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Long Swings in Homicide

Long Swings in Homicide. 1. 1. Outline. Evidence of Long Swings in Homicide Evidence of Long Swings in Other Disciplines Long Swing Cycle Concepts: Kondratieff Waves More about ecological cycles Models. 2. 2. Part I. Evidence of Long Swings in Homicide. US Bureau of Justice Statistics

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Long Swings in Homicide

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  1. Long Swings in Homicide 1 1

  2. Outline • Evidence of Long Swings in Homicide • Evidence of Long Swings in Other Disciplines • Long Swing Cycle Concepts: Kondratieff Waves • More about ecological cycles • Models 2 2

  3. Part I. Evidence of Long Swings in Homicide • US Bureau of Justice Statistics • Report to the Nation On Crime and Justice, second edition • California Department of Justice, Homicide in California 3 3

  4. Bureau of Justice Statistics, BJS “Homicide Trends in the United States, 1980-2008”, 11-16-2011 “Homicide Trends in the United States”, 7-1-2007 4 4

  5. Bureau of Justice Statistics Peak to Peak: 50 years 5 5

  6. Report to the Nation ….p.15 6 6

  7. 7

  8. 1980 8 8

  9. Executions in the US 1930-2007 http://www.ojp.usdoj.gov/bjs Peak to Peak: About 65 years 9 9

  10. 10

  11. Part Two: Evidence of Long Swings In Other Disciplines • Engineering • 50 year cycles in transportation technology • 50 year cycles in energy technology • Economic Demography • Simon Kuznets, “Long Swings in the Growth of Population and Related Economic Variables” • Richard Easterlin, Population, labor Force, and Long Swings in Economic Growth • Ecology • Hudson Bay Company 11

  12. Cesare Marchetti 12 12

  13. Erie Canal 13

  14. 10% 90% 1890 1921 1859 14 14

  15. Cesare Marchetti: Energy Technology: Coal, Oil, Gas, Nuclear 52 years 57 years 56 years 15 15

  16. 16

  17. 17

  18. Richard Easterlin 20 year swings 18

  19. Cycles in Nature Canadian Lynx and Snowshoe Hare, data from the Hudson Bay Company, nearly a century of annual data, 1845-1935 The Lotka-Volterra Model (Sarah Jenson and Stacy Randolph, Berkeley ppt., Slides 4-9) 19

  20. 20

  21. What Causes These Cycles in Nature? • At least two kinds of cycles • Harmonics or sin and cosine waves • Deterministic but chaotic cycles 21

  22. Part Three: Thinking About Long Waves In Economics • Kondratieff Wave 22 22

  23. Nikolai Kondratieff (1892-1938) Brought to attention in Joseph Schumpeter’s Business Cycles (1939) 23 23

  24. 2008-2014: Hard Winter 24 24

  25. 25 25

  26. Cesare Marchetti“Fifty-Year Pulsation In Human Affairs”Futures 17(3):376-388 (1986)www.cesaremarchetti.org/archive/scan/MARCHETTI-069.pdf • Example: the construction of railroad miles is logistically distributed 26 26

  27. Cesare Marchetti 27 27

  28. Theodore Modis Figure 4. The data points represent the percentage deviation of energy consumption in the US from the natural growth-trend indicated by a fitted S-curve. The gray band is an 8% interval around a sine wave with period 56 years. The black dots and black triangles show what happened after the graph was first put together in 1988.[7] Presently we are entering a “spring” season. WWI occurred in late “summer” whereas WWII in late “winter”. 28 28

  29. Part Four: More About Ecological Cycles 29

  30. Well Documented Cycles 30

  31. Similar Data from North Canada 31

  32. Weather: “The Butterfly Effect” 32

  33. The Predator-Prey Relationship • Predator-prey relationships have always occupied a special place in ecology • Ideal topic for systems dynamics • Examine interaction between deer and predators on Kaibab Plateau • Learn about possible behavior of predator and prey populations if predators had not been removed in the early 1900s

  34. NetLogo Predator-Prey Model

  35. Questions? How to Model?

  36. Part Five: The Lotka-Volterra Model • Built on economic concepts • Exponential population growth • Exponential decay • Adds in the interaction effect • We can estimate the model parameters using regression • We can use simulation to study cyclical behavior

  37. Lotka-Volterra Model Vito Volterra (1860-1940) famous Italian mathematician Retired from pure mathematics in 1920 Son-in-law: D’Ancona Alfred J. Lotka (1880-1949) American mathematical biologist primary example: plant population/herbivorous animal dependent on that plant for food

  38. Predator-Prey 1926: Vito Volterra, model of prey fish and predator fish in the Adriatic during WWI 1925: Alfred Lotka, model of chemical Rx. Where chemical concentrations oscillate 38 38 38

  39. Applications of Predator-Prey 39 39 39 Resource-consumer Plant-herbivore Parasite-host Tumor cells or virus-immune system Susceptible-infectious interactions

  40. Non-Linear Differential Equations 40 40 40 dx/dt = x(α – βy), where x is the # of some prey (Hare) dy/dt = -y(γ – δx), where y is the # of some predator (Lynx) α, β, γ, and δ are parameters describing the interaction of the two species d/dt ln x = (dx/dt)/x =(α – βy), without predator, y, exponential growth at rate α d/dt ln y = (dy/dt)/y = - (γ – δx), without prey, x, exponential decay like an isotope at rate 

  41. Population Growth: P(t) = P(0)eat

  42. lnP(t) = lnP(1960) + at

  43. CA Population: exponential rate of growth, 1995-2007 is 1.4%

  44. Prey (Hare Equation) • Hare(t) = Hare(t=0) ea*t , where a is the exponential growth rate • Ln Hare(t) = ln Hare(t=0) + a*t, where a is slope of ln Hare(t) vs. t • ∆ ln hare(t) = a, where a is the fractional rate of growth of hares • So ∆ ln hare(t) = ∆ hare(t)/hare(t-1)=[hare(t) – hare(t-1)]/hare(t-1) • Add in interaction effect of predators; ∆ ln Hare(t) = a – b*Lynx • So the lynx eating the hares keep the hares from growing so fast • To estimate parameters a and b, regress ∆ hare(t)/hare(t-1) against Lynx

  45. Hudson Bay Co. Data: Snowshoe Hare & Canadian Lynx, 1845-1935

  46. [Hare(1865)-Hare(1863)]/Hare(1864)Vs. Lynx (1864) etc. 1863-1934 • ∆ hare(t)/hare(t-1) = 0.77 – 0.025 Lynx • a = 0.77, b = 0.025 (a = 0.63, b = 0.022)

  47. [Lynx(1847)-Lynx(1845)]/Hare(1846)Vs. Lynx (1846) etc. 1846-1906 ∆ Lynx(t)/Lynx(t-1) = -0.24 + 0.005 Hare c = 0.24, d= 0.005 ( c = 0.27,d = 0.006)

  48. Simulations: 1845-1935 • Mathematica http://mathworld.wolfram.com/Lotka-VolterraEquations.html • Predator-prey equations • Predator-prey model

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