population dynamics of insects

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population dynamics of insects

Roberto A. KraenkelInstitute for Theoretical Physics - UNESP

São Paulo, BR

kraenkel@ift.unesp.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

ift-unesppopulation dynamics of insects

ift-unesppopulation dynamics of insects

• 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

ift-unesppopulation dynamics of insects

Let us now look at some examples involving a particular

species : blowflies of the species Chrysomya albiceps

ift-unesppopulation dynamics of insects

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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.

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with Gabriel A. Maciel

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• Two species model

with Gabriel A. Maciel

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• Two species model

• Competition

with Gabriel A. Maciel

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• 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

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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

•kraenkel@ift.unesp.br