20 Predator satiation and foraging time

Predator satiation and handling time effects

Ecosim and Ecospace allow you to represent two factors that may limit prey consumption rates per predator (Q/B):

1. foraging time adjustments related to predation risk and/or satiation; and
2. handling time effects.
3. Parameters for both are specified via the Ecosim Group info form.

Satiation and/or choices to forage for short times in order to avoid higher predation risk are represented by setting non-zero values for the Ecosim > Input > Group info > Feeding time adjustment rate of a group: larger values of this rate represent more rapid adjustment of foraging time. Non-zero foraging time adjustment rates cause Ecosim/Ecospace to update relative foraging time during each simulation so as to represent predators as trying to maintain Q/B near the Ecopath input base rate. For some organisms (particularly marine mammals) this foraging time adjustment may represent animals always trying to feed to satiation (Q/B from Ecopath the satiation feeding rate) and taking more or less time to reach satiation depending on prey densities (and possibly also facing higher predation risk when foraging times are longer). For other organisms, the Ecopath base Q/B may represent a much lower feeding rate than the animal could achieve under “safe” laboratory conditions, and in this case we view the base Q/B as an evolutionary “target” rate representing results of natural selection for balancing benefits from feeding with predation risk costs of spending more time feeding.

Handling time effects represent the notion that predators have limited time available for foraging and this time can be used up by “handling time” (pursuit/manipulation/ingestion time per prey captured) rather than searching for prey, when prey densities are high. The Ecosim > Input > Group info > QB_max/QB₀ (for handling time) (>1) parameter allows you to set ratios of maximum to Ecopath base food consumption rates per individual (or per biomass). These ratios are set to large values (1000) by default, which allows predators to increase their feeding rates without limit as prey densities increase (i.e., not limited by time required to handle each prey). In most scenarios, limitation of prey vulnerability prevents this unreasonable assumption from having noticeable effect. But in scenarios where vulnerable prey densities of at least one type do increase greatly, setting a low value (e.g., 2 or 3) for the predator’s maximum/base feeding rate ratio allows you to represent limits on feeding rate associated with time needed to handle each prey. Without such limits, your predictions of increase in predator Q/B, and hence productivity, at low predator density (or high prey density) might be too optimistic and lead you to errors like overestimating sustainable harvest rate for the predator. Also, ignoring handling time effects when one prey type increases greatly can cause an underestimate of the ‘buffering’ effect that such increases can have on predation rates felt by other prey: if the predator consumes more of the abundant prey, and spends more time handling/resting because of this, predation rates on other prey species should decrease.

Ecosim/Ecospace calculates feeding rates of predators using the “multispecies disc equation”, a generalization of Holling’s type II functional response model for multiple prey types (see the Holling functional response chapter). Using the maximum/base feeding rate ratio R_j from the Ecosim > Input > Group info form along with the Ecopath base food consumption rate per predator, the program calculates a maximum ration and effective handling time per prey biomass eaten (handling time = 1 / (maximum prey biomass eaten per time)). This handling time (Holling’s h parameter) is used to calculate the denominator in the disc equation formulation Q_ij/B_j , biomass of prey type i consumed per time per unit biomass of predator j, as Q_ij/B_j  = a_ij V_ij / (1 + h_j ∑_k a_kj V_kj) where a_ij is the rate of effective search by predator j for type i prey, h_j is the predator handling time parameter, V_ij is the instantaneous density of prey type i vulnerable to predator j, and the sum in the denominator is over all prey types k taken by the predator. A useful fact about the multispecies disc equation is that D_j, the proportion of time spent feeding (reactive to prey rather than handling), is given by Dj=1/(1 + h_j ∑_k a_kj V_kj). For more information about how the disc equation D_j enters food consumption rate calculations along with other factors that influence feeding, see the Foraging arena chapter. The solution for vulnerable prey densities V_ij needed in the disc equation calculation over time involves  a numerical procedure that can occasionally cause annoying “chatter” in the Ecosim results when handling times are large (ratio of maximum/base consumption rate small).

A helpful fact about the D_j proportion of time spent feeding in the disc equation formulation is that it can be calculated simply from the user-provided ratio R_j of maximum to ecopath base ration, as just D_j=R_j/(R_j-1). This is used to initialize the D_j at the start of each Ecosim run.

Bioenergetics models for fish most often indicate that feeding rates are low compared to maximum ration; typical ratios of estimated to maximum ration (Hewett-Johnson^[1] P parameter) are around 0.3-0.4. These estimates imply R_j (maximum/Ecopath base ration) values of at least 2-4. If you choose to use such realistic values instead of the default 1000, and if this causes Ecosim/Ecospace to show oscillatory behaviour, you need to consider two possibilities:

• The oscillatory behaviour may be a numerical artifact of the procedure used to update D_j; or
• The model’s “correct” behaviour for the parameter combinations you have provided is indeed a predator-prey cycle.

If the oscillation has a period of several time steps (months), it is very likely a predator-prey cycle. Persistent predator-prey cycles are commonly predicted by models that include handling time, along with strong top-down control (high vulnerability multipliers v_ij of prey to predators). If you think the cycle is unrealistic, you should adjust the prey vulnerabilities multipliers (Ecosim > Input > Vulnerabilities) to lower values (toward “bottom up”, prey vulnerability control) rather than just setting high R_j values. If you see very short cycles indicating numerical instability in the D_j adjustment procedure (usually happens for fast turnover groups like micro-zooplankton), you should set higher R_j values for the offending groups. This amounts to recognizing that Ecosim may be limited in its ability to represent very fast dynamic changes in groups that turn over very rapidly.