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ift -unesp population dynamics of insects Roberto A. Kraenkel Institute for Theoretical Physics - UNESP São Paulo, BR [email protected]
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population dynamics of insects
Roberto A. KraenkelInstitute for Theoretical Physics - UNESP
São Paulo, BR
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outline
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outline
• crash course on population dynamics
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outline
• crash course on population dynamics
• what is special with insects
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outline
• crash course on population dynamics
• what is special with insects
• competition & predation
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outline
• crash course on population dynamics
• what is special with insects
• competition & predation
• insects in space & time
ift-unespcrash course on population dynamics
ift-unespcrash course on population dynamics
• it’s about populations, not individuals
ift-unespcrash course on 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
ift-unespcrash course on 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
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processes
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processes
• Growth
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processes
• Growth
• by reproduction
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processes
• Growth
• by reproduction
• by consumption of abiotic resources
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processes
• Growth
• by reproduction
• by consumption of abiotic resources
biotic
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processes
• Growth
• by reproduction
• by consumption of abiotic resources
biotic abiotic
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saturation
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saturation
• Growth has to saturate:
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saturation
• Growth has to saturate:
logistic type
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interactions i
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interactions i
• competition for resources : 2-species, Lotka-Volterra type.
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interactions i
• competition for resources : 2-species, Lotka-Volterra type.
• principle of competitive exclusion: if strong enough, competition leads to exclusion of one species.
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interactions i
• competition for resources : 2-species, Lotka-Volterra type.
• principle of competitive exclusion: if strong enough, competition leads to exclusion of one species.
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interactions i
• competition for resources : 2-species, Lotka-Volterra type.
• principle of competitive exclusion: if strong enough, competition leads to exclusion of one species.
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interactions ii
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interactions ii
• predation ( trophic interactions):
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interactions ii
• predation ( trophic interactions):
• asymmetric -- one predator, one prey
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interactions ii
• predation ( trophic interactions):
• asymmetric -- one predator, one prey
• Lotka-Volterra
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interactions ii
• predation ( trophic interactions):
• asymmetric -- one predator, one prey
• Lotka-Volterra
dV
dt= aV
dV
dt= V (a ! bP )
dP
dt= !dP
dP
dt= P (cV ! d)
dV
dt= V (a ! bP )
dP
dt= P (cV ! d)
1
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interactions ii
• predation ( trophic interactions):
• asymmetric -- one predator, one prey
• Lotka-Volterra
Cycles
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movement
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movement
• macroscopically, the most simple assumption is that of a diffusive spreading of the population.
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movement
• macroscopically, the most simple assumption is that of a diffusive spreading of the population.
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movement
• macroscopically, the most simple assumption is that of a diffusive spreading of the population.
This is compatible with a brownian movement of individuals
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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:
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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:
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insects
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insects
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insectsare a class within the arthropods that have an exoskeleton, a three-part body (head, thorax, and abdomen), three pairs of jointed legs, compound eyes, and two antennae.
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insectsare a class within the arthropods that have an exoskeleton, a three-part body (head, thorax, and abdomen), three pairs of jointed legs, compound eyes, and two antennae.
Most insects put eggs, which hatch to give birth to larvae
Larvae undergo metamorphosis: after a pupae or nymphae stage, they become adults
ift-unesppopulation biology of insects
ift-unesppopulation biology of insects
• What’s special with insects?
ift-unesppopulation biology of insects
• What’s special with insects?
• From the point of view of the population dynamics:
ift-unesppopulation biology of 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.
ift-unesppopulation biology of 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
ift-unesppopulation biology of 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
ift-unesppopulation biology of 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 ==> ....
ift-unesppopulation biology of 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
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• The simplest model is due to Prout & McChesnay (1985)
ift-unesppopulation dynamics of insects
• The simplest model is due to Prout & McChesnay (1985)
• It is a discrete time model
ift-unesppopulation dynamics of insects
• The simplest model is due to Prout & McChesnay (1985)
• It is a discrete time model
• Adults (v) generate larvae (u)
ift-unesppopulation dynamics of 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
ift-unesppopulation dynamics of 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
ift-unesppopulation dynamics of insects
ut = Svt exp(!svt) (0.1)
vt+1 =1
2Fut exp(!fvt) (0.2)
(0.3)
1
ift-unesppopulation dynamics of insects
ut = Svt exp(!svt) (0.1)
vt+1 =1
2Fut exp(!fvt) (0.2)
(0.3)
ut = Svt exp(!svt) (0.4)
vt+1 =1
2FSvt exp(!(f + s)vt) (0.5)
(0.6)
1
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Let us now look at some examples involving a particular
species : blowflies of the species Chrysomya albiceps
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Chrysomya albiceps
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Chrysomya albiceps
• Facts:
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Chrysomya albiceps
• Facts:
• originally from Africa
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Chrysomya albiceps
• Facts:
• originally from Africa
• introduced in the Americas circa 1975
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Chrysomya albiceps
• Facts:
• originally from Africa
• introduced in the Americas circa 1975
• it dislocated native blowflies ( Cochliomya macellaria)
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Chrysomya albiceps
• Facts:
• originally from Africa
• introduced in the Americas circa 1975
• it dislocated native blowflies ( Cochliomya macellaria)
• it predates other blowflies
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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.
ift-unespcompetition & predation
with Gabriel A. Maciel
ift-unespcompetition & predation
• Two species model
with Gabriel A. Maciel
ift-unespcompetition & predation
• Two species model
• Competition
with Gabriel A. Maciel
ift-unespcompetition & predation
• Two species model
• Competition
• Predation ( Intraguild predation)
with Gabriel A. Maciel
ift-unespcompetition & predation
• Two species model
• Competition
• Predation ( Intraguild predation)
• Each species has two stages
with Gabriel A. Maciel
ift-unespcompetition & predation
• Two species model
• Competition
• Predation ( Intraguild predation)
• Each species has two stages
with Gabriel A. MacielCompetition and predation
only in larval stage
ift-unespcompetition & predation
• Two species model
• Competition
• Predation ( Intraguild predation)
• Each species has two stages
with Gabriel A. MacielCompetition and predation
only in larval stage
ift-unespcompetition & predation
with Gabriel A. Maciel
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invasion
with Renato M. Coutinho
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invasion
• Model for the spatial distribution of C. albiceps
with Renato M. Coutinho
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invasion
• Model for the spatial distribution of C. albiceps
• discrete in time
with Renato M. Coutinho
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invasion
• Model for the spatial distribution of C. albiceps
• discrete in time
• continous in space.
with Renato M. Coutinho
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invasion
• Model for the spatial distribution of C. albiceps
• discrete in time
• continous in space.
single species model
with Renato M. Coutinho
only adults disperse
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invasion
• Model for the spatial distribution of C. albiceps
• discrete in time
• continous in space.
uses a gaussian kernel
single species model
with Renato M. Coutinho
only adults disperse
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invasion
• Model for the spatial distribution of C. albiceps
• discrete in time
• continous in space.
generalizes M. Kot resuts uses a gaussian kernel
single species model
with Renato M. Coutinho
only adults disperse
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invasion
with Renato M. Coutinho
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invasion
with Renato M. Coutinho
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invasion
propagation front with constant speedwith Renato M. Coutinho
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invasionwith Renato M. Coutinho
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invasion
• Compare with observations of C. albiceps in Brazil?
with Renato M. Coutinho
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invasion
• Compare with observations of C. albiceps in Brazil?
• Need data on dispersion + lab data on vital rates
with Renato M. Coutinho
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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
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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
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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
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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
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invasionwith Renato M. Coutinho
Prediction for invasion speed is between 0.3 to 2. 2 km per day
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invasionwith Renato M. Coutinho
Prediction for invasion speed is between 0.3 to 2. 2 km per day
which corresponds to historical records of the invasion
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invasionwith Renato M. Coutinho
Prediction for invasion speed is between 0.3 to 2. 2 km per day
which corresponds to historical records of the invasion
Nice!!
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final comments
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final comments
• Population dynamics of insects goes trough modelling different stages
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final comments
• Population dynamics of insects goes trough modelling different stages
• Each stage may have different ecological functions
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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
ift-unespThank you for your attention
