Ecospace has three options for modeling the movement and survival-growth of multi-stanza groups – groups that represent ontogenetic stages of a species, such as larvae, juvenile and adult fish: the Basic Partial Differential Equations (PDE) model applied to split pools of biomass in the original Ecospace model, the EwE6 multi-stanza model and the Individual-Based Model (IBM; Walters et al., 2010, 1999).

Basic PDE

This is the original implementation of multi-stanza accounting in Ecospace and is included for legacy reasons (Walters et al., 1999). This option does not account for size-age structure within each life stages of the multi-stanza group, but links one species related to different pools of biomass. Instead, it treated each life stage as its own functional group that assumed the size-age structure was at equilibrium for the life stage. Because of this, the PDE does not give an accurate accounting for numbers at age, and body weight is calculated on a grid averaged value. If a model contains multi-stanza groups, it is recommended that one of the other options are used.

EwE6 Multi-Stanza Model

The EwE6 multi-stanza model is the default option. This model includes a single spatially averaged size-age structure model that is used to populate the Ecospace grid cells. Spatial distributions are handled by the diffusion model in the same manner as the non-multi-stanza biomass pool groups. Weighted, spatially averaged consumption and total mortality rates are calculated across the map for each model time step (Walters et al., 2010). These spatially averaged values update numbers- and weights-at-age of the single size-age structure model. Once this is done, the map-averaged biomass for each life stage of the multi-stanza group can be integrated from the numbers- and weight-at-age. These averaged biomasses are then populated back into the grid cells based on the original biomass weighting of each cell. This algorithm maintains the Ecosim style numbers and weights at monthly ages accounting, with fecundity rates based on body weight above weight at maturity, and size-number dependent monthly egg production used to predict recruitment rates to age 0 fish. However, because it is based on spatially averaged values, any local differences in consumption and/or mortality rates are lost. For example, the consumption and mortality rates inside an MPA will be the average across the modeled area, not just the values inside the MPA. Similarly, local effects on consumption and mortality of habitat restoration will be averaged over the model domain (Walters et al., 2010).

IBM

In the IBM Ecospace predicts spatial changes in consumption and mortality rates by dividing each multi-stanza population into a user-controlled number of packets (a.k.a. cohorts or super-individuals). Each packet is assumed to represent a group of identical individuals of the same age and each packet maintains its own multi-stanza size-age structure. At initialization of a run, each packet is populated with the same monthly numbers-at-age and weight-at-age, then uniformly distributed over the grid cells with a habitat capacity greater than 0.1. At each monthly time step, each packet is tracked independently as it moves around the grid cells. This allows each packet to derive its consumption and mortality rates from the conditions in the local cell it finds itself in at the beginning of the time step. By doing this, each packet can respond to local ecological conditions as it moves through both space and time (Walters et al., 2010). Monthly recruitment creates new IBM packets with initial age 1 month, spatially distributed in proportion to the distribution of spawning biomass.

Due to the way the number of packets that is used to represent a single month in a multi-stanza life stage is calculated, multi-stanza life stages that span a shorter time frame (or number of months), are represented by fewer packets. An implication of this is that if the number of packets is too low, the spatial distribution will be unrealistically patchy, and the life stage’s survival-growth will be dominated by the ecological conditions of only the few cells that the packets happened to find itself in due to random movement. The package multiplier used to scale the total number of packets needs to be high enough to give realistic spatial distribution for the shortest-lived life stages of multi-stanza groups. However, if it is too high the computational speed may be slow. Setting the number of packets is a tradeoff between computational speed and the need to be high enough that it will predict realistic spatial distributions (Walters et al., 2010).

The movement in the IBM model is controlled by the same parameters as the non-multi-stanza species base dispersal rate, relative vulnerability to predation in bad habitat, relative movement speed to cell fitness, relative dispersal in bad habitat, advection, migration and the foraging capacity of neighboring grid cells. The base dispersal rate and grid cell size are the main drivers of the IBM dispersal rates with foraging capacity, advection and migration weighting the direction of the movement. Monthly movements are a series of incremental steps with each step being no larger than half a cell. The direction for each move can only be in one of the cardinal directions (N, S, E, W). If a packet cannot escape the grid cell from its current location, because it can only move a maximum of half a cell, then it will move in a uniform random direction in one of the four directions. Otherwise, if it can escape the current cell in one move, the probability of it moving in any one direction will be a random choice weighted by the foraging suitability of the neighboring cells (Walters et al., 2010).

While a packet can move through multiple grid cells in a time step, the consumption and mortality rates are derived from the grid cell it finds itself in at the start of a time step, and these rates are not integrated across the cells it traveled through during the time step to get to its current location. This assumes the grid cell size and dispersal rates are such that a packet can only move over a few grid cells in a time step, or the spatial distribution of food availability and mortality rates does not vary greatly over the grid cells a packet traveled through in a single time step. As with other Ecospace model configurations, when using the IBM one needs to make sure that the spatial resolution of the basemap, the spatial distribution of habitat or foraging capacity and dispersal rates capture the behavior of the multi-stanza life stages.

The initial spawning location of each packet can be set to either recruit where spawned, current location of the spawner, or to be moved to randomly selected nursery cells, a grid cell with habitat capacity greater than 0.1 for the age 0 life stage of the multi-stanza group. This allows the habitat of spawning adults and start-age recruits to be spatially separated in such a way that the movement model could not transport them across the grid cells in a single time step. This prevents the recruits from incurring unrealistically high mortality rates as they move into better foraging capacity. Packets that age from one life stage to the next can also be randomly moved at stanza entry into cells that have a foraging capacity of greater than 0.5 for the life stage they are aging into. Again, this prevents the life stage from incurring unrealistic mortality rates as it moves into areas of better foraging.

The multi-stanza plus IBM model has not been intensively featured in publications yet (but see Espinosa-Romero et al., 2011; Grüss et al., 2016; Püts et al., 2020). There are many potential applications that can benefit from these capabilities, including the evaluation of MPAs and MPA connectivity, the effects of climate change or the impacts of invasive species. The current IBM model application correctly incorporates current velocities to move advected multi-stanza packets. This makes Ecospace especially useful for studying protected area connectivity.

Adaption

The chapter is in part adapted, with permission,  from:

De Mutsert K, Marta Coll, Jeroen Steenbeek, Cameron Ainsworth, Joe Buszowski, David Chagaris, Villy Christensen, Sheila J.J. Heymans, Kristy A. Lewis, Simone Libralato, Greig Oldford, Chiara Piroddi, Giovanni Romagnoni, Natalia Serpetti, Michael Spence, Carl Walters. 2023. Advances in spatial-temporal coastal and marine ecosystem modeling using Ecopath with Ecosim and Ecospace. Treatise on Estuarine and Coastal Science, 2nd Edition. Elsevier.