Explaining empirical dynamic modelling using verbal, graphical and mathematical approaches.

Empirical dynamic modelling (EDM) is becoming an increasingly popular method for understanding the dynamics of ecosystems. It has been applied to laboratory, terrestrial, freshwater and marine systems, used to forecast natural populations and has addressed fundamental ecological questions. Despite its increasing use, we have not found full explanations of EDM in the ecological literature, limiting understanding and reproducibility. Here we expand upon existing work by providing a detailed introduction to EDM. We use three progressively more complex approaches. A short verbal explanation of EDM is then explicitly demonstrated by graphically working through a simple example. We then introduce a full mathematical description of the steps involved. Conceptually, EDM translates a time series of data into a path through a multi-dimensional space, whose axes are lagged values of the time series. A time step is chosen from which to make a prediction. The state of the system at that time step corresponds to a 'focal point' in the multi-dimensional space. The set (called the library) of candidate nearest neighbours to the focal point is constructed, to determine the nearest neighbours that are then used to make the prediction. Our mathematical explanation explicitly documents which points in the multi-dimensional space should not be considered as focal points. We suggest a new option for excluding points from the library that may be useful for short-term time series that are often found in ecology. We focus on the core simplex and S-map algorithms of EDM. Our new R package, pbsEDM, enhances understanding (by outputting intermediate calculations), reproduces our results and can be applied to new data. Our work improves the clarity of the inner workings of EDM, a prerequisite for EDM to reach its full potential in ecology and have wide uptake in the provision of advice to managers of natural resources.

Weakened portfolio effects constrain management effectiveness for population aggregates.

Population diversity can reduce temporal variability in aggregate population abundances in a process known as the portfolio effect. Portfolio effects may weaken, however, due to greater synchrony among component populations. While weakened portfolio effects have been previously documented, the consequences of reduced stability on meeting conservation goals for population aggregates that are harvested (e.g., stock aggregates in fisheries) are rarely quantified. Here, we demonstrate how changes in variability within components, synchrony among components, and population productivity interact to influence the probability of achieving an array of management objectives for Fraser River sockeye salmon: a stock aggregate of high economic, ecological, and cultural value. We first present evidence that component variability and synchrony have increased over the last two decades, consistent with a weakening portfolio effect. We then parameterize a stochastic, closed-loop model that simulates the population dynamics of each stock, the fishery that harvests the stock aggregate, and the management framework used to establish mixed-stock exploitation rates. We find that while median aggregate abundance and catch through time were relatively insensitive to greater aggregate variability, catch stability and performance metrics associated with achieving management targets generally declined as component variability and synchrony increased. A notable exception we observed is that harvest control means that scale exploitation rates based on aggregate abundance may be more effective as synchrony increases. Reductions in productivity led to broad declines in performance, but also moderated the impacts of component variability and synchrony on the proportion of component stocks above management targets and catch stability. Our results suggest that even precautionary management strategies that account for declines in productivity may underestimate risk, particularly to socioeconomic objectives, if they fail to consider changes in aggregate variability. Adequately incorporating changes in portfolio effect strength may be particularly relevant when developing recovery strategies that are robust to climate change, which is likely to increase synchrony and component variability.

Effects of ocean acidification on temperate coastal marine ecosystems and fisheries in the northeast Pacific.

As the oceans absorb anthropogenic CO2 they become more acidic, a problem termed ocean acidification (OA). Since this increase in CO2 is occurring rapidly, OA may have profound implications for marine ecosystems. In the temperate northeast Pacific, fisheries play key economic and cultural roles and provide significant employment, especially in rural areas. In British Columbia (BC), sport (recreational) fishing generates more income than commercial fishing (including the expanding aquaculture industry). Salmon (fished recreationally and farmed) and Pacific Halibut are responsible for the majority of fishery-related income. This region naturally has relatively acidic (low pH) waters due to ocean circulation, and so may be particularly vulnerable to OA. We have analyzed available data to provide a current description of the marine ecosystem, focusing on vertical distributions of commercially harvested groups in BC in the context of local carbon and pH conditions. We then evaluated the potential impact of OA on this temperate marine system using currently available studies. Our results highlight significant knowledge gaps. Above trophic levels 2-3 (where most local fishery-income is generated), little is known about the direct impact of OA, and more importantly about the combined impact of multi-stressors, like temperature, that are also changing as our climate changes. There is evidence that OA may have indirect negative impacts on finfish through changes at lower trophic levels and in habitats. In particular, OA may lead to increased fish-killing algal blooms that can affect the lucrative salmon aquaculture industry. On the other hand, some species of locally farmed shellfish have been well-studied and exhibit significant negative direct impacts associated with OA, especially at the larval stage. We summarize the direct and indirect impacts of OA on all groups of marine organisms in this region and provide conclusions, ordered by immediacy and certainty.

Performance of salmon fishery portfolios across western North America.

Quantifying the variability in the delivery of ecosystem services across the landscape can be used to set appropriate management targets, evaluate resilience and target conservation efforts. Ecosystem functions and services may exhibit portfolio-type dynamics, whereby diversity within lower levels promotes stability at more aggregated levels. Portfolio theory provides a framework to characterize the relative performance among ecosystems and the processes that drive differences in performance. We assessed Pacific salmon Oncorhynchus spp. portfolio performance across their native latitudinal range focusing on the reliability of salmon returns as a metric with which to assess the function of salmon ecosystems and their services to humans. We used the Sharpe ratio (e.g. the size of the total salmon return to the portfolio relative to its variability (risk)) to evaluate the performance of Chinook and sockeye salmon portfolios across the west coast of North America. We evaluated the effects on portfolio performance from the variance of and covariance among salmon returns within each portfolio, and the association between portfolio performance and watershed attributes. We found a positive latitudinal trend in the risk-adjusted performance of Chinook and sockeye salmon portfolios that also correlated negatively with anthropogenic impact on watersheds (e.g. dams and land-use change). High-latitude Chinook salmon portfolios were on average 2·5 times more reliable, and their portfolio risk was mainly due to low variance in the individual assets. Sockeye salmon portfolios were also more reliable at higher latitudes, but sources of risk varied among the highest performing portfolios. Synthesis and applications. Portfolio theory provides a straightforward method for characterizing the resilience of salmon ecosystems and their services. Natural variability in portfolio performance among undeveloped watersheds provides a benchmark for restoration efforts. Locally and regionally, assessing the sources of portfolio risk can guide actions to maintain existing resilience (protect habitat and disturbance regimes that maintain response diversity; employ harvest strategies sensitive to different portfolio components) or improve restoration activities. Improving our understanding of portfolio reliability may allow for management of natural resources that is robust to ongoing environmental change. Portfolio theory provides a straightforward method for characterizing the resilience of salmon ecosystems and their services. Natural variability in portfolio performance among undeveloped watersheds provides a benchmark for restoration efforts. Locally and regionally, assessing the sources of portfolio risk can guide actions to maintain existing resilience (protect habitat and disturbance regimes that maintain response diversity; employ harvest strategies sensitive to different portfolio components) or improve restoration activities. Improving our understanding of portfolio reliability may allow for management of natural resources that is robust to ongoing environmental change.