Mathematical Models
Interested in a more in-depth description of our models? Below, you can find more detailed descriptions of the three potential models we are considering to investigate each driver of recruitment
Multivariate Auto-Regressive State Space Models (MARSS Package)
These models have been applied to linear stochastic dynamical systems and are a more classical time series analysis approach (Holmes et al. 2014, Tolimieri et al. 2017). The MARSS package has been successfully used to evaluate recruitment patterns from 30 different marine stocks from Australia, New Zealand, Chile, South Africa, and Falkland Islands as they relate to three climate indices (Castillo-Jordan et al. 2015).
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It has also be used to look for common trends in recruitment success across different stocks in New Zealand (Zimmermann et al. 2019) which could be analogous to the different spatial zones for Cisco in Lake Superior that others have used when analyzing recruitment (Rook et al. 2012, 2013).
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Another benefit of the MARSS package is that is allows for different time series to be combined (i.e if there was a sampling gear change in the fisheries independent survey, you can still use the full time series while acknowledging this change point), which will most likely increase the temporal span of usable available data for this project.
How will we be using MARSS?
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Aggregate fish data using USGS Age-1 spring bottom trawl data
Compile covariates (abiotic and biotic influences on cisco)
Calculate monthly averages and lag variables according to ecological relevance
Run MARSS and find out which months and covariates have the most impact on cisco recruitment
