​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Un modello minimo per la crescita esponenziale di una popolazione microbica

Modelo SIR com taxa de mortes.

Un modello minimo per la crescita esponenziale di una popolazione microbica, con popolazione massima limitata

Un modello minimo per la crescita esponenziale di una popolazione microbica, con popolazione massima limitata

For at least some period of time there are many situations in which the growth of a population (or some other type of stock) is directly proportional to the size of the stock.  For example, the initial rate of growth when an invasive species is introduced, money in the bank given a fixed interest rate and no withdrawals, etc.  If material or energy are in any way necessary, unconstrained growth eventually must become constrained.

NICOLE DESARIO 

AP BIOLOGY 

JUNE 2013


There are many factors that lead to an increased risk of osteoporosis later in life. Some of these risks are congenital; fixed risks that were acquired during fetal development. Other risks are created or reduced by an individual depending on their lifestyle; which make them unfixed variables. 

Definition: OSTEOPOROSIS (Also known as degenerative bone disease) - "is a disease of bones that leads to an increased risk of fracture. In osteoporosis, the bone mineral density (BMD) of an individual is reduced, bone micro-architecture deteriorates, and the amount and variety of proteins in bone and variety of proteins in bone are altered. Osteoporosis is defined by the World Health Organization as a bone mineral density of 2.5 standard deviations or more below the mean peak bone mass (average of young healthy adults)."

NON-MODIFIABLE RISK FACTORS (Explained)

Age: Increased age increases likelihood of developing osteoporosis

Sex: Females are more likely to experience osteoporosis fragility fractures

Race: Osteoporosis is more common in people of European and Asian decent

Frame: Thin-framed individuals do not stress their bones as much as heavier-set individuals, and therefore do not have as "thick" bones, and are more likely to develop fragile bones (osteoporosis) 

Family history: 30 genes are linked to development of osteoporosis, so an individual can be anywhere between 25 and 80% more likely to develop osteoporosis if it exists in the family. (my mother has it, so I am very likely to develop it if I don't actively make the efforts to protect my bones from degenerating over time.)

Insufficient Prenatal Care: During development in the womb if a fetus does not receive appropriate nutrition, it may develop malnutrition-related deficiency diseases.

(POTENTIALLY) MODIFIABLE RISK FACTORS (Explained)

Smoking/Drinking: Excessive use could lead to increased risk because alcohol use decreases your ability to absorb nutrients. It interferes with the absorption of calcium and Vit D (stomach, pancreas and liver affected). Alcohol also kills osteoblasts, the bone-making cells. It also increases bone-damaging hormones cortisol and parathyroid hormone 

Medication Use: Some medications increase risk of osteoporosis however discontinuing use of said medications is often impossible, and therefore the modifiable risk is non-modifiable at times.

Dietary Habits: Majority of bone development happens before an individual reaches the age of 20, so if dietary requirements of calcium, vitamin D, and phosphorus are insufficient, there will be a greater chance of osteoporosis later in life. 

Hormone Levels: In females, estrogen deficiency following menopause or oophorectomy is correlated with rapid reduction in bone mineral density, while in men, a decrease in testosterone levels has a comparable (but less pronounced) effect.

Sedentary Lifestyle: Staying active and stressing your bones decreases chances of osteoporosis because it encourages osteoblastic activity, if an individual is extremely sedentary, (coupled with a thin frame possibly) they are very susceptible to osteoporosis, and should consider getting active. Also, an individual with more sun exposure absorbs more Vit D.

Fractures: Increased breakage of bones creates weak points where BMD cannot recover to what it was prior to the fracture. Individuals should stay out of fights, reduce falling, and avoid clumsy behavior.

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

A model of the exponential growth and collapse of E. coli.

biology project

​Modelo retirado do link 

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Volterra equations

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.