# Biology Models

These models and simulations have been tagged “Biology”.

Causal loop diagram illustrating the goal-seeking pull of Satiation in organisms that ingest food.
Simulation of MTBF with controls

F(t) = 1 - e ^ -λt
Where
• F(t) is the probability of failure
• λ is the failure rate in 1/time unit (1/h, for example)
• t is the observed service life (h, for example)

The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime,
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early Life
If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

Useful Life
The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.

Wearout
The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period.
THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

Simulation of MTBF with controls

F(t) = 1 - e ^ -λt
Where
• F(t) is the probability of failure
• λ is the failure rate in 1/time unit (1/h, for example)
• t is the observed service life (h, for example)

The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime,
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early Life
If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

Useful Life
The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.

Wearout
The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period.
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.
Adapted from ​Fig 5.1 p102 From Thompson's Mind in Life Book
Simulation of MTBF with controls

F(t) = 1 - e ^ -λt
Where
• F(t) is the probability of failure
• λ is the failure rate in 1/time unit (1/h, for example)
• t is the observed service life (h, for example)

The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime,
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early Life
If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

Useful Life
The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.

Wearout
The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period.
THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

This model is a basic model on how the glucose level in blood is maintained.

Clone of Bio103 Predator-Prey Model ("Lotka'Volterra")
Thanks to Insight Author: John Petersen

Edits by Andy Long

Everything that follows the dashes was created by John Petersen (or at least came from his Insight model). I just wanted to make a few comments.

We are looking at Hare and Lynx, of course. Clone this insight, and change the names.

Then read the text below, to get acquainted with one of the most important and well-known examples of a simple system of differential equations in all of mathematics.

http://www.nku.edu/~longa/classes/mat375/mathematica/Lotka-Volterra.nb
------------------------------------------------------------

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system.

For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system.

The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926).  Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them.  Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined.

Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed.

Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey.  It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most predator-prey dynamics in nature.  And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.

The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.
2. The food supply of the predator population depends entirely on the size of the prey population.
3. The rate of change of population is proportional to its size.
4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.
5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey
When multiplied out, the prey equation becomes
dx/dtαx - βxy
The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

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.

Summary of evolution and the modern synthesis with genetics. See also the more recent extended synthesis IM-2099
From Fig 12.2 p317 Pigliucci M and Muller GB (2010) Evolution: The Extended Synthesis

​Predator-prey models are the building masses of the bio-and environments as bio masses are become out of their asset masses. Species contend, advance and scatter essentially to look for assets to support their battle for their very presence. Contingent upon their particular settings of uses, they can take the types of asset resource-consumer, plant-herbivore, parasite-have, tumor cells- immune structure, vulnerable irresistible collaborations, and so on. They manage the general misfortune win connections and thus may have applications outside of biological systems. At the point when focused connections are painstakingly inspected, they are regularly in actuality a few types of predator-prey communication in simulation.

Looking at Lotka-Volterra Model:

The well known Italian mathematician Vito Volterra proposed a differential condition model to clarify the watched increment in predator fish in the Adriatic Sea during World War I. Simultaneously in the United States, the conditions contemplated by Volterra were determined freely by Alfred Lotka (1925) to portray a theoretical synthetic response wherein the concoction fixations waver. The Lotka-Volterra model is the least complex model of predator-prey communications. It depends on direct per capita development rates, which are composed as f=b−py and g=rx−d.

A detailed explanation of the parameters:

• The parameter b is the development rate of species x (the prey) without communication with species y (the predators). Prey numbers are reduced by these collaborations: The per capita development rate diminishes (here directly) with expanding y, conceivably getting to be negative.
• The parameter p estimates the effect of predation on x˙/x.
• The parameter d is the death rate of species y without connection with species x.
• The term rx means the net rate of development of the predator population in light of the size of the prey population.

Reference:

http://www.scholarpedia.org/article/Predator-prey_model

Simulation of MTBF with controls

F(t) = 1 - e ^ -λt
Where
• F(t) is the probability of failure
• λ is the failure rate in 1/time unit (1/h, for example)
• t is the observed service life (h, for example)

The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime,
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early Life
If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

Useful Life
The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.

Wearout
The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period.
A model of the exponential growth and collapse of E. coli.
Un modello minimo per la crescita esponenziale di una popolazione microbica
Model simulating the interactions between sika deer, red deer and wolves in Jutland, Denmark.
The model also includes hunting on the two deer species.
The model kan simulate four conditions: No hunting and no predation, hunting without predation, predation without huning and both hunting and predation.