Tutorial: Stock recovery scenarios

The cod population in Anchovy Bay has been depleted, and there is concern for its recovery. Assessments in the 1980s indicated overexploitation to be the cause of the population decline, and the trawl fishery for cod was closed in 1990, despite concerns for the socio-economic consequences. It was some comfort, however, that the stock was predicted to rebound within a few (cod) populations, perhaps in a decade or so.

By 2010, the cod population, however, had shown little sign of recovery. In this tutorial, we use a previously constructed, (but slightly modified) ecosystem model of Anchovy Bay to evaluate alternative hypotheses for why the cod population has not recovered to its 1970-level in spite of a strong reduction in fishing pressure.

Download the Anchovy Bay Cod Recovery.ecomdb database along with the cod recovery.csv time series file from this zip file. Open the EwE software and load the Anchovy Bay model, the Ecosim scenario, and import the cod recovery time series file. Then run Ecosim, and note the Summed Squared residuals (SS, on the run screen, top left corner). You can scroll through the groups, to see the trajectory for each (along with the groups contribution to the SS).  Also, open the Group plot form (Ecosim > Output > Ecosim group plots), and examine the plots for each of the functional groups/species. You will notice that the fits to time series are pretty poor – which shouldn’t be surprising as we are only starting the fitting process now.

For the fitting, we will consider the combined impact of fisheries, environmental conditions, and food web structure. We do that in a semi-structured manner.

Predictions of the impact of fisheries will, in any model, depend on density-dependent factors. In Ecosim, the most important factor is the vulnerability multiplier. Vulnerability multipliers express how much the predation pressure that a given predator causes on its prey can be increased if the predator was to increase to its carrying capacity. If the predator is at carrying capacity, it cannot increase the predation pressure on its prey (that’s what being at carrying capacity means), so the vulnerability multiplier should be 1. If, on the other hand, the predator has been depleted, the vulnerability multipliers should be higher. The default setting for vulnerability is 2, i.e. a predator can at most double the predation mortality it’s causing on its prey.

If you examine the Ecosim group plots after the first run, you’ll notice for seals that the time series indicate a strong increase (7x) in the seal population, while Ecosim indicates less than a doubling. Why? The default vulnerability is part of the problem. Try increasing the vulnerability multipliers for seals as consumers, (Ecosim > Input > Vulnerabilities, click the column heading for column 2 (i.e. for cod as consumer), enter, e.g., 10 in the Set input box in the top right corner, and click Apply).

Run Ecosim again, and check the trajectory for seals. Better? You can also try to lower the vulnerability multipliers, e.g., to 1.1 and see what happens. By the way, the vulnerability multipliers scale from 1 to infinity, it can never be lower than 1, that would mean that the predator had exceeded its carrying capacity in the Ecopath baseline). Most of the ‘action’ is in the 1-20 range, as you increase the vulnerabilities beyond that it gradually has less and less impact.  Note that the Ecosim time series fitting may come back with very high vulnerability multipliers – it may be that changing the multiplier from, e.g., 100 to 100,000 decreases the SS a tiny tiny bit. If that happens, the best is to manually reduce the multipliers and check if it makes any difference in the SS.

For cod, we know that it has been exploited as a target fishery in Anchovy Bay for more than a century, so it would not have been close to its carrying capacity in 1970, (the year for which the Anchovy Bay ecosystem model was constructed, which provides reference points for vulnerability multipliers and other settings).  So, to improve the fit, how should you change the vulnerability setting for cod as a consumer? Try it.

The above goes to show that vulnerability multipliers are not ‘nuisance’ parameters, they have a clear interpretation that makes sense from an ecological perspective, and could in principle be estimated independently of the ecosystem model. The main hurdle for this, however, is that while carrying capacity is on old and well-founded concept, it changes, every day, so it would be difficult, (but perhaps not impossible) to estimate it independently – this factor is indeed what most single-species assessment estimate (B_t/B_o) – though with little basis in reality.

Therefore, our best option is to use constraints in our model, to estimate the density-dependent vulnerability multipliers. We can do this using ‘observations’, made accessible to the model through time series files. In our case (cod recovery.csv), it is rather restricted what we have: seals have increased, cod declined and have not recovered, whiting have increased a bit, and shrimp catches have increased. The principle here is: the more information we have, the more constraints this pose for the model. Therefore, the more data, the more difficult the fitting becomes, but the more confident we can be about the model behavior.

To use the time series for fitting, go to Ecosim > Tools > Fit to time series. Click Search groups with time series, and Search. Ecosim will now run a time series fitting, trying to find vulnerability multipliers that minimizes the SS. You will likely see some reduction in SS, but nothing spectacular. Next, go back to Ecosim, Output, Run Ecosim, and make a run. Examine the group plots. You will likely find that the fit for seals is good, but not the fit for cod, which likely have recovered to the 1970-level as a result of the lower fishing pressure in Anchovy Bay since 1990. Also, shrimp catches don’t even get near to matching the level from the time series.

In conclusion for where we are so far, time series fitting to evaluate the impact of fishing provides some information, but doesn’t explain why cod hasn’t recovered. Is it the environment that has changed then? Reset the environmental forcing function by going to Ecosim > Input > Forcing functions, click the 1: Fitting function, and click Reset.

Next question is: Is it the environment then? To evaluate this, we need information about how the environmental productivity of Anchovy Bay has changed since 1970, with the most important indicator being primary production. Unfortunately, such long-term information is hardly ever available as oceanographers tend to run their models for short time periods only. There is indeed a gap between oceanography and fisheries, and we need to fill it.

In lieu of environmental productivity data, we can ask Ecosim to estimate a ‘primary production anomaly’ (PPA), i.e. how might relative primary production have to have changed over time to fit the time series better. First, go to Ecosim > Input > Forcing function > Apply FF (producer), click the spreadsheet cell for phytoplankton, select 1: Fitting, and click the arrow to the right to apply this forcing function. This only means that you’ve associated primary productivity with the forcing function. Go to Ecosim > Tools > Fit to time series, and click Search groups with time series, click Vulnerability Search (i.e., checked), click Anomaly Search. Then click the Search, Anomaly Search tab.  You should now see the 1: Fitting forcing function on the form. Next, increase the Spline points on the form, e.g., to 8, and click Search. Ecosim now starts a search, resetting vulnerability multipliers and evaluating the combined effects of density dependence (vulnerabilities) and environmental productivity changes (primary production anomaly).

The SS will likely have decreased somewhat (keep track!), but not a lot, so what has it done? Go back to Ecosim > Output > Run Ecosim, and make a new run – the vulnerability multipliers and primary production anomaly from the search have been transferred there already. Examine the Ecosim group plots, check the estimated vulnerabilities and the primary production pattern. You’ll find that there isn’t much improvement for cod. Why?

One part of the answer is that the time series fitting puts the same weight on all of the time series as entered. There’s a weight attributed to each, and the time series file we read in had a weight of 1 for all. If you really want the search to prioritize cod, you could give the cod biomass time series a higher weight, perhaps 10 or even 100. The downside is that you’d be twisting your ecosystem model in the direction of a single-species model.

What then?

Perhaps cod reacts differently to environmental change than the ecosystem overall? To evaluate this, let’s consider how temperature impacts cod (they like cooler water), and fortunately temperature is usually one of the time series we may obtain from the oceanographers.

If you look in Ecosim > Input > Forcing functions, you should find a T bottom time series. Let’s apply this to cod. Go to Ecosim > Input > Functional responses, here there should be a Temp cold environmental response function, which we’ll use for cod. Click Ecosim > Input > Functional response > Apply functional responses, click the cell intersecting Cod juv. with T bottom, and transfer Temp cold to Applied responses. Do the same for Cod ad.  Does it improve the fit? Some, but cod is likely still not recovering to the 1970-level.

Fit to time series again, use the Search group with time series option, but add shrimp as consumer to the fitting (select a non-used color, and click the column heading for group 10).

Examine the fit. You’ll likely find that seals increase more in Ecosim than in the time series. The search has chosen a higher vulnerability for seals in order to get more increase and therefore more predation pressure on cod, to help keep that group down. If you examine the diet composition for seals, you’ll see that cod is a very minor component, but this represents a high predation pressure on cod.

Next, examine the diet compositions. You’ll see the whiting does not eat cod. That’s unlikely to be correct, so try including it. For instance, by letting juv. whiting take 0.005 juv. cod (and change the proportion of zooplankton in the juv. whiting diet to 0.9. For ad. whiting change the proportion of juv. cod to 0.03, for ad. cod to 0.01, and for benthos to 0.34. Run Ecosim, then do a new fit to time series, again with fitting for groups 2, 4, 6, 10, i.e. groups with reference time series including shrimp, (which has a catch time series).

How does this look? Does cod recover now?

You likely have a pretty good fit now, examine it, each group, vulnerability multipliers, … Think about how you got the fit. Also, try to get the predictions to break down again. Play! But reflect on what you’re doing and notice what effect you see for different scenarios.

Even if you now have a good fit, try one more thing. Redo the time fit, but this time also include an Anomaly search for a primary production anomaly (using spline points, still 8 perhaps). Do the search, and when it’s done compare to the derived forcing function (1: fitting) to the forcing function that was actually used when constructing the model (3: True PP). You’ll likely find some resemblance between the two shapes, but also that the (1: fitting) shows much more variation. The reason for this is that the search criteria is chasing observations, and can do that without penalty as the time series we use in this example have very little constraints. You can get an idea about this by going back to Ecosim and do a run. You’ll likely see some strange things happen in between years with observations

Primary production (PP) should preferably not change over time with more than perhaps +/- 20% or so, and in this case the change was likely much more. Try setting the PP Variance to 0.01, (which will provide a much lower prior for the sampling). This likely caused much less variation in the PP anomaly plot.

Examine the Akaike Information Criteria estimates from the various run on the time series plot, what does that tell you?