The spread of a genetic mutation in a population of mice can be modeled by the differ- ential equation P, 2P.(1-Р) . (1-3P) where P is the fraction of the mice that have the new gene. (This means that 0 s P a) Find the equilibrium points of this model and determine the stability of each one. b) If 10% of the mice have the new gene (so P-0.1) initially, what fraction of the population will have the new gene in the long run? c) What if the initial fraction is 90% of the mice?
Answers
a) P = 0 and 1 are both stable equilibrium points
b) The only positive root is P = 0, which means that the new gene will not spread in the population.
c) The only positive root is P = 1, which means that the new gene will eventually spread to the entire population.
a) To find the equilibrium points, we need to solve the differential equation P' = 2P(1-P)(1-3P) = 0. This equation has three roots: P = 0, P = 1/3, and P = 1. To determine the stability of each equilibrium point, we need to examine the sign of the derivative of P around each point. We have P' < 0 for P in (0, 1/3), P' > 0 for P in (1/3, 1), and P' < 0 for P > 1. Therefore, P = 0 and P = 1 are both stable equilibrium points, while P = 1/3 is an unstable equilibrium point.
b) If the initial fraction of mice with the new gene is 0.1, we can use the equation P' = 2P(1-P)(1-3P) to find the long-term fraction of mice with the new gene. At equilibrium, we have P' = 0, so we need to solve 2P(1-P)(1-3P) = 0. The only positive root is P = 0, which means that the new gene will not spread in the population.
c) If the initial fraction of mice with the new gene is 0.9, we can again use the equation P' = 2P(1-P)(1-3P) to find the long-term fraction of mice with the new gene. At equilibrium, we have P' = 0, so we need to solve 2P(1-P)(1-3P) = 0. The only positive root is P = 1, which means that the new gene will eventually spread to the entire population.
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Related Questions
I need help with this Biology
Answers
Answer:
A.
Explanation:
All the microbes I were living inside the person's body die when the person dies
A weak acid or base used to neutralize a strong acid or base
Answers
Answer:
To neutralize acids, a weak base is used. Bases have a bitter or astringent taste and a pH greater than 7. Common bases are sodium hydroxide, potassium hydroxide and ammonium hydroxide. Bases are neutralized by using a weak acid. Products for Acid and Base Neutralization
Explanation:
To neutralize acids, a weak base is used. Bases have a bitter or astringent taste and a pH greater than 7. Common bases are sodium hydroxide, potassium hydroxide and ammonium hydroxide. Bases are neutralized by using a weak acid. Products for Acid and Base Neutralization
how do bacteria protect their genetic material and cytoplasm during harsh conditions?
Answers
The predator-prey relationship is a key factor in balancing the resources in the ecosystem. Population size can be affected if this relationship is not balanced. How does the predator-prey relationship affect population size?
Answers
Answer:
a predator kills off the pray, take the predator away and u get too much prey so they eat all the grass or berries and die of starvation
which statement is true about the chemical elements found in living things? question 5 options: only haploid cells contain hydrogen and carbon unicellular organisms have different types of elements from multicellular organisms. animal cells and plant cells contain very different elements. all cells contain the elements carbon, nitrogen, hydrogen, and oxygen.
Answers
The statement that is true about the types of all cells contain the elements carbon, nitrogen, hydrogen, and oxygen.
What are macro-elements?Macro-elements are elements that are needed by living organisms in large quantities.These elements are present in living cells to aid in growth and development. Examples of these elements include;CarbonHydrogenOxygenNitrogenTherefore, the statement that is true about the types of chemical elements in living cells is that all cells contain the same key elements such as carbon, nitrogen, and oxygen.Macro elements include chloride, calcium, phosphorous, magnesium, sodium, potassium, and iron. The trace elements include cobalt, boron, chromium, copper, sulfur, iodine, fluoride, selenium, manganese, zinc, and molybdenum Macronutrients, or macros, are essential nutrients the body needs in large quantities to remain healthy. Macronutrients provide the body with energy, help prevent disease, and allow the body to function correctly. There are three main types of macronutrients: proteins, fats, and carbohydrates.To learn more about macro-elements refers to:
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What happens during a claustrophobic attack?
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It can trigger symptoms of anxiety ranging from mild sweating or trembling to fainting or a panic attack.
It can trigger symptoms of anxiety ranging from mild sweating or trembling to fainting or a panic attack.Common claustrophobia triggers include small rooms, elevators, closets, MRI scanners, airplanes, and other small or tight spaces.
PLZZZZZZZZ HELPPPPP ASAPPPPPPP IM TIMED
Answers
Answer: mouth = chemical physical stomach = chemical physical small and large = physical
Explanation: my mom taught me this she is a doctor
Answer:
Explanation:
Mouth is physical and chemical, the act of chewing is physical by tearing food into smaller pieces, and your saliva is chemical by beginning to break down carbohydrates.
Stomach is chemical and physical.
Churning in the stomach and peristalsis is also part of mechanical digestion. Peristalsis is the involuntary contraction and relaxation of the muscles in your stomach. Chemically your stomach breaks down proteins with hydrochloric acid.
Small Intestine has both, for physical it has segmentation and peristalsis, which helps mix the food mush with digestive juices, and chemical with the secretions of enzymes that help break down protein, fat, carbs, in order for the body to absorb different molecules.
Large Intestine is also both. Physically water is absorbed back into the body. Chemically, bacteria breaks down undigested materials, and helps produce certain vitamins.
Which component in blood is directly related to Hemophilia? Why?
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Answer:
Hemophilia is a hereditary bleeding disorder caused by a deficiency in one of two blood clotting factors: factor VIII or factor IX. Several different gene abnormalities can cause the disorder.
Explanation:
When does genetic mutation occur
Answers
So basically they happen when the dna is being replicated but a mistake occurs and isn’t corrected quickly xoxo
Rocks that undergo an elastic strain Group of answer choices
Fold by plastic strain. Break. Return to their original shape after
the stress is removed. Lengthen or are pulled apart.
Answers
The rocks that undergo an elastic strain are the ones that return to their original shape after the stress is removed.
When rocks experience elastic strain, they deform temporarily under stress but retain their ability to spring back to their original shape once the stress is released. This elastic behavior occurs due to the rearrangement of rock particles and the stretching of chemical bonds within the rock structure. The rocks exhibit a reversible deformation, meaning that they can withstand stress up to a certain point without permanent damage.
Elastic strain is commonly observed in materials such as rubber bands or springs, which can be stretched or compressed and then return to their original shape. Similarly, rocks with elastic properties can undergo temporary deformation without undergoing permanent changes. This elasticity is a result of the rock's ability to store and release strain energy.
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describes how an organelle contributes to the ability of the cell to perform life functions?
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Answer:
Cell organelles are small structures that exist within cells and perform specialized functions
Based upon the presence and absence of membrane cell organelles can be classified into three types:
Membrane less: Cell organelle that lack membrane for example ribosomes they are not bounded by any membrane. Single membraned: Cell organelle that are bounded by single membrane but they are only found in Eukaryotic cell. For example lysosome, Endoplasmic reticulum, lysosome, vacuole. Double membraned: Cell organelle that are bounded by double membrane. Example chloroplast and mitochondria, they are only present in eukaryotic cell.1.
The fox population in a certain region has an annual growth rate of 5 percent per year. It is estimated that the population in the year 2000 was 23500 . (a) Find a function in the form \( P(t)=a b^{t}
Answers
The fox population can be modeled using an exponential growth function of the form P(t) = ab^t, where P(t) represents the population at time t, a is the initial population, b is the growth factor, and t represents the number of years.
In this case, the population in the year 2000 was given as 23500. We can use this information to find the values of a and b in the exponential growth function. Since the population has an annual growth rate of 5 percent, the growth factor (b) would be 1 + growth rate = 1 + 0.05 = 1.05.
To find the value of a, we substitute the given population value for the year 2000 into the exponential growth function: P(0) = ab^0 = a(1.05)^0 = a. Therefore, a = 23500.
Now we have the values of a and b, and the exponential growth function for the fox population becomes P(t) = 23500 * (1.05)^t, where t represents the number of years since the year 2000.
This function can be used to estimate the fox population for any given year after 2000 by substituting the desired value of t into the equation.
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What is the definition of cell
Answers
Answer:
Small and sparsely furnished room, especially in a prison or convent.
"the detainees are together in cells with capacity for four or five people"
Cell of a honeycomb.
Explanation:
I hope to help you
A 10-micrometer cell is viewed through a 10x objective and a 10x eyepiece. How large will the cell appear to the microscope user?
Answers
Answer:
A 10x Eyepiece magnifies 10 times; in other words, an object viewed through the eyepiece, in focus, will seem ten times larger than normal. ... In this case, a 10x Eyepiece and a 10x Objective Lens would combine to show a 100x image, or an image 100 times the actual size.
Explanation:
If a 10-micrometer cell is viewed through a 10x objective and a 10x eyepiece, the cell will appear 100 times bigger than normal to the microscope user.
Magnification is defined as the ratio of the image distance to the object distance.
Magnification determines the number of times an image is larger or smaller than the object.
If the magnification is greater than 1, it means that the image is enlarged but if the magnification is less than 1, the image is a diminished image.
According to the question, if a 10-micrometer cell is viewed through a 10x objective and a 10x eyepiece, the total magnification will be:
M = Mo × Me
M = 10 × 10
M = 100
This shows that if a 10-micrometer cell is viewed through a 10x objective and a 10x eyepiece, the cell will appear 100 times bigger than normal to the microscope user.
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Check the image for question
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Hope this helps
which of the following do meiosis and mitosis have in common
Answers
Answer:
The first one:
A. Meiosis and Mitosis have something in common in a sense that they are considered to be reduction divisions as the processes result in additional cells.
The chemical or molecule that the enzyme is changing or affecting is _____________
activation energy
a substrate
an active site
Answers
Answer:
A substrate
Explanation:
Do plant cells always have cell walls
Answers
Answer: no they don’t they only have one
Explanation:
Arwan finds a piece of quartz while hiking in the mountains. When he returns to school, he takes it to his science teacher. She helps him determine the mass to be 788.9 g. She also tells Arwan that the density of quartz is 2.6 .
Answers
The volume of Arwan’s piece of quartz is 303.42 cm³
What is volume?Volume is described as a measure of occupied three-dimensional space or the amount of space that a substance or object occupies, or that is enclosed within a container.
Mass of the Quartz piece brought by Arwan = 788.9 g
Density of the quartz = 2.6g/ cm³
Density of the substance is described as mass present in per unit volume of the substance. It is measured in gram per centimeter cube.
Density = mass/volume
2.6 = 788.9/ volume
volume = 303.42 cm³ .
Density is denoted as mass of a unit volume of a material substance. The formula for density is d = M/V, where d is density, M is mass, and V is volume.
Density has the units of measurement in mass divided by volume such as grams per centimeters cube (g/cm3) or kilograms per liter (kg/l)
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The complete question is:
Arwan finds a piece of quartz while hiking in the mountains. When he returns to school, he takes it to his science teacher. She helps him determine the mass to be 788.9 g. She also tells Arwan that the density of quartz is 2.6 . What is the volume of Arwan’s piece of quartz?
What is atmospheric perspective? a. the effect produced by rounding objects to appear three-dimensional. b. the effect produced by techniques that make objects appear to go back into the distance, creating a realistic look. c. the effect produced by diffusion of light in the atmosphere whereby more distant objects have less clarity of outline and are lighter in tone. please select the best answer from the choices provided a b c
Answers
The Atmospheric perspective is the effect produced by diffusion of light in the atmosphere whereby more distant objects have less clarity of outline and are lighter in tone.
What is atmospheric perspective?Atmospheric perspective refers to a form.of illusional effect and atmosphere produce or reflect on an object. It is also the method use to create the illusion of depth in a painting or drawing work by changing the colour so as to simulate changes effected by the atmosphere on the colours of things seen at a distance.
Therefore, The Atmospheric perspective is the effect produced by diffusion of light in the atmosphere whereby more distant objects have less clarity of outline and are lighter in tone.
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Answer:
Its CExplanation:
Many deciduous trees, such as sycamores and aspens, drop their leaves each year. After some time, the nutrients from the leaves become part of the soil and are available again. Which of these types of organisms in an ecosystem is necessary for the nutrients in dropped leaves to become available?
A. consumers
B. decomposers
C. producers
D. herbivores
Answers
Answer: a
Explanation:
Many deciduous trees, such as sycamores and aspens, drop their leaves each year. After some time, the nutrients from the leaves become part of the soil and are available again. These type of the nutrients are made available to the soil again by the decomposers.
Deciduous trees are the trees that shed their leaves that sheds off their leaves once in a year usually in autumn.
Decompsers are the organisms that feed on the dead living organisms and their waste to produce energy for themselves including dead matter of plants, animals, fallen off leaves, excreta and other items.
They release the nutrients that are sequestrated in organic matter into the soil so that it can be used up by the plants.
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Is osmosis an example of facilitated diffusion or active transport ? explain why.
Answers
Answer:
Diffusion I think.....
2. What is the term for the waste
generated from ore mines?
slurry
tailings
impoundments
Answers
Slurry is a liquid concrete or cement
Impoundments are enclosures of water
If brown fur is the dominant trait observed in a population
of rabbits, which possible genotypes could a rabbit with
brown fur have?
Answers
B : brown fur
b: not brown/ white
Heterozygous: Bb
Homozygous : BB
In some plants, phloem cells are connected end-to-end by sieve plates, creating a direct connection between the cytoplasm of phloem cells. What is one possible benefit of having phloem cells connected in this manner?
Answers
Answer:
Explanation:
This is because the sieve plate interconnected like that help in exchange of substances or transport of substances between element cell and it act as a barrier to prevent the sap from been loss when phloem is damaged or cut. The sieve plates form the sieve tube which is the conducting element of the phloem. It is formed from series of elongated cells that are interconnected by perforations in their walls.
Head lice, small insects, are found on two elementary school students. As these two students
interact on the playground, some lice move from one student to the other. Which of the following is
most likely taking place in this scenario?
A-Gene flow
B-genetic drift
C-natural selection
D-nonrandom mating
Answers
Archaic Homo sapiens appear in the fossil record during the Pleistocene epoch, an epoch marked by great climatic stability. true/ false
Answers
False. The Pleistocene epoch was actually marked by a series of glacial and interglacial periods, characterized by significant climatic fluctuations.
Archaic Homo sapiens, also known as Homo heidelbergensis, first appeared in the fossil record around 600,000 years ago, during the Middle Pleistocene. These early humans were able to adapt to changing environmental conditions, including fluctuations in temperature and sea level, and they were capable of using fire and creating more sophisticated tools than their predecessors. The Pleistocene epoch was actually marked by a series of glacial and interglacial periods, characterized by significant climatic fluctuations. However, their survival was still largely dependent on their ability to navigate a constantly changing and challenging landscape. The Pleistocene epoch ultimately came to an end around 11,700 years ago, marking the transition to the current Holocene epoch, which has been characterized by relatively stable climatic conditions.
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What is the function of digestive function? Explain in brief
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Answer:
The function of the digestive system is digestion and absorption. Digestion is the breakdown of food into small molecules, which are then absorbed into the body. The digestive system is divided into two major parts: The digestive tract (alimentary canal) is a continuous tube with two openings: the mouth and the anus
Explanation:
I HOPE IT'S HELP :)What are the main functions of polysaccharides in plants?
• A. Provide water and oxygen
O B. Remove carbon and minerals
O C. Provide support and energy
• D. Capture water and sunlight
Answers
Answer:
The main functions of polysaccharides in plants are :-
C. Provide support and energy
Hope it helps!
Answer:
The answer is C.
C. Provide support and energy
Explanation:
2 characteristics of bisexual flowers
Answers
Answer:Bisexual flowers are complete flowers, containing both androecium and gynoecium in one flower. Therefore, bisexual flowers contain both stamens and pistils in the same flower. Hence, bisexual flowers are called hermaphrodite or androgynous flowers as well.
Explanation: