positive feedback explained births = birth_fraction * population birth_fraction = c, a positive...
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![Page 1: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/1.jpg)
Positive Feedback Explained
Population
Births
Birth Fraction
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Noname 1
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Noname 2
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Noname 3
Births = Birth_Fraction * PopulationBirth_Fraction = c, a positive constant
You are here
![Page 2: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/2.jpg)
Isolate Feedback Loop
Assume all other flows remain unchanged.Check how change in Population affects flow in question.Is Population change reinforced or counteracted by change in flow?Reinforced = positive feedback.Counteracted = negative feedback.
![Page 3: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/3.jpg)
Positive Feedback – Pop Increase
Population
Births
Birth Fraction
Deaths
Table 1
Population(t) = Population(t - dt) + (Births - Deaths) * dtINIT Population = 1000
INFLOWS:Births = Birth_Fraction*PopulationOUTFLOWS:Deaths = 100Birth_Fraction = .11Note numbers
![Page 4: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/4.jpg)
Population Table
Population increases.All flows except Birth remain unchanged.Birth inflow increases.Population increases even more.Reinforces increase.Thus, positive feedback.
Time Population
0 1,000.00
1 1,010.00
2 1,021.10
3 1,033.42
4 1,047.10
5 1,062.28
6 1,079.13
7 1,097.83
8 1,118.59
9 1,141.64
10 1,167.22
11 1,195.61
Final 1,227.13
![Page 5: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/5.jpg)
Graph of Population
900.00
1,000.00
1,100.00
1,200.00
1,300.00
0 1 2 3 4 5 6 7 8 9 10 11 12
Years
Population
![Page 6: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/6.jpg)
Description of Graph
IncreasingIncreasing at an increasing rate Concave up
NOT leveling off Would have to change concavity
What will happen to the population if this continues?
![Page 7: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/7.jpg)
When Population Increases
Population increases by P. To P + P.
Hold other flows unchanged. P = Births + (all other flows in/out:
constant) So without any changes in Birth inflow,
Population will again increase by P.
Births = Birth_Fraction*(P + P). Births increase by Birth_Fraction * P.
Population increases by more than P. By P + Birth_Fraction * P
Reinforces increase in Population.
![Page 8: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/8.jpg)
Positive Feedback – Pop Decrease
Population
Births
Birth Fraction
Deaths
Table 1
Population(t) = Population(t - dt) + (Births - Deaths) * dtINIT Population = 1000
INFLOWS:Births = Birth_Fraction*PopulationOUTFLOWS:Deaths = 120Birth_Fraction = .11
Note change
![Page 9: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/9.jpg)
Population Table
Population decreases.All flows except Birth remain unchanged.Birth inflow decreases.Population decreases even more.Reinforces decrease.Thus, positive feedback.
Time Population0 1,000.00
1 990.00
2 978.90
3 966.58
4 952.90
5 937.72
6 920.87
7 902.17
8 881.41
9 858.36
10 832.78
11 804.39
Final 772.87
![Page 10: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/10.jpg)
Graph of Population
700.00
800.00
900.00
1,000.00
1,100.00
0 1 2 3 4 5 6 7 8 9 10 11 12
Years
Population
![Page 11: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/11.jpg)
Description of Graph
DecreasingDecreasing at an increasing rate Concave down
NOT leveling off Would have to change concavity
What will happen to the population if this continues?
![Page 12: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/12.jpg)
When Population Decreases
Population decreases by |P|. To P + P.
Hold other flows unchanged. P = Births + (all other flows in/out: constant) So without any changes in Birth inflow,
Population will again decrease by |P|.
Births = Birth_Fraction*(P + P). Births decrease by |Birth_Fraction * P|.
Population decreases by more than |P|. By |P + Birth_Fraction * P|.
Reinforces decrease in population.
![Page 13: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/13.jpg)
Negative Feedback Explained
Births = Birth_Fraction * PopulationBirth_Fraction = graph(population), decreasing
Population
Births
~
Birth Fraction
?
Noname 1
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Noname 2
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Noname 3
![Page 14: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/14.jpg)
Isolate Feedback Loop
Assume all other flows remain unchanged.Check how change in Population affects flow in question.Is population change reinforced or counteracted by change in flow?Reinforced = positive feedback.Counteracted = negative feedback.
![Page 15: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/15.jpg)
Negative Feedback – Pop Increase
Population
Births
~
Birth Fraction
Deaths
Table 1
Population(t) = Population(t - dt) + (Births - Deaths) * dtINIT Population = 1000
INFLOWS:Births = Birth_Fraction*PopulationOUTFLOWS:Deaths = 100Birth_Fraction = GRAPH(Population)(900, 0.14), (1000, 0.11), (1100, 0.08)
Which loop?
![Page 16: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/16.jpg)
Birth Fraction Graph
![Page 17: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/17.jpg)
Population Table
Population increases.All flows except Birth remain unchanged.Birth Fraction decreases.Birth inflow decreases.Population increases, but not as much.Counteracts increase.Thus, negative feedback.
Time Birth Fraction Population
0 0.110000 1,000.00
1 0.107000 1,010.00
2 0.104579 1,018.07
3 0.102638 1,024.54
4 0.101091 1,029.70
5 0.099863 1,033.79
6 0.098892 1,037.03
7 0.098126 1,039.58
8 0.097523 1,041.59
9 0.097049 1,043.17
10 0.096678 1,044.41
11 0.096386 1,045.38
Final 0.096158 1,046.14
![Page 18: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/18.jpg)
Graph of Population
1,000.00
1,010.00
1,020.00
1,030.00
1,040.00
1,050.00
0 1 2 3 4 5 6 7 8 9 10 11 12
Years
Population
![Page 19: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/19.jpg)
Description of Graph
IncreasingIncreasing at a decreasing rate Concave down
Leveling off approaching a horizontal asymptote approaching a stable value
What will happen to the population if this continues?
![Page 20: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/20.jpg)
Negative Feedback – Pop Decrease
Population
Births
~
Birth Fraction
Deaths
Table 1
Population(t) = Population(t - dt) + (Births - Deaths) * dtINIT Population = 1000
INFLOWS:Births = Birth_Fraction*PopulationOUTFLOWS:Deaths = 120Birth_Fraction = GRAPH(Population)(900, 0.14), (1000, 0.11), (1100, 0.08)
Which loop?
Note change
![Page 21: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/21.jpg)
Population Table
Population decreases.All flows except Birth remain unchanged.Birth Fraction increases.Birth inflow increases.Population decreases, but not as much.Counteracts decrease.Thus, negative feedback.
Time Birth Fraction Population0 0.1100001,000.00
1 0.113000 990.00
2 0.115439 981.87
3 0.117435 975.22
4 0.119078 969.74
5 0.120435 965.22
6 0.121562 961.46
7 0.122499 958.34
8 0.123280 955.73
9 0.123933 953.56
10 0.124480 951.73
11 0.124938 950.21
Final 0.125323 948.92
![Page 22: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/22.jpg)
Graph of Population
940.00
950.00
960.00
970.00
980.00
990.00
1,000.00
0 1 2 3 4 5 6 7 8 9 10 11 12
Years
Population
![Page 23: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/23.jpg)
Description of Graph
DecreasingDecreasing at a decreasing rate Concave up
Leveling off Approaching a horizontal asymptote Approaching a stable value
What will happen to the population if this continues?
![Page 24: Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here](https://reader035.vdocuments.mx/reader035/viewer/2022070306/5517365f550346f5558b5f84/html5/thumbnails/24.jpg)
To think about
What happens if the loop(s) are on the outflow?
Population
Births Deaths
Death Fraction
Graph 1
Population(t) = Population(t - dt) + (Births - Deaths) * dtINIT Population = 1000 {persons}
INFLOWS:Births = 100 {persons/year}OUTFLOWS:Deaths = Population*Death_Fraction {persons/year}Death_Fraction = .11 {persons/person/year}