensionality of data and identify the most important factors influencing hop quality and yield.
• Genomic Selection Models: These sophisticated statistical models are used to predict the performance of individuals based on their genomic information, significantly accelerating the selection process.
• Mixed Models: These account for the influence of random factors such as environmental variation and genetic relationships between plants, enhancing the accuracy of the analysis.

We utilize specialized statistical software packages (e.g., R, SAS) to perform these analyses and interpret the results. This data-driven approach is crucial for making informed decisions, guiding our breeding strategies, and maximizing the success of our program. The results of these analyses are carefully documented and help us track progress and make informed decisions.

Ethical considerations in hop breeding are paramount, focusing on environmental responsibility, economic fairness, and social impact. We must prioritize developing varieties that minimize the need for pesticides and fertilizers, reducing the environmental footprint of hop production. This involves selecting for disease resistance and employing sustainable agricultural practices. Furthermore, we need to ensure equitable access to improved hop varieties, preventing monopolies and supporting smaller growers. Open communication and collaboration with stakeholders, including growers, brewers, and consumers, are essential to address potential ethical concerns proactively. For example, a breeding program might focus on developing varieties resistant to downy mildew, reducing the need for chemical treatments and benefiting both the environment and farmer profits, while simultaneously ensuring the availability of these improved varieties to a diverse range of growers.

Data management in hop breeding is crucial. We use sophisticated database systems, often linked to Geographical Information Systems (GIS), to track thousands of hop plants across multiple field trials. Data includes traits like yield, alpha acid content, beta acid content, disease resistance, and aroma profile, collected meticulously across years. We use statistical software like R and SAS to analyze this data, employing techniques like ANOVA (Analysis of Variance), regression analysis, and genomic selection. For example, we might analyze the relationship between specific genetic markers and alpha acid content to identify genes responsible for high alpha acid production, thus aiding in selection. Data visualization tools are vital for presenting complex results clearly to stakeholders.

My experience with hop field trials involves designing experiments following rigorous statistical principles. We employ randomized complete block designs or augmented designs, ensuring that environmental variation is minimized and the effects of different hop varieties can be accurately assessed. Field trials are replicated across multiple locations and years to account for environmental variability and to ensure that the results are robust. Careful record-keeping is essential, with regular observations recorded and detailed photos taken to document plant health and development. For example, in a trial comparing five new hop varieties, we would use a randomized complete block design replicated three times across two locations. We would meticulously assess yield, disease incidence, and cone quality across each replication. Analyzing this data allows us to determine which varieties perform consistently well across diverse environments.

A successful hop breeding program needs several key characteristics. First, a clear breeding objective is critical: are we focusing on yield, alpha acid content, specific aroma profiles, or disease resistance? Second, access to diverse germplasm (the genetic material) is fundamental for creating variation and selecting superior plants. Third, efficient selection methods are crucial, employing both phenotypic (observable traits) and genotypic (genetic) data. Fourth, robust field testing procedures across multiple environments and years allow us to validate the performance of new varieties under various conditions. Finally, strong collaboration with growers and brewers ensures that the new hop varieties are well-suited to market demands. For instance, a brewer might specify a desired aroma profile, guiding the breeding program towards a specific target.

Collaboration is the backbone of successful hop breeding. We work closely with universities, research institutions, growers, and breweries. Universities contribute expertise in genetics and statistical analysis. Research institutions provide access to advanced technologies like genomic sequencing. Growers offer valuable insights into the practical challenges of hop cultivation, and brewers provide feedback on the brewing characteristics of new varieties. This collaborative approach ensures that our breeding efforts are aligned with market needs and produce varieties that meet both agronomic and commercial expectations. For example, collaborating with a brewing company allows us to test new varieties in their brewing process, providing direct feedback on their performance and aroma contribution to the final product.

Ensuring sustainability in hop breeding involves prioritizing the development of varieties that reduce the reliance on pesticides, herbicides, and fertilizers. This includes selecting for disease resistance, drought tolerance, and efficient nutrient use. We also promote integrated pest management strategies and sustainable agricultural practices within the breeding program itself. Furthermore, breeding for varieties with improved malting qualities can reduce the environmental impact of the entire brewing process. We also aim for genetic diversity within our breeding populations to avoid vulnerability to emerging diseases or environmental changes. For example, selecting for varieties with natural resistance to downy mildew reduces the need for chemical fungicides, contributing to a more sustainable farming practice.

Scaling up hop breeding technology presents several challenges. The long generation time of hops (several years from seed to mature plant) slows down the breeding cycle. High costs associated with phenotyping large populations and advanced genomic analyses can be prohibitive. The need for large-scale field trials across diverse environments necessitates significant resources. Moreover, the integration of new technologies, like marker-assisted selection or genomic selection, requires specialized expertise and infrastructure. Overcoming these challenges often involves seeking funding from various sources, partnering with larger organizations to share resources, and adopting efficient high-throughput phenotyping techniques. For instance, using drones to assess disease incidence across large hop fields can significantly speed up data collection and analysis, allowing for greater efficiency in breeding programs.

Genomic selection (GS) is a powerful tool revolutionizing hop breeding by leveraging the entire genome to predict the breeding value of individual plants. Instead of relying solely on phenotypic data (observable traits), GS uses molecular markers across the genome to estimate the genetic merit of a plant for specific traits like yield, alpha acid content, or disease resistance. This allows us to select superior plants even before they express the traits fully, significantly accelerating the breeding cycle.

In my experience, we’ve utilized GS in our hop breeding program to identify superior clones for alpha acid content. We collected genomic data from a diverse panel of hop genotypes and then developed a prediction model using machine learning algorithms. This model allowed us to accurately predict the alpha acid content of new seedlings based on their genomic profiles, enabling us to select the highest-performing plants for further evaluation and release. This approach dramatically reduced the time and resources needed to identify superior varieties, compared to traditional phenotypic selection.

Keeping abreast of the latest hop breeding advances involves a multi-pronged approach. I actively participate in international conferences like those hosted by the American Society for Horticultural Science or the Institute of Brewing and Distilling, which showcase cutting-edge research and facilitate networking with leading experts. I regularly read scientific journals such as Horticultural Science, Journal of the Institute of Brewing, and others specializing in plant breeding and genomics. Online resources like databases of scientific publications (like PubMed) also provide access to a vast amount of information. Additionally, collaboration with researchers in universities and private companies involved in hop genetics is essential for staying informed and at the cutting edge.

Furthermore, engaging in continuous professional development through workshops and training courses dedicated to genomics and advanced breeding techniques ensures my knowledge remains current and practical.

Marker-assisted selection (MAS) uses DNA markers linked to desirable genes to select plants with favorable traits more efficiently. Imagine it like having a map that highlights the location of genes controlling important hop characteristics. Instead of waiting to see if a plant expresses a specific trait (e.g., disease resistance), we can use MAS to directly identify plants carrying the desired gene variant even at the seedling stage. This speeds up the selection process and minimizes the risk of selecting inferior plants.

For instance, if a marker is found strongly associated with resistance to downy mildew, we can directly select seedlings with that marker, increasing the chances of obtaining disease-resistant cultivars. This is particularly important in hop breeding because several crucial traits, such as alpha acid content and disease resistance, are often controlled by multiple genes with complex interactions. MAS simplifies this complexity, significantly enhancing efficiency and accuracy in the breeding process.

CRISPR-Cas9 gene editing technology holds immense potential for hop breeding. CRISPR allows for precise modification of specific genes, unlike traditional breeding methods, which often involve introducing large sections of DNA. This precision enables us to develop new hop varieties with desired traits much more quickly and accurately.

For example, CRISPR could be used to enhance alpha acid production by modifying genes involved in the biosynthetic pathway. Similarly, we could introduce resistance to specific diseases or pests by editing genes that confer susceptibility. In short, CRISPR offers a powerful tool to tailor hop genetics to meet the specific needs of brewers, including improved aroma profiles, higher yields, and enhanced disease resistance.

However, it is crucial to proceed with caution, considering the ethical implications and regulatory requirements surrounding the use of gene-editing technologies in agriculture.

My experience encompasses a wide range of hop varieties, each possessing unique characteristics crucial for brewing. For example, Citra is known for its citrusy and tropical aromas, making it a popular choice for IPAs. Cascade, on the other hand, offers a more classic, floral aroma profile, suitable for various beer styles. Centennial provides a balance of bitterness and aroma, while varieties like Magnum are primarily valued for their high alpha acid content, contributing significantly to beer bitterness.

Beyond aroma and bitterness, other traits like yield, disease resistance, and even the ease of harvesting vary significantly between varieties. Understanding these diverse characteristics is essential for selecting appropriate parents in breeding programs and meeting the specific needs of brewers.

Selecting parent plants for hop breeding programs is a critical step that dictates the success of the program. The selection process involves careful consideration of several factors. First, we need to identify superior parental lines that already excel in specific desirable traits. This selection might be based on field trials data (phenotypic selection), genomic data (genomic selection), or a combination of both.

We aim for genetic diversity among parents to maximize the chances of generating offspring with superior combinations of traits. General combining ability (GCA) and specific combining ability (SCA) are evaluated to assess the suitability of parental combinations. GCA predicts the average performance of offspring from a given parent, while SCA evaluates the interaction between specific parental combinations. Ultimately, the goal is to create offspring that outperform their parents in terms of yield, quality, and disease resistance.

Hops are susceptible to a range of diseases and pests that significantly impact yield and quality. Downy mildew (Pseudoperonospora humuli) is a devastating fungal disease causing significant yield losses. Powdery mildew (Podosphaera macularis) is another prevalent fungal disease affecting hop production. Verticillium wilt, caused by the fungus Verticillium albo-atrum, is a serious soilborne disease that can severely reduce yields.

Among pests, aphids, such as the hop aphid (Phorodon humuli), can transmit viruses and significantly reduce yields. Other notable pests include spider mites and various moth species that damage hop cones. Understanding these threats is crucial for breeding programs focused on developing disease- and pest-resistant hop varieties.