product rule

Examples of product rule in the following topics:

• Rules of Probability for Mendelian Inheritance

  • The product rule of probability can be applied to this phenomenon of the independent transmission of characteristics.
  • The word "and" is a signal to apply the product rule.
  • Consider how the product rule is applied to a dihybrid : the probability of having both dominant traits in the F2 progeny is the product of the probabilities of having the dominant trait for each characteristic.
  • The word "or" indicates that you should apply the sum rule.
  • You should also notice that we used the product rule to calculate the probability of PH and QT and also the probability of PT and QH, before we summed them.

• Mendel's Law of Independent Assortment

  • The sorting of alleles for texture and color are independent events, so we can apply the product rule.
  • Round/green and wrinkled/yellow offspring can also be calculated using the product rule as each of these genotypes includes one dominant and one recessive phenotype.
  • Note that this process is a diagrammatic version of the product rule.

• Chemical Reactions and Molecules

  • According to the octet rule, elements are most stable when their outermost shell is filled with electrons.
  • An arrow is typically drawn between the reactants and products to indicate the direction of the chemical reaction.
  • In reversible reactions, reactants are turned into products, but when the concentration of product goes beyond a certain threshold, some of these products will be converted back into reactants; at this point, the designations of products and reactants are reversed.
  • This back and forth continues until a certain relative balance between reactants and products occurs: a state called equilibrium.
  • In biological reactions, however, equilibrium is rarely obtained because the concentrations of the reactants or products or both are constantly changing, often with a product of one reaction being a reactant for another.

• Abiotic Factors Influencing Plant Growth

  • Temperature and moisture are important influences on plant production (primary productivity) and the amount of organic matter available as food (net primary productivity).
  • Almost all life on earth is directly or indirectly reliant on primary production.
  • Very productive biomes have a high level of aboveground biomass.
  • The magnitude and distribution of global primary production varies between biomes.
  • However, warm and wet climates have the greatest amount of annual biomass production.

• Productivity within Trophic Levels

  • Productivity, measured by gross and net primary productivity, is defined as the amount of energy that is incorporated into a biomass.
  • The rate at which photosynthetic primary producers incorporate energy from the sun is called gross primary productivity.
  • An example of gross primary productivity is the compartment diagram of energy flow within the Silver Springs aquatic ecosystem .
  • The net productivity is then available to the primary consumers at the next trophic level.
  • Explain the concept of primary production and distinguish between gross primary production and net primary production

• Early Biotechnology: Cheese, Bread, Wine, Beer, and Yogurt

  • Some of the earliest biotechnology used prokaryotes for the production of food products such as cheese, bread, wine, beer, and yogurt.
  • Cheese production began around 4,000–7,000 years ago when humans began to breed animals and process their milk.
  • Additionally, evidence suggests that cultured milk products, such as yogurt, have existed for at least 4,000 years.
  • These products use prokaryotes (as with cheese) to provide flavor and to protect the food product from other unwanted microbes.
  • Discuss the origins of food biotechnology as indicated by the production of cheese, bread, wine, beer, and yogurt

• Production of Vaccines, Antibiotics, and Hormones

  • Biotechnological advances in gene manipulation techniques have further resulted in the production of vaccines, antibiotics, and hormones.
  • Antibiotics are biotechnological products that inhibit bacterial growth or kill bacteria.
  • Previously, it was only possible to treat diabetes with pig insulin, which caused allergic reactions in humans because of differences in the gene product.
  • The bacteria was then grown and the hormone isolated, enabling large scale commercial production.

• Hormonal Regulation of the Reproductive System

  • In both males and females, FSH stimulates gamete production and LH stimulates production of hormones by the gonads.
  • An increase in gonad hormone levels inhibits GnRH production through a negative feedback loop .
  • FSH production is inhibited by the hormone inhibin, which is released by the testes.
  • LH stimulates production of the sex hormones (androgens) by the Leydig cells of the testes.
  • Prolactin stimulates the production of milk by the mammary glands, following childbirth.

• Pineal Gland and Gonads

  • The pineal gland is responsible for melatonin production, while the gonads secrete hormones relating to sexual characteristic development.
  • The rate of melatonin production is affected by the photoperiod.
  • During the day photoperiod, little melatonin is produced; however, melatonin production increases during the dark photoperiod (night).
  • Their main role is the production of steroid hormones.
  • The testes produce androgens, which allow for the development of secondary sex characteristics and the production of sperm cells.

• Speciation

  • There are exceptions to this rule.
  • Many species are similar enough that hybrid offspring are possible and may often occur in nature, but for the majority of species this rule generally holds.