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Why use Multivariate Autoregressive Modeling?. S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007. S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007. Temperature Nutrients Photoperiod. Storm activity Fishing pressure.

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slide1

Why use Multivariate Autoregressive Modeling?

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide3

Temperature

Nutrients

Photoperiod

...

Storm activity

Fishing pressure

...

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide4

Temperature

Nutrients

Photoperiod

...

Storm activity

Fishing pressure

...

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide5

Endogenous interactions

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide6

And exogenous forces...

Temperature ... Nutrients .... Photoperiod ... Storm activity ... Fishing pressure ...

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide7

Biologically plausible interactions...

Temperature ... Nutrients .... Photoperiod ... Storm activity ... Fishing pressure ...

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide8

Let’s reduce this set of interactions to those that are

strongest....

TotalPhosphorus

Hampton, Scheuerell, & Schindler 2006

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide9

Experiments & Observation

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide10

Long-term observational & experimental data

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide11

Can we characterize food web interactions based on monitoring data?

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide12

For example....

Experimental evidence for food web effects of cyanobacteria blooms

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide13

Evidence for these relationships in natural data?

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide14

ln Cryptomonad bv

ln Daphnia ind L-1

ln Oscillatoria biovolume

Evidence for these relationships in natural data?

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide15

Lake Washington food web

Nutrients

Temperature

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide16

Multispecies Autoregressive Models (MARs)

Ives, Dennis, Cottingham, & Carpenter. 2003. Ecol. Monogr. 73(2)

Log abundance of species i tomorrow

Log abundance of species i today

xi(t+1) = xi(t) + ai + [S bi,j xj(t)] + [S ci,k uk(t)]

Species-specific constant

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide17

Multispecies Autoregressive Models (MARs)

Ives, Dennis, Cottingham, & Carpenter. 2003. Ecol. Monogr. 73(2)

Log abundance of species i tomorrow

Effect of species j on species i

Log abundance of species i today

xi(t+1) = xi(t) + ai + [S bi,j xj(t)] + [S ci,k uk(t)]

Species-specific constant

Log abundance of species j today

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide18

Multispecies Autoregressive Models (MARs)

Ives, Dennis, Cottingham, & Carpenter. 2003. Ecol. Monogr. 73(2)

Log abundance of species i tomorrow

Effect of species j on species i

Log abundance of species i today

Effect of environmental variable k on species i

xi(t+1) = xi(t) + ai + [S bi,j xj(t)] + [S ci,k uk(t)]

Species-specific constant

Level of environmental variable k today

Log abundance of species j today

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide19

xi(t+1) = xi(t) + ai + [S bi,j xj(t)] + [S ci,k uk(t)]

  • Multispecies Autoregressive Models (MARs)
    • Coefficients represent interaction strength

Ives, Dennis, Cottingham, & Carpenter. 2003. Ecol. Monogr. 73(2)

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide20

MAR food web construction for Lake Washington

TotalPhosphorus

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide21

MAR food web construction for Lake Washington

1962 - 1972

TotalPhosphorus

Hampton, Scheuerell, & Schindler 2006

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007

slide22

MAR food web construction for Lake Washington

1962 - 1972

TotalPhosphorus

Hampton, Scheuerell, & Schindler 2006

S.E. Hampton, NCEAS, UCSB, hampton@nceas.ucsb.edu, 7 July 2007