Why use Multivariate Autoregressive Modeling?

of 22/22
Why use Multivariat e Autoregress ive Modeling? . Hampton, NCEAS, UCSB, [email protected], 7 July 2007
  • date post

    30-Dec-2015
  • Category

    Documents

  • view

    33
  • download

    4

Embed Size (px)

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 Presentation

Transcript of Why use Multivariate Autoregressive Modeling?

  • 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

  • TemperatureNutrientsPhotoperiod...Storm activityFishing pressure...S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

  • TemperatureNutrientsPhotoperiod...Storm activityFishing pressure...S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

  • Endogenous interactionsS.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

  • Lets reduce this set of interactions to those that arestrongest....Total PhosphorusHampton, Scheuerell, & Schindler 2006S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

  • Experiments & ObservationS.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

  • Long-term observational & experimental dataS.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

  • 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 bloomsS.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?S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

  • Lake Washington food webTemperatureNutrientsS.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

  • Multispecies Autoregressive Models (MARs)

    Log abundance of species i tomorrowLog abundance of species i todaySpecies-specific constantxi(t+1) = xi(t) + ai + [S bi,j xj(t)] + [S 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 tomorrowLog abundance of species i todaySpecies-specific constantLog abundance of species j todayEffect of species j on species ixi(t+1) = xi(t) + ai + [S bi,j xj(t)] + [S 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 tomorrowLog abundance of species i todaySpecies-specific constantLog abundance of species j todayEffect of species j on species iEffect of environmental variable k on species iLevel of environmental variable k todayxi(t+1) = xi(t) + ai + [S bi,j xj(t)] + [S 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 strengthIves, Dennis, Cottingham, & Carpenter. 2003. Ecol. Monogr. 73(2)S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

  • MAR food web construction for Lake WashingtonTotal PhosphorusS.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

  • MAR food web construction for Lake Washington1962 - 1972Total PhosphorusHampton, Scheuerell, & Schindler 2006S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

  • MAR food web construction for Lake Washington1962 - 1972Total PhosphorusHampton, Scheuerell, & Schindler 2006S.E. Hampton, NCEAS, UCSB, [email protected], 7 July 2007

    Many researchers become interested in multivariate analyses at a point when they recognize that a particular species of interest is embedded in a food webMany researchers become interested in multivariate analyses at a point when they recognize that a particular species of interest is embedded in a food webMany researchers become interested in multivariate analyses at a point when they recognize that a particular species of interest is embedded in a food web and subject to many environmental forces, so that understanding why a particular species is declining or increasing is not particularly straight-forward. Others may have basic questions about the structure of a food web and the properties it imparts to ecosystem functions, without any interest at all in species. Many researchers become interested in multivariate analyses at a point when they recognize that a particular species of interest is embedded in a food web and subject to many environmental forces, so that understanding why a particular species is declining or increasing is not particularly straight-forward. Others may have basic questions about the structure of a food web and the properties it imparts to ecosystem functions, without any interest at all in species. Traditionally, to understand links in food webs, ecologists have isolated interactions through experimentation...However, realistically, species are embedded in food webs interacting with so many organisms that experimentation could not possibly capture all of the interactionsHowever, realistically, species are embedded in food webs interacting with so many organisms that experimentation could not possibly capture all of the interactionsLuckily many of us have long-term data, from single systems or several systems of interest, and we should be able to find out what interactions in the food web and what the structure of the food web is like by studying what the dynamics are over time.Great deal of data, Imagine hundreds of these time series and now we have the opportunity and challenge to make any sense of them.Standard monitoring results in hundreds of time series like theseMonitoring data are noisy, may be difficult to interpret until many data points are accumulatedUltimately should be able to use these data to determine whether there are correlations that suggest interactions of competition, predation that test the conceptual models we have for food web functioningObscured by temporal variability and relationships with other organisms that modify the interactions among Daphnia and algae. We know that each compartment is affected by multiple organisms and abiotic factors. For example Daphnia may be using all of these food resources variously, and they also contribute to growth of its competitors, who contribute to growth of its predators as well. Temp and nutrients can affect all the compartments differently and to varying degrees, and change accordingly through seasons and across years.So the problem is how to approach a multivariate problem like this in time series measurements?

    Abundance tomorrow predicted by abundance todayA constantEffects of other species (b) and their abundances todayEffects of exogenous variables such as temperature and those levels todayAbundance tomorrow predicted by abundance todayA constantEffects of other species (b) and their abundances todayEffects of exogenous variables such as temperature and those levels todayAbundance tomorrow predicted by abundance todayA constantEffects of other species (b) and their abundances todayEffects of exogenous variables such as temperature and those levels todayThe MAR process determines which are informative for each species and estimates these coefficients, telling you how strongly species interact and how strongly an environmental variable affects the system, given all the possible pathways through which species and variables may interact.So we tell the model how many interactions are actually plausible clearly a number that is intractable experimentally and the model kicks out the uninformative links, leaving us with a manageable setFood web resulting from an analysis of the eutrophied period of Lake Washington, and well focus on those aspects that were previously thought important based on experimentation and observation