1. Positive Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = c, a positive constant You are here

2. 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.

3. Positive Feedback – Pop Increase Note numbers

4. Population Table Population increases. All flows except Birth remain unchanged. Birth inflow increases. Population increases even more. Reinforces increase. Thus, positive feedback. Time Population 01,000.00 11,010.00 21,021.10 31,033.42 41,047.10 51,062.28 61,079.13 71,097.83 81,118.59 91,141.64 101,167.22 111,195.61 Final1,227.13

5. Graph of Population

6. Description of Graph Increasing Increasing at an increasing rate Concave up NOT leveling off Would have to change concavity What will happen to the population if this continues?

7. 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.

8. Positive Feedback – Pop Decrease Note change

9. Population Table Population decreases. All flows except Birth remain unchanged. Birth inflow decreases. Population decreases even more. Reinforces decrease. Thus, positive feedback. Time Population 01,000.00 1990.00 2978.90 3966.58 4952.90 5937.72 6920.87 7902.17 8881.41 9858.36 10832.78 11804.39 Final772.87

10. Graph of Population

11. Description of Graph Decreasing Decreasing at an increasing rate Concave down NOT leveling off Would have to change concavity What will happen to the population if this continues?

12. 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.

13. Negative Feedback Explained Births = Birth_Fraction * Population Birth_Fraction = graph(population), decreasing

14. 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.

15. Negative Feedback – Pop Increase Which loop?

16. Birth Fraction Graph

17. 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 00.1100001,000.00 10.1070001,010.00 20.1045791,018.07 30.1026381,024.54 40.1010911,029.70 50.0998631,033.79 60.0988921,037.03 70.0981261,039.58 80.0975231,041.59 90.0970491,043.17 100.0966781,044.41 110.0963861,045.38 Final0.0961581,046.14

18. Graph of Population

19. Description of Graph Increasing Increasing 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?

20. Negative Feedback – Pop Decrease Which loop? Note change

21. 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 Population 00.1100001,000.00 10.113000990.00 20.115439981.87 30.117435975.22 40.119078969.74 50.120435965.22 60.121562961.46 70.122499958.34 80.123280955.73 90.123933953.56 100.124480951.73 110.124938950.21 Final0.125323948.92

22. Graph of Population

23. Description of Graph Decreasing Decreasing 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?

24. To think about What happens if the loop(s) are on the outflow? Population(t) = Population(t - dt) + (Births - Deaths) * dt INIT Population = 1000 {persons} INFLOWS: Births = 100 {persons/year} OUTFLOWS: Deaths = Population*Death_Fraction {persons/year} Death_Fraction =.11 {persons/person/year}