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.

Published on: **Mar 4, 2016**

- 1. ift-unesppopulation dynamics of insects Roberto A. Kraenkel Institute for Theoretical Physics - UNESP São Paulo, BR kraenkel@ift.unesp.br
- 2. ift-unespoutline
- 3. ift-unesp outline• crash course on population dynamics
- 4. ift-unesp outline• crash course on population dynamics• what is special with insects
- 5. ift-unesp outline• crash course on population dynamics• what is special with insects• competition & predation
- 6. ift-unesp outline• crash course on population dynamics• what is special with insects• competition & predation• insects in space & time
- 7. crash course on ift-unesppopulation dynamics
- 8. crash course on ift-unesp population dynamics• it’s about populations, not individuals
- 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. 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. ift-unespprocesses
- 12. ift-unesp processes• Growth
- 13. ift-unesp processes• Growth • by reproduction
- 14. ift-unesp processes• Growth • by reproduction • by consumption of abiotic resources
- 15. ift-unesp processes• Growth • by reproduction • by consumption of abiotic resources biotic
- 16. ift-unesp processes• Growth • by reproduction • by consumption of abiotic resources biotic abiotic
- 17. ift-unespsaturation
- 18. ift-unesp saturation• Growth has to saturate:
- 19. ift-unesp saturation• Growth has to saturate: logistic type
- 20. ift-unespinteractions i
- 21. ift-unesp interactions i• competition for resources : 2-species, Lotka-Volterra type.
- 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. 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. 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. ift-unespinteractions ii
- 26. ift-unesp interactions ii• predation ( trophic interactions):
- 27. ift-unesp interactions ii• predation ( trophic interactions):• asymmetric -- one predator, one prey
- 28. ift-unesp interactions ii• predation ( trophic interactions):• asymmetric -- one predator, one prey• Lotka-Volterra
- 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. ift-unesp interactions ii• predation ( trophic interactions): C y• asymmetric -- one predator, one prey c• Lotka-Volterra l e s
- 31. ift-unespmovement
- 32. ift-unesp movement• macroscopically, the most simple assumption is that of a diffusive spreading of the population.
- 33. ift-unesp movement• macroscopically, the most simple assumption is that of a diffusive spreading of the population.
- 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. 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. 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. ift-unespinsects
- 38. ift-unespinsects
- 39. ift-unespinsectsare a class withinthe arthropodsthat have anexoskeleton, athree-part body(head, thorax, andabdomen), threepairs of jointedlegs, compoundeyes, and twoantennae.
- 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. population biology of ift-unesp insects
- 42. population biology of ift-unesp insects• What’s special with insects?
- 43. population biology of ift-unesp insects• What’s special with insects?• From the point of view of the population dynamics:
- 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. 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. 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. 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. 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. population dynamics of ift-unesp insects
- 50. population dynamics of ift-unesp insects• The simplest model is due to Prout & McChesnay (1985)
- 51. population dynamics of ift-unesp insects• The simplest model is due to Prout & McChesnay (1985)• It is a discrete time model
- 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. 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. 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. population dynamics of ift-unesp insects ut = Svt exp(−svt ) 1vt+1 = F ut exp(−f vt ) 2
- 56. population dynamics of ift-unesp insects ut = Svt exp(−svt ) 1vt+1 = F Svt exp(−(f + s)vt ) 2
- 57. population dynamics of ift-unesp insects Let us now look at someexamples involving a particular species : blowﬂies of the species Chrysomya albiceps
- 58. population dynamics of ift-unesp insects
- 59. ift-unespChrysomya albiceps
- 60. ift-unesp Chrysomya albiceps• Facts:
- 61. ift-unesp Chrysomya albiceps• Facts: • originally from Africa
- 62. ift-unesp Chrysomya albiceps• Facts: • originally from Africa • introduced in the Americas circa 1975
- 63. ift-unesp Chrysomya albiceps• Facts: • originally from Africa • introduced in the Americas circa 1975 • it dislocated native blowﬂies ( Cochliomya macellaria)
- 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. 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. competition & ift-unesp predation with Gabriel A. Maciel
- 67. competition & ift-unesp predation• Two species model with Gabriel A. Maciel
- 68. competition & ift-unesp predation• Two species model• Competition with Gabriel A. Maciel
- 69. competition & ift-unesp predation• Two species model• Competition• Predation ( Intraguild predation) with Gabriel A. Maciel
- 70. competition & ift-unesp predation• Two species model• Competition• Predation ( Intraguild predation)• Each species has two stages with Gabriel A. Maciel
- 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. 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. competition & ift-unesp predationwith Gabriel A. Maciel
- 74. ift-unesp invasionwith Renato M. Coutinho
- 75. ift-unesp invasion• Model for the spatial distribution of C. albiceps with Renato M. Coutinho
- 76. ift-unesp invasion• Model for the spatial distribution of C. albiceps• discrete in time with Renato M. Coutinho
- 77. ift-unesp invasion• Model for the spatial distribution of C. albiceps• discrete in time• continous in space. with Renato M. Coutinho
- 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. 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. 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. ift-unesp invasionwith Renato M. Coutinho
- 82. ift-unesp invasionwith Renato M. Coutinho
- 83. ift-unesp invasion propagation front withwith Renato M. Coutinho constant speed
- 84. with Renato M. Coutinho ift-unesp invasion
- 85. with Renato M. Coutinho ift-unesp invasion • Compare with observations of C. albiceps in Brazil?
- 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. 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. 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. 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. 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. with Renato M. Coutinho ift-unesp invasionPrediction for invasion speed is between 0.3 to 2. 2 km per day
- 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. 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. ift-unespﬁnal comments
- 95. ift-unesp ﬁnal comments• Population dynamics of insects goes trough modelling different stages
- 96. ift-unesp ﬁnal comments• Population dynamics of insects goes trough modelling different stages• Each stage may have different ecological functions
- 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. Thank you for your ift-unesp attention• kraenkel@ift.unesp.br