4 Assessment method

4.1 Species-scale assessment

The method developed by Halpern et al. (2008) uses 3 types of data, which we will refer to as modules in this assessment: 1) the mapped presence or absence of valued components, i.e. species in this case (\(S_i\)), 2) the spatial distribution and relative intensity (i.e. normalized between 0 and 1) of the environmental drivers considered (\(D_j\)), and 3) the species-specific sensitivity of each species to each driver (\(\mu_{i,j}\)) These data are then incorporated into a grid made up of cells of homogeneous size characterizing the study area.

Cumulative effect predictions (\(C_S\)) are calculated for each cell (\(x\)) of the grid by summing up all individual driver effects over the set of species considered:

\[C_{S_x} = \sum_{i=1}^n \sum_{j=1}^m S_{i,x} * D_{j,x} * \mu_{i,j} \label{eq1}\]

This method proposes the calculation of a relative indicator of cumulative effects to predict the risks associated with the effects of multiple environmental drivers on species. This is in opposition to an absolute indicator of effects, which would identify an observable change in the state of species populations resulting from the effects of cumulative environmental drivers, such as a decline in the beluga whale population in the St. Lawrence Estuary in response to cumulative environmental drivers. A relative indicator instead allows for a comparison of the various environmental drivers according to their intensity within the region studied and their effects on the species considered. The results are therefore more appropriately as a probability of risk. Furthermore, this approach assumes that drivers have additive effects on the valued components considered, which we know is not always the case (Carrier-Belleau et al., 2021; Côté et al., 2016; Crain et al., 2008).

The results of the cumulative effects assessment using this approach are presented in section 7.3 of the report. Cumulative effects predictions can be decomposed to explore the relative contribution of all combinations of drivers and species (Figure 4.1). A complete exploration of all driver-species combinations is therefore possible (Figure 4.1).

Figure 4.1: A fictitious example of spatial assessment of cumulative effects using the methodology suggested by (Halpern et al., 2008). The assessment begins by delineating a study area of interest (A). A picture of the study area is then made by characterizing the distribution of environmental stressors (B) and the valued components (C) allowing the assessment objectives to be reached. The summation of all the environmental stressors allows us to identify the environments that are most exposed to cumulative stress, i.e. cumulative exposure (D). The sum of valued components, on the other hand, allows us to identify the environments in the study area where a higher number of valued components overlap (E). By combining the distribution of environmental stressors and valued components along with the vulnerability of the valued components to the environmental stressors, a relative assessment of individual effects is obtained (F). It is possible to assess the impact of all the environmental stressors on a single valued component (G); similarly, it is possible to assess the impact of a single environmental stressor on all valued components (H). Finding the sum of all the individual impacts provides the relative assessment of cumulative effects incorporating all combinations of environmental stressors and valued components (I).

4.2 Network-scale assessment

The approach developed by Beauchesne et al. (2023) builds on recent progress in theoretical ecology (Beauchesne et al., 2021; Stouffer et al., 2007, 2012) to predict the net effects of environmental drivers by considering both direct and trophically-mediated indirect effects in ecological communities. By focusing on interactions rather than individual species, this approach provides the ability to consider how a focal species is affected by multiple environmental pressures, but also integrates how species it interacts with respond to the same pressures and how their response propagates to the species of interest. In terms of data requirements, this network-scale assessment builds on the same 3 modules as Halpern et al. (2008), i.e. 1) the distribution of species (\(S_i\)), 2) the normalized distribution and intensity of environmental drivers (\(D_j\)), and 3) the species-specific sensitivity of each species to each driver (\(\mu_{i,j}\)); it considers 2 additional modules to complete the assessment: 4) the metaweb of species interactions, i.e. the network of binary biotic interactions structuring local food webs, and 5) the trophic sensitivity of species (\(T_i\)), i.e. their sensitivity to trophically-mediated indirect effects (see below for more details).

The following description of the model and conceptual figure (Figure 4.2) are borrowed directly from (Beauchesne et al., 2023):

Whole food webs can be decomposed into collections of \(p\)-species interactions called motifs (Milo et al., 2002) that provide a mesoscale characterization of the structural properties of ecological networks (Bascompte and Melián, 2005; Bramon Mora et al., 2018; Stouffer et al., 2007; Stouffer and Bascompte, 2010, 2011). In a \(n\)-species food web (\(n \geq p\)), the collection of \(p\)-species motifs (\(p \leq n\)) in which species \(i\) is involved in (\(M_i = \{m_{i,1},m_{i,2},...,m_{i,x}\}\)) forms its motif census (\(M_i\)) (Beauchesne et al., 2021; Stouffer et al., 2012). The motif census provides an overview of all the interactions and connected species likely to affect a species’ dynamics, and the propagation of disturbances through their interactions. Here, we focus exclusively on the most abundant 3-species motifs in empirical food webs (i.e. trophic food chain, omnivory, exploitative and apparent composition) (Camacho et al., 2007; Stouffer and Bascompte, 2010) to assess a species motif census, although the general model would be applicable to any \(p\)-species motifs.

Network-scale cumulative effects scores (\(C_N\)) were predicted in each grid cell as follows:

\[C_{N_x} = \sum_i \frac{1}{|M_i|} \sum_{m_{i,x} \in M_i} \sum_j D_j * \overline{\mu_j} * T_{i_{m_{i,x}}}\]

where \(i\) is the focal species, \(M_i\) is the motif census of species \(i\), \(m_{i,x}\) are the 3-species motifs of interest forming species \(i\)’s motifs census, and \(D_j\) is the log-transformed and scaled intensity of stressor \(j\).

\(\overline{\mu_j}\) corresponds to the joint sensitivity to stressor \(j\) of the species involved in motif \(m_{i,x}\). Here, we explicitly consider that a species’ response to stressors depends on its own response as well as the response of species it interacts with. The joint sensitivity is measured as:

\[\overline{\mu_j} = w_1 \mu_{i,j} + w_2 \sum_k^2 \mu_{k,j}\]

\(\mu_{i,j}\) and \(\mu_{k,j}\) are the sensitivities to stressor \(j\) of focal species \(i\) and of the two species interacting with focal species \(i\) in motif \(m_{i,x}\), respectively. \(w_1\) and \(w_2\) are weighting factors that give a relative importance to direct – i.e. effects to species \(i\) – and indirect – i.e. effects propagating through species \(k\) to species \(i\) – effects in the assessment. \(w_1 + 2 w_2 = 1\) to directly relate the weighting to a percent contribution to direct and indirect effects. For this assessment, we used \(w1 = 0.5\) and \(w2 = 0.25\) to give equal weight to direct and indirect effects.

\(T_{i_{m_{i,x}}}\) is the trophic sensitivity of species \(i\) in motif \(m_{i,x}\). It captures a species sensitivity to trophically-mediated effects, which depends on the structure of the community, the trophic position of focal species \(i\) and the specific entry points of stressors in the system (Beauchesne et al., 2021).

This approach retains some of the limitations and assumptions of the Halpern et al. (2008) approach to cumulative effects assessment (Halpern et al., 2015b; see Halpern and Fujita, 2013; Hodgson et al., 2019), namely that how a single species responds to the direct effects of multiple drivers is assumed linear and additive. Still, the network-scale approach considers the nonlinear and non-additive dynamics of indirect effects propagating through species interactions (see Beauchesne, 2020; Beauchesne et al., 2021; Beauchesne et al., 2023).

Figure 4.2: Network-scale cumulative effects assessment method.** The assessment relies on data-based knowledge on the distribution and relative intensity of environmental stressors (a), the distribution of species (b), the relative sensitivity of species to the effects of stressors (c), the metaweb of ecological interactions – i.e. who eats whom – and the susceptibility of species to the propagation of the effects of stressors through their interactions, i.e their trophic sensitivity. For a particular cell in a regular grid dividing an area of interest, the method extracts the local food web and the intensity of stressors (d). In this example, the focal cell includes 3 stressors (climate change-induced temperature anomalies, commercial shipping, and trawl fishing) affecting 5 species: krill (Euphausiacea), copepods (Copepoda), capelin (Mallotus villosus), Atlantic cod (Gadus morhua), and beluga whales (Delphinapterus leucas). For each species, cumulative effects are predicted across their collection of 3-species interactions, i.e. their motif census. Here, the beluga is involved in 3 motifs: 1 omnivory interaction (beluga-cod-capelin) and 2 tri-trophic food chains (beluga-capelin-krill; beluga-capelin-copepod; e). For each 3-species interaction, direct and indirect effects are those affecting the focal species and those affecting the species it interacts with, respectively. Effects are predicted as the sum of the product of the intensity of stressors, the sensitivity of species to the effects of stressors, and the trophic sensitivity of the focal species. A weight of relative importance is used to combine direct and indirect effects. The total effect is the combination of all predicted effects (f). Net effects on species are then evaluated as the average of total effects predicted across 3-species interactions (g). This process is performed for every cell in the study grid to obtain a map of predicted cumulative effects for every species considered (h). The sum of all species assessments provides the network-scale cumulative effects predictions (i). Figure and caption borrowed from Beauchesne et al. (2023).