Modeling cluster notes

Notes

Dynamic modeling approaches.  Statistical models of many type will be brought to bear on questions in smaller groups.  Here, we feel like we can offer some dynamic modeling approaches to identify bottlenecks, test simple hypotheses, etc.

Types of models:

1) dispersion model

2) life cycle / matrix model / stage-based

3) individual-based model - later future? grant needed?

Overall goal to estimate the relative contribution of climate, land cover, local habitat, etc to presence, reproduction, abundance.

1) Lowest hanging fruit... 

life cycle 

E(t) = A(t-1) * fecundity

L1(t) = E(t) * (S(a)*F)

L2(t) = L1(t) * S(L1)

L3(t) = L2(t) * S(L2)

L4(t) = L3(t) * S(L3)

L5(t) = L4(t) * S(L4)

P(t) = L5(t) * S(L5)

A(t) = P(t) * S(P)

spatial scale - start in midwest with really good data (to define/parameterize life cycle?)

Life cycle model can help us get at the expected natural variation due to monarch population dynamics - and ultimately differentiate expected natural variability from environmental effects.

First stage might simplify this and look at 4 stages and also look at expected transitions from region to region.... think about this tomorrow.

2) movement - dispersion model

build climate / initial population size model based on Journey North and climate data by grid cell

simulate movement in subsequent years and see if it matches what is observed

probably cellular automata - probability of moving cell-to-cell based on temperature

3) combine life cycle with dispersion

4) add individual-based approach based on behavior and success parameterized by many of the other small-group efforts (e.g. multi-scale habitat selection, reproduction, maturation, and movement)

questions

1) What are the demographic bottlenecks limiting adult population size? Application of a stage-based simulation model

 a) what is the relative contribution of each stage to adult density (effects of mortality)?

 b) what are factors affecting dynamics due to density-dependence or external factors?

2) Can we use a dispersion model to replicate observed northern migration patters, given simple climatic variables?

3) Can we combine life cycle model with dispersion model in a spatially-explicit framework to replicate both migration and demographic patterns?

4) Can we take mechanisms worked out from other groups related to habitat selection, movements, natural enemies, demography, etc in an agent-based model?

data use / gaps

  -weather data for mexico

  -departure date

  -movement rate of individuals (north)

  -wind data? 0-4 meter weather station data?

papers

tasks:

1) life-cycle

 a) get survival / fecundity parameter ranges

 b) parameterize simple stage-based model

2) dispersion / cellular automata model

 a) compile climate data

 b) develop climate-first sighting relationships

 c) parameterize dispersion model

3) & 4) future - dependent on other progress