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.

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 population dynamics of insects Presentation Transcript

    • ift-unesppopulation dynamics of insects Roberto A. Kraenkel Institute for Theoretical Physics - UNESP São Paulo, BR kraenkel@ift.unesp.br
    • ift-unespoutline
    • ift-unesp outline• crash course on population dynamics
    • ift-unesp outline• crash course on population dynamics• what is special with insects
    • ift-unesp outline• crash course on population dynamics• what is special with insects• competition & predation
    • ift-unesp outline• crash course on population dynamics• what is special with insects• competition & predation• insects in space & time
    • crash course on ift-unesppopulation dynamics
    • crash course on ift-unesp population dynamics• it’s about populations, not individuals
    • 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
    • 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
    • ift-unespprocesses
    • ift-unesp processes• Growth
    • ift-unesp processes• Growth • by reproduction
    • ift-unesp processes• Growth • by reproduction • by consumption of abiotic resources
    • ift-unesp processes• Growth • by reproduction • by consumption of abiotic resources biotic
    • ift-unesp processes• Growth • by reproduction • by consumption of abiotic resources biotic abiotic
    • ift-unespsaturation
    • ift-unesp saturation• Growth has to saturate:
    • ift-unesp saturation• Growth has to saturate: logistic type
    • ift-unespinteractions i
    • ift-unesp interactions i• competition for resources : 2-species, Lotka-Volterra type.
    • 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.
    • 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.
    • 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.
    • ift-unespinteractions ii
    • ift-unesp interactions ii• predation ( trophic interactions):
    • ift-unesp interactions ii• predation ( trophic interactions):• asymmetric -- one predator, one prey
    • ift-unesp interactions ii• predation ( trophic interactions):• asymmetric -- one predator, one prey• Lotka-Volterra
    • = 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
    • ift-unesp interactions ii• predation ( trophic interactions): C y• asymmetric -- one predator, one prey c• Lotka-Volterra l e s
    • ift-unespmovement
    • ift-unesp movement• macroscopically, the most simple assumption is that of a diffusive spreading of the population.
    • ift-unesp movement• macroscopically, the most simple assumption is that of a diffusive spreading of the population.
    • 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
    • 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:
    • 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:
    • ift-unespinsects
    • ift-unespinsects
    • ift-unespinsectsare a class withinthe arthropodsthat have anexoskeleton, athree-part body(head, thorax, andabdomen), threepairs of jointedlegs, compoundeyes, and twoantennae.
    • 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
    • population biology of ift-unesp insects
    • population biology of ift-unesp insects• What’s special with insects?
    • population biology of ift-unesp insects• What’s special with insects?• From the point of view of the population dynamics:
    • 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.
    • 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
    • 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
    • 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 ==> ....
    • 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
    • population dynamics of ift-unesp insects
    • population dynamics of ift-unesp insects• The simplest model is due to Prout & McChesnay (1985)
    • population dynamics of ift-unesp insects• The simplest model is due to Prout & McChesnay (1985)• It is a discrete time model
    • 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)
    • 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
    • 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
    • population dynamics of ift-unesp insects ut = Svt exp(−svt ) 1vt+1 = F ut exp(−f vt ) 2
    • population dynamics of ift-unesp insects ut = Svt exp(−svt ) 1vt+1 = F Svt exp(−(f + s)vt ) 2
    • population dynamics of ift-unesp insects Let us now look at someexamples involving a particular species : blowflies of the species Chrysomya albiceps
    • population dynamics of ift-unesp insects
    • ift-unespChrysomya albiceps
    • ift-unesp Chrysomya albiceps• Facts:
    • ift-unesp Chrysomya albiceps• Facts: • originally from Africa
    • ift-unesp Chrysomya albiceps• Facts: • originally from Africa • introduced in the Americas circa 1975
    • ift-unesp Chrysomya albiceps• Facts: • originally from Africa • introduced in the Americas circa 1975 • it dislocated native blowflies ( Cochliomya macellaria)
    • ift-unesp Chrysomya albiceps• Facts: • originally from Africa • introduced in the Americas circa 1975 • it dislocated native blowflies ( Cochliomya macellaria) • it predates other blowflies
    • 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.
    • competition & ift-unesp predation with Gabriel A. Maciel
    • competition & ift-unesp predation• Two species model with Gabriel A. Maciel
    • competition & ift-unesp predation• Two species model• Competition with Gabriel A. Maciel
    • competition & ift-unesp predation• Two species model• Competition• Predation ( Intraguild predation) with Gabriel A. Maciel
    • competition & ift-unesp predation• Two species model• Competition• Predation ( Intraguild predation)• Each species has two stages with Gabriel A. Maciel
    • 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
    • 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
    • competition & ift-unesp predationwith Gabriel A. Maciel
    • ift-unesp invasionwith Renato M. Coutinho
    • ift-unesp invasion• Model for the spatial distribution of C. albiceps with Renato M. Coutinho
    • ift-unesp invasion• Model for the spatial distribution of C. albiceps• discrete in time with Renato M. Coutinho
    • ift-unesp invasion• Model for the spatial distribution of C. albiceps• discrete in time• continous in space. with Renato M. Coutinho
    • 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
    • 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
    • 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
    • ift-unesp invasionwith Renato M. Coutinho
    • ift-unesp invasionwith Renato M. Coutinho
    • ift-unesp invasion propagation front withwith Renato M. Coutinho constant speed
    • with Renato M. Coutinho ift-unesp invasion
    • with Renato M. Coutinho ift-unesp invasion • Compare with observations of C. albiceps in Brazil?
    • with Renato M. Coutinho ift-unesp invasion • Compare with observations of C. albiceps in Brazil? • Need data on dispersion + lab data on vital rates
    • 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)
    • 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
    • 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
    • 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
    • with Renato M. Coutinho ift-unesp invasionPrediction for invasion speed is between 0.3 to 2. 2 km per day
    • 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
    • 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!!
    • ift-unespfinal comments
    • ift-unesp final comments• Population dynamics of insects goes trough modelling different stages
    • ift-unesp final comments• Population dynamics of insects goes trough modelling different stages• Each stage may have different ecological functions
    • 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
    • Thank you for your ift-unesp attention• kraenkel@ift.unesp.br