Acción 1: desafíos de la economía digital

More complex representations of top predators will usually increase the cost associated with development and use of these models.Fulton et al.(2003) suggest that the predictive capacity of ecosystem models is highest at some intermediate level of complexity. Thus identifying an optimal level of detail or complexity in an ecosystem model is an important, yet challenging factor in the process of developing models. In this regard, an important question is ‘What level of detail in the representation of top predators is needed for an end-to-end ecosystem model to be fit for purpose?’. In this section, we use qualitative network models for a relatively simple Southern Ocean pelagic foodweb to demonstrate how changes in representation of higher trophic level functional groups can affect model outcomes.

Qualitative network modelling provides a relatively simple demonstration of ecological feed- backs and foodweb responses to perturbation, without the fine details that are needed for more comprehensive, quantitative ecosystem models (Levins,1966;Dambacher et al.,2002; Melbourne-Thomas et al.,2012). Links between components within a system are represented directionally as positive (→) or negative (•) interactions (Figure 2.1). Uncertain (or weak) linkages are represented as dashed (- - -) lines. Responses of the model to perturbations are evaluated through qualitatively specified community matrices, which capture the interactions between components within a system based on the signs of the linkages in the model (→= 1, • = -1, and no link = 0) (Dambacher et al.,2002). The inverse of these matrices predict

the ultimate effect of a press perturbation on all community members by estimating the change in equilibrium following a perturbation (Dambacher et al.,2002).

ModelP1 ModelP2 ModelP3 ModelP4 HerbivorousPmacrozooplankton LargePautotrophs PelagicPfish SmallPmesopelagics CarnivorousPmacrozooplankton SmallPautotrophs HeterotrophicPmicrozooplankton

Nutrients Temperature Bacteria PreyPaccessibility CentralPplacePforagers MigratoryPforagers ClimatePchange TopPpredators

*

*

Figure 2.1. Nested qualitative network model representing a generalised Southern Ocean

pelagic foodweb. Linkages between model variables represent positive (→) and negative (•) effects. Uncertain linkages are represented by dashed lines (the uncertain linkage from pelagic predators to nutrients follows the current research of the roles whales play in in- creasing the amount of bio-available iron (e.g.Ratnarajah et al.,2016)). Self-limitation

(Dambacher et al.,2002) is applied to all variables. These nested models capture four lev- els of complexity: Model 1 (represented by the black components) represents a biogeo- chemical model; Model 2 (both black and yellow components) includes the biogeochemi- cal model and a mid-trophic level; Model 3 (black, yellow and blue components) includes the addition of a generalised top predator (here assumed to be a combination of colony breeders (e.g. seals, penguins) and pelagic predators (e.g. whales, orcas)); Model 4 (black, yellow, blue and pink components) separates the top predators into two specific groups (colony breeders and pelagic predators). A positive perturbation in climate is applied to all four models through an increase in temperature; additionally, in Models 3 and 4 this perturbation also impacts the accessibility of prey to top predators. The single asterisk (*) indicates that scenarios are simulated for positive (a) and negative (b) effects of a positive perturbation in climate change on prey accessibility in Models 3 and 4.

Melbourne-Thomas et al.(2012) describe a simulation approach to qualitative network mod- elling in which interaction weights are randomly assigned from a uniform distribution (values between -1 and 1). Eigenvalues of each simulated (quantitatively specified) community matrix

determine its stability (seeMelbourne-Thomas et al.,2012); unstable matrices are discarded while stable matrices are used for predictions of the modelled system to the applied pertur- bations. The sampling procedure is repeated until a pre-determined number of simulations have been achieved. Further details on model simulations and methodology can be found in (Melbourne-Thomas et al.,2012).

We developed a series of nested qualitative network models with four levels of increasing complexity (Figure 2.1): the first is a biogeochemical model (including nutrients, bacteria, two autotroph aggregates and three zooplankton aggregates); the second model includes mid trophic levels (small mesopelagics and pelagic fish); the third model includes a generalised top predator (colony breeders and pelagic predators are combined); the fourth model includes a more detailed representation of top predators (colony breeders and pelagic predators are separated into two groups). Self-limitation (Dambacher et al., 2002) is applied to each variable in the model, which captures un-modelled, limiting processes such as predation for variables without explicit predation from higher trophic levels (Model 1, 2). We applied a positive perturbation in ‘climate change’ (a broad term which includes environmental changes that affect foodwebs following an increase in overall temperature) to each model. The variable ‘prey accessibility’, introduced in Model 3, represents the ‘ease’ (or energetic cost) with which top predators can access and consume their prey (small mesopelagics and pelagic fish). This variable modifies the interactions between predator and prey through multiplications of the signs in the matrix (Dambacher and Ramos-Jiliberto, 2007). In our models, prey accessibility is directly influenced by either a positive or negative effect of a positive perturbation in climate change (scenario a vs b; Figure 2.1). Here, a negative effect of climate change on prey accessibility decreases the accessibility of prey to predators, while a positive effect of climate change on prey accessibility increases the accessibility of prey to predators. The prey accessibility as represented in Model 3 has a different effect on colony breeders compared with pelagic predators; pelagic predators have the ability to forage in a range of locations and are not as limited by changes in their prey-field. Therefore, in Model 4, the effects of prey accessibility are only applied to colony breeders as these are limited in their possible foraging distances during the breeding season because of the need to return to land to breed or feed offspring (e.g.Bedford et al.,2015). An example of a negative effect

of climate change on prey accessibility is where climate change might cause a range shift (Bates et al.,2014) in target prey species, forcing predators to travel further from colonies to access prey. Conversely, a positive effect of climate change on prey accessibility might arise where a decrease in sea-ice extent means that prey are more accessible to predators at key times of year (Constable et al.,2014).

Analyses were conducted in R (version 3.3.2; R Core Team, 2016) following the method

of Melbourne-Thomas et al. (2012) and results are visualised using the method described by Marzloff et al. (2016). Results from 1000 simulation runs of the qualitative network model under a positive perturbation to climate change (Figure 2.2) show that an increase in complexity of predator representations can influence ecosystem responses to applied pertur- bations. Model 1 presents a comparison in the form of a null case where no higher trophic level predators are included (biogeochemical model). Further model comparisons show vary- ing ecosystem responses with the addition of predators at a range of complexities and trophic levels (Models 2, 3, 4). For example, with the inclusion of predation in Model 2 carnivorous macrozooplankton show a more positive response to a positive perturbation in climate change (Figure 2.2). The inclusion of higher trophic level predators in Models 3 and 4 introduces higher level feedbacks that also affect ecosystem responses to perturbation. Specifically, the response of pelagic fish changes from ambiguous (Model 2) to negative (Models 3a, 4a), when predators are introduced (or positive in Models 3b, 4b, following a negative prey ac- cessibility to higher trophic level predators). Large and small autotrophs appear to show less pronounced (more ambiguous) responses to climate change in models that include top predators.

The responses of top predators themselves depend strongly on the complexity with which they were represented; there is a clear difference between the responses of a generalised top predator (Models 3a, 3b) and the response seen when the top predator group is partitioned between those with unrestricted pelagic foraging and those restricted to colonies during breeding (Models 4a, 4b) given a positive perturbation in climate change. Comparison of the representations of top predators at two levels of complexity (Models 3, 4) indicates that the combined, more general, representation of top predators (Model 3a) show an ambiguous response to the applied perturbation in climate change. Whereas colony breeders and pelagic predators, when separated (Model 4a), show distinctly different responses to the positive perturbation in climate change. The model simulation indicates that a positive perturbation in climate change has a positive effect on colony breeders, but a negative effect on pelagic predators.

Results of model simulations with positive perturbations in climate change in combination with a negative effect on prey accessibility (Model 3b, 4b) indicate an overall negative re- sponse by top predators (Model 3b), whereas for the more detailed representation of top predators, only the colony breeders reflect this response (Model 4b). Pelagic predators re- spond ambiguously to a positive perturbation in climate change combined with a negative effect on prey accessibility.

Figure 2.2. Results from 1000 simulation runs of the nested qualitative network models,

as presented in Figure 2.1. The results show the probability of a positive (red) or negative (blue) response to a positive perturbation to climate change. Variable and Model names match those in Figure 2.1; note that the top predators for Model 3 are a generalised com- bination of colony breeders and pelagic predators (Model 4). The effect of climate change on prey accessibility is applied to Models 3 and 4; where 3a, 4a represent a positive effect, and 3b, 4b represent a negative effect. White boxes represent ambiguous results over all simulations (i.e. half positive and half negative results from simulation runs), and the grey represent zero change in response to a perturbation in climate change (i.e. no effect on nutrients in Models 1, 2).

While qualitative network modelling can capture feedbacks, a limitation of this approach is that it does not directly capture non-linear responses, such as prey-switching behaviours by predators. We note that our models are therefore conservative as these non-linear responses

may result in increased differences between different model formulations. Regardless, the examples of our simple qualitative network model show that representing top predators as a single group can lead to different ecosystem-level responses to climate change than when they are more explicitly modelled. Thus, the level of detail with which top predators are represented in ecosystem models can influence predictions of ecosystem responses to perturbations (see also Fulton et al.,2003).

2.4

Representing predators in detail through implementation

of DEB-IBMs

Our analysis of commonly used approaches for representing predators in end-to-end ecosys- tem models highlights that higher trophic level predators with complex life histories are often not well represented in these models. The network modelling we have conducted demon- strates that ecosystem-level outcomes from models in response to perturbations are likely to be dependent on the complexity of the representation of top predators. Consequently it is important to assess whether top predators such as seabirds and marine mammals are represented with sufficient detail for model outcomes to be fit for purpose.

The predator-prey relationships that are important to capture in models relate to the strength of predation per capita (availability/accessibility of prey, behaviour and consumption rates of predators) and the abundance of predators. In order to satisfactorily represent top down effects, i.e. the mortality of prey, it will be important to capture when either of these may change over time.

Dynamics of populations are driven by life histories (key life stages) and breeding behaviours. These can be challenging to represent, particularly for land-based breeders. For example females may choose not to breed every year; energy intake and use changes when individuals fast during moulting, birthing, or weaning; individuals may exhibit site fidelity (Arthur et al., 2015) and be affected by localised prey depletion or other environmental changes. Individual- based models (IBMs, or agent-based models: ABMs) can be used to more closely represent complex life histories and behaviours. These models represent autonomous individuals, where each individual (or agent) has their own characteristics and goals to pursue (DeAngelis and Mooij, 2005; Grimm et al., 2005; Macal and North, 2010; DeAngelis and Grimm, 2014). Typically, IBMs are used to more closely represent a species interaction with the ecosystem through representing behaviour in response to habitat or system cues (Hindell et al., 2011;

Raymond et al.,2014;Young et al.,2015); the linkages of individual components within that system (Grimm, 1999); and to address complex, multi-level interactions within the system (Grimm et al.,2005;Railsback and Grimm,2011), such as competition and prey-switching. These models are well suited for a range of different species, including high trophic level predators, and are becoming common tools for including behaviour and multiple life stages in ecosystem models (see Grimm, 1999; Thiele et al., 2011). In ecology, IBMs have been developed in a range of fields (see reviews by Grimm,1999;DeAngelis and Grimm,2014). Although there has been an increase in the development of IBMs for fish species there are still very few models that have been developed for seabirds and marine mammals. Bailleul et al. (2013) used IBMs to study the migration phenology of beluga whalesDelphinapterus

leucas in the Arctic. Salihoglu et al. (2001) used an IBM to show the importance of food

quality and quantity in determining the ability of Ad´elie penguinPygoscelis adeliae chicks to

reach optimum fledging weights, in spite of variability in Antarctic krill Euphausia superba

abundance during the breeding season. These two models indicate the different levels of detail which can be used in IBMs, and show how IBMs can be used as standalone models to represent colony breeding and pelagic predators for studies specifically focussing on the se- lected species. With regards to ecosystem based management (e.g.Horne et al.,2010), these

models would ideally be included in broad scale frameworks, such as end-to-end ecosystem models, that encompass multiple species. A recent example of this development is applied byFiechter et al.(2016) for the representation of male California sea lions in the California Current.

The suitability of IBMs for more realistically representing higher trophic levels make them a useful tool for further development of predator representations in end-to-end ecosystem models. A recent review bySibly et al.(2013) on including energy budgets in IBMs identified the Dynamic Energy Budget (DEB) theory (Kooijman, 2010b; Sousa et al., 2010; Jusup et al., 2017) as an effective approach to model the use and flow of energy by individuals. The theory aims to understand the dynamics of biological systems, from cells to ecosystems, via a balanced approach for mass and energy (Kooijman,2010b;Martin et al., 2012). This is achieved by considering the assimilation and energy use of an individual organism for growth, maintenance and reproduction (van der Meer,2006;Kooijman,2010b;Nisbet et al., 2012;Martin et al.,2013) throughout its life-cycle (Figure 2.3). Maury (2010) successfully implemented DEB theory in the development of APECOSM for the representation of large predatory fish (tuna species) through a size based approach in an open ocean ecosystem model.

Food Storage Faeces Structure Metabolic rate Metabolic work Sexual reproductive organs growth somatic maintenance maturity maintenance reproduction maturation uptake assimilation utilization ĸ 1-κ

Figure 2.3. A dynamic energy budget model representation (adapted fromKooijman,

2010b) for a general organism. Food is ingested; energy is extracted and added to the re- serves (storage), and utilised for; growth; somatic maintenance; maturity maintenance, and; reproduction maturation. Absolute priority is given to energy allocation for growth and somatic maintenance (κ). Any ‘left over’ energy (1 -κ) is utilised for maturation (em-

bryos and juveniles) or reproduction and maturity maintenance (adults) (kappa rule Kooij- man,2010b).

Dynamic energy budgets can be incorporated into individual-based models to form a generic modelling framework, called DEB-IBM (Martin et al., 2012). By itself, DEB theory uses a deterministic approach, however, in combination with IBMs, DEB-IBM allows for the inclu- sion of stochasticity to provide a framework for investigating effects at a population level (Martin et al., 2012). The DEB-IBM approach has been used previously for studies on low trophic levels (e.g. rotifer (zooplankton) cultures (Alver et al.,2006) and water-flea species (Kooijman et al.,1989;Martin et al.,2013)), however this approach is yet to be applied to higher trophic levels. A template designed byMartin et al.(2012) bases representations of in- dividuals on well-tested physiological principles and uses DEB theory in a population context. Considering the ability to analyse population characteristics and predator-prey interactions when combining DEB theory and IBMs (Martin et al., 2012) and the ability to include the complex life histories and breeding behaviour of seabirds and marine mammals, we propose that representations of top predators in ecosystem models could be greatly improved through implementation of DEB-IBMs.