population dynamics of insects

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population dynamics of insects

Roberto A. KraenkelInstitute for Theoretical Physics - UNESP

São Paulo, BR

[email protected]

mailto:[email protected]


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outline

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outline

• crash course on population dynamics

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outline


• what is special with insects

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outline



• competition & predation

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outline



• competition & predation

• insects in space & time

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



• 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


biotic

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processes

• Growth

• by reproduction


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


• principle of competitive exclusion: if strong enough, competition leads to exclusion of one species.

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interactions i



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interactions i



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interactions ii

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interactions ii

• predation ( trophic interactions):

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interactions ii


• asymmetric -- one predator, one prey

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interactions ii



• Lotka-Volterra

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interactions ii



• 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



• 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


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movement


This is compatible with a brownian movement of individuals

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movement



If you put diffusion + growth + saturation:

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movement



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


• 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 disperse

• adults ==> larvae==> adults ==> ....






• adults disperse

• adults ==> larvae==> adults ==> ....

• dynamics can be discrete in time: non overlapping generations

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





• Larvae generate the next generation of adults

• nonlinear terms are such as not to generate negative populations


ut = Svt exp(!svt) (0.1)

vt+1 =1

2Fut exp(!fvt) (0.2)

(0.3)

1



vt+1 =1

2Fut exp(!fvt) (0.2)

(0.3)


vt+1 =1

2FSvt exp(!(f + s)vt) (0.5)

(0.6)

1


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:


• introduced in the Americas circa 1975

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Chrysomya albiceps

• Facts:



• it dislocated native blowflies ( Cochliomya macellaria)

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Chrysomya albiceps

• Facts:




• it predates other blowflies

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Chrysomya albiceps

• Facts:




• 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


• Two species model




• Competition




• Competition

• Predation ( Intraguild predation)




• Competition


• Each species has two stages




• Competition



with Gabriel A. MacielCompetition and predation

only in larval stage



• Competition



with Gabriel A. MacielCompetition and predation

only in larval stage



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invasion

with Renato M. Coutinho

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invasion

• Model for the spatial distribution of C. albiceps


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invasion


• discrete in time


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invasion



• continous in space.


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invasion




single species model


only adults disperse

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invasion




uses a gaussian kernel




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invasion




generalizes M. Kot resuts uses a gaussian kernel




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invasion


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invasion


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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?


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invasion


• Need data on dispersion + lab data on vital rates


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invasion



• Dispersion data available for the same species in South Africa ( 1984)


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invasion




• Re-analisys of SA data + lab mesurements


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invasion






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invasion






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Prediction for invasion speed is between 0.3 to 2. 2 km per day

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which corresponds to historical records of the invasion

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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


• Each stage may have different ecological functions

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final comments


• Each stage may have different ecological functions

• Data are rare and not very precise

ift-unespThank you for your attention

•[email protected]



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population dynamics of insects