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!!
  94. 94. ift-unespfinal comments
  95. 95. ift-unesp final comments• Population dynamics of insects goes trough modelling different stages
  96. 96. ift-unesp final comments• Population dynamics of insects goes trough modelling different stages• Each stage may have different ecological functions
  97. 97. ift-unesp final comments• Population dynamics of insects goes trough modelling different stages• Each stage may have different ecological functions• Data are rare and not very precise
  98. 98. Thank you for your ift-unesp attention• kraenkel@ift.unesp.br

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