why use multivariate autoregressive modeling?
DESCRIPTION
Why use Multivariate Autoregressive Modeling?. S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007. S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007. Temperature Nutrients Photoperiod. Storm activity Fishing pressure. - PowerPoint PPT PresentationTRANSCRIPT
Why use Multivariate Autoregressive Modeling?
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
a) Temperature
-0.2
-0.1
0
0.1
0.2
0.3
TemperatureNutrientsPhotoperiod...
Storm activityFishing pressure
...
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
a) Temperature
-0.2
-0.1
0
0.1
0.2
0.3
TemperatureNutrientsPhotoperiod...
Storm activityFishing pressure
...
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
And exogenous forces...
Temperature ... Nutrients .... Photoperiod ... Storm activity ... Fishing pressure ...
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Biologically plausible interactions...
Temperature ... Nutrients .... Photoperiod ... Storm activity ... Fishing pressure ...
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Let’s reduce this set of interactions to those that arestrongest....
Total Phosphorus
Hampton, Scheuerell, & Schindler 2006S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Long-term observational & experimental data
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Temperature
10
15
20
1960 1965 1970 1975 1980 1985 1990 1995 2000
Phosphorus
1060
110160
1960 1965 1970 1975 1980 1985 1990 1995 2000
Diatoms
0100200300
1960 1965 1970 1975 1980 1985 1990 1995 2000
Green algae
0
50
100
1960 1965 1970 1975 1980 1985 1990 1995 2000
Daphnia
0
50
100
1960 1965 1970 1975 1980 1985 1990 1995 2000
Can we characterize food web interactions based on monitoring data?
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
For example....Experimental evidence for food web effects of cyanobacteria blooms
0
1000
2000
3000
4000
5000
0 100 200 300 400
Oscillatoria/ml
Cry
pto
mo
nas/m
l
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Evidence for these relationships in natural data?
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Evidence for these relationships in natural data?
0
5
10
15
0 5 10 15
0
1
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4
0 5 10 15
ln Oscillatoria biovolume
ln C
rypto
monad b
vln
Daphnia
ind L
-
1
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Lake Washington food web
Temperature
Nutrients
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Multispecies Autoregressive Models (MARs)
Log abundance of species i tomorrow
Log abundance of species i today
Species-specific constant
xi(t+1) = xi(t) + ai + [bi,j xj(t)] + [ci,k uk(t)]
Ives, Dennis, Cottingham, & Carpenter. 2003. Ecol. Monogr. 73(2)
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Multispecies Autoregressive Models (MARs)
Log abundance of species i tomorrow
Log abundance of species i today
Species-specific constant
Log abundance of species j today
Effect of species j on species i
xi(t+1) = xi(t) + ai + [bi,j xj(t)] + [ci,k uk(t)]
Ives, Dennis, Cottingham, & Carpenter. 2003. Ecol. Monogr. 73(2)
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Multispecies Autoregressive Models (MARs)
Log abundance of species i tomorrow
Log abundance of species i today
Species-specific constant
Log abundance of species j today
Effect of species j on species i
Effect of environmental variable k on species i
Level of environmental variable k today
xi(t+1) = xi(t) + ai + [bi,j xj(t)] + [ci,k uk(t)]
Ives, Dennis, Cottingham, & Carpenter. 2003. Ecol. Monogr. 73(2)
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
Multispecies Autoregressive Models (MARs)
Coefficients represent interaction strength
xi(t+1) = xi(t) + ai + [bi,j xj(t)] + [ci,k uk(t)]
Ives, Dennis, Cottingham, & Carpenter. 2003. Ecol. Monogr. 73(2)
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
MAR food web construction for Lake Washington
Total Phosphorus
S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
MAR food web construction for Lake Washington
1962 - 1972
Total Phosphorus
Hampton, Scheuerell, & Schindler 2006S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007
MAR food web construction for Lake Washington
1962 - 1972
Total Phosphorus
Hampton, Scheuerell, & Schindler 2006S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007