Tutorial: Food chain model
Studies have indicated that fishing pressure on reef piscivores can have surprisingly small impact on their prey, reef planktivores.
Construct a simple ecosystem model to study this closer. The model can be a straight food chain, e.g., with the following functional groups and parameters.
Create a new model Menu > File > New model and name it (e.g., “Food chain”). The model will be saved as a database with .ewemdb extension. Go to Ecopath > Input > Basic input > Define groups and click Insert four times. In the Group name column, enter the first four group names from the table below. (Detritus will already be there). Make Phytoplankton a Producer. [While here, change the default colours to Random]. Click OK.
Enter the following parameters on the Ecopath > Input > Basic input form, (cut/paste works from Excel to EwE, but probably not from the table below)
| Group | Biomass (t km-2) | P/B (year-1) | P/Q |
| Piscivores | 0.5 | 0.5 | 0.2 |
| Planktivores | 2 | 1 | 0.25 |
| Zooplankton | 2 | 10 | 0.3 |
| Phytoplankton | 5 | 100 | |
| Detritus | 10 |
Diets: A straight chain as in the figure. Enter them at the Ecopath > Input > Diet composition form.
Fisheries: there’s already a fleet defined by default, so go to Ecopath > Fishery > Landings, and enter a landing of 0.1 t · km-2 · year-1 of reef piscivores. [Yes, we give units, units are important and best left explicit!]
Balance the model (Ecopath > Output > Basic estimates) and examine the outputs. Make sure the model is balanced! If not (check your input data), balance it!
Open a new scenario in Ecosim by going to Ecosim > Output > Run Ecosim, and name it, (e.g, “Scene 1”). Click Run. What do you see? Why is it flatlining?
The two principal ways of forcing Ecosim are through fishing effort (by fishing fleet) or through fishing mortality (by functional group).
First try to increase fishing for piscivores over time by doubling fishing effort for the fleet taking reef piscivores by drawing an increasing shape at Ecosim > Input > Fishing Effort. Run Ecosim again, what happens now. Who increases, who doesn’t, why? Discuss cascading effects, does it occur, and how does it propagate through the food chain?
You can see the results in more detail if you go to Ecosim > Output > Ecosim results, and click Group, landed by. Here you can see how much the biomasses of piscivores and planktivores changed over time (by default it compares the first year of a run with the last year, but you can change that to get results for any time period). Does the increased catch of piscivores cause amplification or dampening through the food web?
You can study the results in more details if you go to Ecosim > Output > Group plots. These plots are very informative, showing time dynamics of what happens with fishing, predators and prey for each group.
Ecosim predictions are especially sensitive to vulnerability multiplier settings (Ecosim > Input > Vulnerabilities). Vulnerability multipliers are the key foraging arena parameter, it captures capture density-dependent effects. Think of it like this, the vulnerability multiplier expresses how many times a given predator can increase the predation mortality it is causing on its prey, if the predator abundance were to increase to its carrying capacity. A vulnerability multiplier of 1 thus tells us that the predator is at its carrying capacity – and hence can increase no more unless its prey becomes more abundant. That means it’s ‘bottom-up’ control. Conversely, high vulnerability multipliers (e.g., 100) tell us that the predator is far from carrying capacity – that’s ‘top-down’ control.
Go to the Ecosim > Input > Vulnerabilities form, and set the vulnerability multiplier for piscivores eating planktivores to 5, run the model again, what happens. Reset the vulnerability to 2.
Try setting the vulnerability multiplier for planktivores eating zooplankton to 5. Run again. What happens now? Does the planktivores behave much differently from when using the default vulnerability multiplier?
Finally, try setting the vulnerability multipliers for all three interactions to 100. Run again. This setting turns the model into a Lotka-Volterra model, which tends to be unstable and produce cycles. Lotka-Volterra models also tend to self-simplify where groups die out. Did that happen in your model?
Reset your model to default vulnerabilities (2).
As you can tell from the above, the vulnerability multipliers are important, and we will return to that later in this textbook when discussing the foraging arena and time series fitting, which indeed has vulnerability multipliers and density-dependence as key factors.
Now let’s try fishing some reef plantivores, do the following
- Go to Ecopath > Fishery > Fleets, Define fleets and add a second fleet, e.g., gill netters.
- On Ecosim > Input > Fishing effort, click Reset All
- Run Ecosim. It should flatline.
- Go back to Ecosim > Input > Fishing effort, and double the fishing effort for your new fleet
Run Ecosim again, what happens?
Examine the group plot (Ecosim > Output > Ecosim group plots for reef planktivores, and note how the catch of the second fleet doubled along with the fishing mortality for the group. Then check the Mortality: total, fishing, predation plot. Here, from the baseline to the red line represents predation mortality, from the red to the blue line is fishing mortality, and from the blue to the black line is total mortality. What happened to predation mortality when fishing increased?
Feeding time – variable or fixed?
Fish tend to have diurnal patterns, often to reduce predation risk while still being able to feed. If you dive at a reef around dusk, you may see a flurry of activities, finely tuned to eat while not being eaten. This may be of less concern for top predators and marine birds who more likely will spend more time feeding when food abundance is low.
We can consider this in Ecosim (and Ecospace) with the relative feeding time parameter at Ecosim > Input > Group info > Feeding time adjust. rate. The default setting for this parameter is 0.5 (range [0,1]), which will allow a predator to change feeding time as needed.
Check that your model flatlines. The go to Ecosim > Input > Fishing effort, click on the first fleet at the bottom panel, then click Set to value and enter 1.1 to increase fishing effort for the fleet catching reef planktivores with 10%. Run Ecosim. What happens? Is the model stable?
Next, remove feeding time adjustment, go to Ecosim > Input > Group info > Feeding time adjust. rate and set this parameter to 0 for all groups. Run Ecosim again, what happens now?
Stable state?
Reset the fishing mortality and any other parameters you may have changed in your model. Do an Ecosim run and check that it flatlines.
Go back to Ecopath > Input > Other production and set the biomass accumulation rate to -0.1 for piscivores. Go back to Ecosim, and run it again, (you’ll be asked if you want to save your Ecopath model, just do that).
The negative biomass accumulation term tells Ecosim that the fishing mortality on piscivores at the Ecopath baseline wasn’t sustainable. (You can zoom in on the Ecosim > Output > Run Ecosim plot to see the details for the first 15 years or so better). Notice the initial decline in piscivores, and the simple but clear cascading impacts through the food chain.
Notice the initial cycling that occurs, and that the system after some years stabilizes to a new equilibrium that is different from the original. Which groups decreased, which increased?
Does this make sense?
A lesson is that if the baseline Ecopath model has a biomass accumulation term, the system is not in stable state and we may expect a new stable state to emerge
Paradox of enrichment
The term paradox of enrichment was coined and developed by Michael Rosenzweig in the early 1970s, and is used to describe how an increase in system productivity may cause a system to become unstable. In a simple system, it can be that food supply make a species like rabbit overabundant causing its population to increase, followed by an increase in its predator, e.g, lynx. The predator population may then overshoot, causing the prey to crash, and it can potentially lead to local extinctions. The term is called a paradox as seems unreal that an increase in primary productivity should have such drastic effects.
But standard Lotka-Volterra models indeed behave like that. The foraging arena theory provides us with an explanation why this paradox is not an aspect of reality.
We can explore this with the model we just built. Open your model, make an Ecosim run and check that the model flatlines and that the vulnerabilities are at default (2). Download a time series file (PP paradox.csv) from this link. Go to Ecosim > Input > Time series > Import and browse to import the PP paradox.csv file. This will import a forcing function with relative primary production values. Go to Ecosim > Input > Forcing functions > Apply forcing (producer) and click the box by the phytoplankton group. On the pop-up form, click 1: PP and the arrow pointing right to apply the forcing function. This will link the primary production anomaly from the time series file with the phytoplankton group, and force its productivity over time.
Now go back and run Ecosim. Is it system stable? What does the enrichment do through the food web? Dampening or amplification?
Next, change the vulnerability multipliers (Ecosim > Input > Vulnerabilities) for all groups to 10 (more top-down control, further from carrying capacity). Run Ecosim again. What happens?
Next set the vulnerability multiplier for zooplankton to phytoplankton to 1. Run and study
Then, also set planktivores to zooplankton multiplier to 1. What happens now?
You now probably have a stable system with some amplification through the food web, but stable! In this configuration, the lower trophic levels were at carrying capacity when the model run started (but reef piscivores were further from their carrying capacity). The primary production anomaly (+10%) we read in increased the productivity at the lower to intermediate trophic levels (+20%) while reef piscivores, which were further from their carrying capacity (multiplier of 10) increased even more (28%).
