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population dynamics of insects

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Very brief mathematical introduction to the population dynamics of insects. Last part, on spatial spread is new. Joint work with W.A.C. Godoy and R.M. Coutinho.

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population dynamics of insects

1. 1. ift-unesppopulation dynamics of insects Roberto A. Kraenkel Institute for Theoretical Physics - UNESP São Paulo, BR kraenkel@ift.unesp.br
2. 2. ift-unespoutline
3. 3. ift-unesp outline• crash course on population dynamics
4. 4. ift-unesp outline• crash course on population dynamics• what is special with insects
5. 5. ift-unesp outline• crash course on population dynamics• what is special with insects• competition & predation
6. 6. ift-unesp outline• crash course on population dynamics• what is special with insects• competition & predation• insects in space & time
7. 7. crash course on ift-unesppopulation dynamics
8. 8. crash course on ift-unesp population dynamics• it’s about populations, not individuals
9. 9. crash course on ift-unesp population dynamics• it’s about populations, not individuals• mathematically, a population is described either by its density or by the total number of individuals in a region
10. 10. crash course on ift-unesp population dynamics• it’s about populations, not individuals• mathematically, a population is described either by its density or by the total number of individuals in a region• to describe its dynamics in space and time we have to model the main processes the population is subject to
11. 11. ift-unespprocesses
12. 12. ift-unesp processes• Growth
13. 13. ift-unesp processes• Growth • by reproduction
14. 14. ift-unesp processes• Growth • by reproduction • by consumption of abiotic resources
15. 15. ift-unesp processes• Growth • by reproduction • by consumption of abiotic resources biotic
16. 16. ift-unesp processes• Growth • by reproduction • by consumption of abiotic resources biotic abiotic
17. 17. ift-unespsaturation
18. 18. ift-unesp saturation• Growth has to saturate:
19. 19. ift-unesp saturation• Growth has to saturate: logistic type
20. 20. ift-unespinteractions i
21. 21. ift-unesp interactions i• competition for resources : 2-species, Lotka-Volterra type.
22. 22. ift-unesp interactions i• competition for resources : 2-species, Lotka-Volterra type.• principle of competitive exclusion: if strong enough, competition leads to exclusion of one species.
23. 23. ift-unesp interactions i• competition for resources : 2-species, Lotka-Volterra type.• principle of competitive exclusion: if strong enough, competition leads to exclusion of one species.
24. 24. ift-unesp interactions i• competition for resources : 2-species, Lotka-Volterra type.• principle of competitive exclusion: if strong enough, competition leads to exclusion of one species.
25. 25. ift-unespinteractions ii
26. 26. ift-unesp interactions ii• predation ( trophic interactions):
27. 27. ift-unesp interactions ii• predation ( trophic interactions):• asymmetric -- one predator, one prey
28. 28. ift-unesp interactions ii• predation ( trophic interactions):• asymmetric -- one predator, one prey• Lotka-Volterra
29. 29. = P (cV − d) ift-unesp dt interactions ii dV = V (a − bP )• predation ( trophic interactions): dt• asymmetric -- one predator, one prey• Lotka-Volterra dP = P (cV − d) dt
30. 30. ift-unesp interactions ii• predation ( trophic interactions): C y• asymmetric -- one predator, one prey c• Lotka-Volterra l e s
31. 31. ift-unespmovement
32. 32. ift-unesp movement• macroscopically, the most simple assumption is that of a diffusive spreading of the population.
33. 33. ift-unesp movement• macroscopically, the most simple assumption is that of a diffusive spreading of the population.
34. 34. ift-unesp movement • macroscopically, the most simple assumption is that of a diffusive spreading of the population.This is compatible with a brownian movement of individuals
35. 35. ift-unesp movement • macroscopically, the most simple assumption is that of a diffusive spreading of the population.This is compatible with a brownian movement of individuals If you put diffusion + growth + saturation:
36. 36. ift-unesp movement • macroscopically, the most simple assumption is that of a diffusive spreading of the population.This is compatible with a brownian movement of individuals If you put diffusion + growth + saturation:
37. 37. ift-unespinsects
38. 38. ift-unespinsects
39. 39. ift-unespinsectsare a class withinthe arthropodsthat have anexoskeleton, athree-part body(head, thorax, andabdomen), threepairs of jointedlegs, compoundeyes, and twoantennae.
40. 40. ift-unesp insects are a class within the arthropods that have an exoskeleton, a three-part body (head, thorax, and abdomen), three pairs of jointed Most insects put eggs, which hatch to give legs, compound birth to larvae eyes, and two antennae. Larvae undergo metamorphosis: after apupae or nymphae stage, they become adults
41. 41. population biology of ift-unesp insects
42. 42. population biology of ift-unesp insects• What’s special with insects?
43. 43. population biology of ift-unesp insects• What’s special with insects?• From the point of view of the population dynamics:
44. 44. population biology of ift-unesp insects• What’s special with insects?• From the point of view of the population dynamics: • the ecological function of larvae and adult stage are different.
45. 45. population biology of ift-unesp insects• What’s special with insects?• From the point of view of the population dynamics: • the ecological function of larvae and adult stage are different. • usually larvae are responsible for the populational regulation
46. 46. population biology of ift-unesp insects• What’s special with insects?• From the point of view of the population dynamics: • the ecological function of larvae and adult stage are different. • usually larvae are responsible for the populational regulation • adults disperse
47. 47. population biology of ift-unesp insects• What’s special with insects?• From the point of view of the population dynamics: • the ecological function of larvae and adult stage are different. • usually larvae are responsible for the populational regulation • adults disperse • adults ==> larvae==> adults ==> ....
48. 48. population biology of ift-unesp insects• What’s special with insects?• From the point of view of the population dynamics: • the ecological function of larvae and adult stage are different. • usually larvae are responsible for the populational regulation • adults disperse • adults ==> larvae==> adults ==> .... • dynamics can be discrete in time: non overlapping generations
49. 49. population dynamics of ift-unesp insects
50. 50. population dynamics of ift-unesp insects• The simplest model is due to Prout & McChesnay (1985)
51. 51. population dynamics of ift-unesp insects• The simplest model is due to Prout & McChesnay (1985)• It is a discrete time model
52. 52. population dynamics of ift-unesp insects• The simplest model is due to Prout & McChesnay (1985)• It is a discrete time model• Adults (v) generate larvae (u)
53. 53. population dynamics of ift-unesp insects• The simplest model is due to Prout & McChesnay (1985)• It is a discrete time model• Adults (v) generate larvae (u)• Larvae generate the next generation of adults
54. 54. population dynamics of ift-unesp insects• The simplest model is due to Prout & McChesnay (1985)• It is a discrete time model• Adults (v) generate larvae (u)• Larvae generate the next generation of adults• nonlinear terms are such as not to generate negative populations
55. 55. population dynamics of ift-unesp insects ut = Svt exp(−svt ) 1vt+1 = F ut exp(−f vt ) 2
56. 56. population dynamics of ift-unesp insects ut = Svt exp(−svt ) 1vt+1 = F Svt exp(−(f + s)vt ) 2
57. 57. population dynamics of ift-unesp insects Let us now look at someexamples involving a particular species : blowﬂies of the species Chrysomya albiceps
58. 58. population dynamics of ift-unesp insects
59. 59. ift-unespChrysomya albiceps
60. 60. ift-unesp Chrysomya albiceps• Facts:
61. 61. ift-unesp Chrysomya albiceps• Facts: • originally from Africa
62. 62. ift-unesp Chrysomya albiceps• Facts: • originally from Africa • introduced in the Americas circa 1975
63. 63. ift-unesp Chrysomya albiceps• Facts: • originally from Africa • introduced in the Americas circa 1975 • it dislocated native blowﬂies ( Cochliomya macellaria)
64. 64. ift-unesp Chrysomya albiceps• Facts: • originally from Africa • introduced in the Americas circa 1975 • it dislocated native blowﬂies ( Cochliomya macellaria) • it predates other blowﬂies
65. 65. ift-unesp Chrysomya albiceps• Facts: • originally from Africa • introduced in the Americas circa 1975 • it dislocated native blowﬂies ( Cochliomya macellaria) • it predates other blowﬂies • its introdiction occured tpgether with the introduction of one of its prey , C. megachephala.
66. 66. competition & ift-unesp predation with Gabriel A. Maciel
67. 67. competition & ift-unesp predation• Two species model with Gabriel A. Maciel
68. 68. competition & ift-unesp predation• Two species model• Competition with Gabriel A. Maciel
69. 69. competition & ift-unesp predation• Two species model• Competition• Predation ( Intraguild predation) with Gabriel A. Maciel
70. 70. competition & ift-unesp predation• Two species model• Competition• Predation ( Intraguild predation)• Each species has two stages with Gabriel A. Maciel
71. 71. competition & ift-unesp predation • Two species model • Competition • Predation ( Intraguild predation) • Each species has two stagesCompetition and predation only in larval stage with Gabriel A. Maciel
72. 72. competition & ift-unesp predation • Two species model • Competition • Predation ( Intraguild predation) • Each species has two stagesCompetition and predation only in larval stage with Gabriel A. Maciel
73. 73. competition & ift-unesp predationwith Gabriel A. Maciel
74. 74. ift-unesp invasionwith Renato M. Coutinho
75. 75. ift-unesp invasion• Model for the spatial distribution of C. albiceps with Renato M. Coutinho
76. 76. ift-unesp invasion• Model for the spatial distribution of C. albiceps• discrete in time with Renato M. Coutinho
77. 77. ift-unesp invasion• Model for the spatial distribution of C. albiceps• discrete in time• continous in space. with Renato M. Coutinho
78. 78. ift-unesp invasion • Model for the spatial distribution of C. albiceps • discrete in time • continous in space.only adults disperse single species model with Renato M. Coutinho
79. 79. ift-unesp invasion uses a gaussian kernel • Model for the spatial distribution of C. albiceps • discrete in time • continous in space.only adults disperse single species model with Renato M. Coutinho
80. 80. ift-unesp invasiongeneralizes M. Kot resuts uses a gaussian kernel • Model for the spatial distribution of C. albiceps • discrete in time • continous in space. only adults disperse single species model with Renato M. Coutinho
81. 81. ift-unesp invasionwith Renato M. Coutinho
82. 82. ift-unesp invasionwith Renato M. Coutinho
83. 83. ift-unesp invasion propagation front withwith Renato M. Coutinho constant speed
84. 84. with Renato M. Coutinho ift-unesp invasion
85. 85. with Renato M. Coutinho ift-unesp invasion • Compare with observations of C. albiceps in Brazil?
86. 86. with Renato M. Coutinho ift-unesp invasion • Compare with observations of C. albiceps in Brazil? • Need data on dispersion + lab data on vital rates
87. 87. with Renato M. Coutinho ift-unesp invasion • Compare with observations of C. albiceps in Brazil? • Need data on dispersion + lab data on vital rates • Dispersion data available for the same species in South Africa ( 1984)
88. 88. with Renato M. Coutinho ift-unesp invasion • Compare with observations of C. albiceps in Brazil? • Need data on dispersion + lab data on vital rates • Dispersion data available for the same species in South Africa ( 1984) • Re-analisys of SA data + lab mesurements
89. 89. with Renato M. Coutinho ift-unesp invasion • Compare with observations of C. albiceps in Brazil? • Need data on dispersion + lab data on vital rates • Dispersion data available for the same species in South Africa ( 1984) • Re-analisys of SA data + lab mesurements
90. 90. with Renato M. Coutinho ift-unesp invasion • Compare with observations of C. albiceps in Brazil? • Need data on dispersion + lab data on vital rates • Dispersion data available for the same species in South Africa ( 1984) • Re-analisys of SA data + lab mesurements
91. 91. with Renato M. Coutinho ift-unesp invasionPrediction for invasion speed is between 0.3 to 2. 2 km per day
92. 92. with Renato M. Coutinho ift-unesp invasionPrediction for invasion speed is between 0.3 to 2. 2 km per day which corresponds to historical records of the invasion
93. 93. with Renato M. Coutinho ift-unesp invasionPrediction for invasion speed is between 0.3 to 2. 2 km per day which corresponds to historical records of the invasion Nice!!