We used EcoTroph-Dyn, a dynamic version derived from the steady-state EcoTroph trophodynamic modelling approach first proposed by Gascuel (2005) and further developed by Gascuel and Pauly (2009). In EcoTroph, biomass is produced by primary producers (TL = 1) and consumed by heterotrophic organisms (TL > 1). Thus, the food web's functioning is represented as a continuous flow of biomass surging up the food webs, from primary producers (low TLs) to top predators (high TLs). The resulting ecosystem structure is a continuous distribution of biomass along a gradient of TLs, i.e. biomass trophic spectra (Gascuel, 2005; Fig. 1). Practically, each biomass trophic spectrum with a TL above 1 is split into small trophic classes bounded by predefined lower and upper trophic levels (with conventional TL width = 0.1 – primarily because of computational efficiency while maintaining a good representation of food web structure and functions – in the steady-state version of EcoTroph). The biomass spectrum in EcoTroph generally refers to the total biomass of all consumers, including organisms living in pelagic, mid-water and benthic habitats. The time needed for the biomass to flow from one trophic class to the next varies along the food chain, with biomass transfers generally being faster in lower TLs (as species generally have short life expectancies) than in the higher ones.

EcoTroph has been applied to study the long-term effects of fishing (e.g. du Pontavice et al., 2023; Gasche et al., 2012; Gasche and Gascuel, 2013; Halouani et al., 2015; Tremblay-Boyer et al., 2011) and climate change (du Pontavice et al., 2021) on ecosystem biomass and production. EcoTroph-Dyn, the dynamic version of EcoTroph, simulates changes in biomass flows in each trophic biomass spectrum at a 15 d time step. This time step was used because it represents the average duration of most naturally occurring or experimentally simulated MHWs (Smale et al., 2015). EcoTroph-Dyn includes algorithms that model changes in flow kinetics, the boundaries of trophic classes, the resulting biomass states and flow between trophic classes and an algorithm that models the biomass loss associated with MHW occurrence. EcoTroph-Dyn's algorithm details are described in Guibourd de Luzinais et al. (2024). Here, we provide a summary of these algorithms.

The quantity of biomass flowing from a trophic class to the next, due to predation or ontogeny, is not conservative and can be calculated at each time step as 1ϕτ+Δτ,t+1=ϕτ,t⋅e-μt+ητ,t⋅Δτt, where μτ (expressed in TL⁻¹) represents the mean natural losses (due to non-predation mortalities, excretion and respiration). The ητ,t parameter (expressed in TL⁻¹) represents the additional loss rate specifically due to mortalities induced by MHW events (see Sect. 3.2.2). Equation (1) additionally describes the transfer efficiency (TE) between continuous TLs, representing the estimated proportion of biomass flow passed from one TL to the next. TE can be formulated as an empirical equation based on SST, as presented by du Pontavice et al. (2021): 2TE=e-μτ=e(-2.162+b+(-0.025+a)⋅SST)⋅1.038013, where a and b are specific parameters for each biome type (du Pontavice et al., 2021) and SST is the sea surface temperature of the time simulated.

The flow kinetic parameter Kτ (expressed in TL yr⁻¹), representing the speed of biomass flows (trophic transfers) from low to high TLs, is inversely proportional to biomass residence time (the time each biomass unit stays at a given TL). Kτ is expressed as a function of trophic level, using the empirical equation described in Gascuel et al. (2008): 3Kτ=20.19⋅τj-3.258⋅e0.041⋅SSTy, where SST_y corresponds to the annual moving average sea surface temperature in year y and τj corresponds to the trophic level of the j TL class.

MHWs cause marine organism mortality, impacting their life expectancy (Smith et al., 2023). In EcoTroph-Dyn, these changes in life expectancy are reflected in the loss rate in the biomass spectrum, representing the proportion of biomass that neither persists nor progresses through the food web (Gascuel et al., 2008; Guibourd de Luzinais et al., 2024; du Pontavice et al., 2021). Therefore, according to equations used in the steady-state version of EcoTroph, the flow kinetic during MHWs increases as follows: 4Kτ=20.19⋅τj-3.258⋅e0.041⋅SSTy⋅(1+ητ), where ητ, the MHW-associated additional loss rate, is only considered during MHWs.

Biomass spectra in EcoTroph-Dyn are split into trophic classes of variable width. The width of trophic classes [τj; τi+1[ was determined based on the estimated mean flow kinetics so that biomass could transfer up a trophic class in each time step (Δt=1/24 year). Thus: 5Δτ=τj+1-τj=Kτ⋅Δt.

According to fluid dynamic equations, the EcoTroph-Dyn state variable Bτ,t represents the biomass present at time step t in the TL class [τ,τ+Δτ[. It is expressed as 6Bτ,t=1Kτ,t⋅ϕτ,t⋅Δτ, where ϕτ,t is the mean quantity of biomass flowing in the trophic class [τ, τ+Δτ[ at time step t and Kτ,t is the mean flow kinetic in the trophic class [τ, τ+Δτ[.

Finally, the production Pτ,t of the trophic class [τ, τ +Δτ[ at time step t is 7Pτ,t=∫s=τs=τ+ΔτΦs,t⋅ds=Φτ,t⋅Δτ.

Hence, according to Eqs. (6) and (7), EcoTroph highlights the fact that biomass stems from the ratio of the production to the flow kinetic. Production is expressed in t⋅ TL ⋅ yr⁻¹; that is, biomass in weight moving up the food web by one TL on average during 1 year.

We compute the loss rate in the biomass flow associated with MHWs based on the percentage of species undergoing thermal stress, i.e. species exposed to temperatures exceeding their thresholds. A detailed description of the MHW loss rate algorithm is described in Appendix A1. Here, we provide the main steps for the incorporation of the effects of marine heatwaves into EcoTroph-Dyn:

Detection and characterisation of MHWs with climatology (period of 1982–2011),

We used an α=0.2 in our simulations. However, we also explored the sensitivity of the results to community resistance capacity by testing four alternative values of α. The α values that we tested were full resistance (α=0, i.e. we fixed ηi=0; no mortality due to thermal stress), partial resistance (α=0.2, 0.5; 20 % and 50 % of the species die because of thermal stress, respectively) and no resistance (α=1; all species die when they are under thermal stress). We performed a three-way ANOVA; that is, a statistical test we used to analyse the effects of trophic levels, biomes and α value on biomass change. We also related the loss rate to the MHW duration over the 15 d by assuming that the duration increased the mortality rate.

The EcoTroph-Dyn model was applied to simulate consumer biomass and production (between TLs 2 and 5.5) from 1998 to 2021 for each 1° × 1° spatial cell of the global ocean (Fig. S1 in the Supplement). Model outputs were summarised spatially by biome: the tropical, temperate or upwelling biome, based on Reygondeau et al. (2013). We excluded polar biomes because net primary production (NPP) data, one of the forcing variables of the EcoTroph-Dyn model, were not available in high-latitude regions during the winter period.

In response to climate change, the NPP and SST are already perturbed. Global total NPP decreased by 1 % in the period 2015–2021 compared to the 1998–2009 period. However, large spatial variability was observed in NPP changes (Fig. 2a). In particular, NPP decreased by 20 % in the northeastern Pacific, while an increase of 20 % was estimated for the Southern Ocean. Under the “without MHW” scenario (Fig. 2b), global average SST increased by 0.28 °C in the period 2015–2021 compared to the 1998–2009 period, with some areas warming by up to 0.5 °C. However, under the “with MHW” scenario (Fig. 2c), SST increased by 0.32 °C in 2015–2021 compared to the period 1998–2009, with some areas, such as the northeastern Pacific, warming by up to 1 °C over the same period. Globally, the estimated increase in average SST from 2015 to 2021 was 4 % higher in the “with MHWs” scenario compared to the “without MHW” scenario.

Under the “with MHWs” scenario, MHWs occurring during the year's warmest month increased in intensity, duration and surface extent from 1998 to 2021 (Fig. 3a, b), with large spatial variability (Fig. 3c, d). MHWs with intensity lower than 3 °C above the climatology were identified on average in 28.5 % of the ocean surface (Fig. 3a). These MHWs lasted, on average, more than 40 d (Fig. 3b). In contrast, MHWs characterised as higher intensity (≥ 3 °C above climatology) were identified in < 20 % of the ocean surface area (Fig. 3a). These relatively more intensive MHWs lasted, on average, 32 d (Fig. 3b). Furthermore, more MHW days of lower intensity were identified for low-latitude regions (23° N–6° S) (Fig. 3c, d) compared to MHW days identified in higher latitude regions (> 23° N and 25° S).

Ecosystem total consumer biomass response to MHWs depended on community resistance capacity. Assuming species have full resistance (α=0) or no resistance (α=1) to MHWs, total consumer biomass was projected to decrease by 2.3 % and 15.3 % in the period 2015–2021 relative to 1998–2009, respectively (Fig. 7a). Simulations using different α values projected changes in total consumer biomass that were consistent in direction but differed significantly in magnitude. A three-way ANOVA was performed to analyse the effect of trophic levels, biomes and α value on biomass change. This ANOVA revealed a statistically significant effect on biomass change of trophic levels, biomes and α values (p value < 2×10-16), individually. Additionally, the interaction between biomes, trophic levels and α value had a significant effect on biomass change (F(27, 16 737) = 442.4, p value <2×10-16). The lower the resistance capacity of species (higher α value), the greater the loss of total consumer biomass. On a biome scale, these variations in biomass loss were greater for the tropics, with values ranging from 3.1 % (α=0) to 20.2 % (α=1) (Fig. 7c). In comparison, sensitivity was lower in the temperate and upwelling biomes, with a decrease between 1.4 % (α=0) and 11.2 % (α=1) and between 3.8 % (α=0) and 12.3 % (α=1), respectively (Fig. 7b and d).

The sensitivity of changes in total consumer biomass to the resistance setting increased with trophic level. At a global scale, the response of low TLs ranged from a consumer biomass decrease of 1.4 % (α=0) to 8.0 % (α=1), while high TLs exhibited values ranging from 0 % (α=0) to 11 % (α=1) (Fig. 7a). Furthermore, the sensitivity of trophic levels to the α value was greater in the tropical biome and lower in the temperate and upwelling biomes relative to that of the global ocean.

Our model projected that the MHW in the northeastern Pacific from 2013 to 2016 (the Blob) resulted in long-term changes in the biomass spectrum in the region (Fig. 8c). Temperature anomalies were on average ≥ 4 °C (between 2013 and 2016) and up to 8 °C in 2015 relative to 1982–2011. This temperature anomaly had some ecological repercussions. On average, without accounting for MHWs, total consumer biomass in our simulation was hindcast to decrease by 1.5 % ± 0.3, 3.1 % ± 0.4, 6.6 % ± 0.2 and 5.2 % ± 0.3 in 2013, 2014, 2015 and 2016, respectively, compared to the reference period of 1998 to 2009 (black line in Fig. 8c). However, when accounting for MHWs with α=0.2, the total consumer biomass loss decreased on average by an additional 3.1 % in 2013, 2014, 2015 and 2016. Furthermore, the difference in linear trend (slope and intercept) between the biomass time series 1998 to 2013 and 2017 to 2021 indicated that the MHW (the Blob) had a significant effect on long-term changes in biomass (GLS, generalized least squares, p value < 0.05).

The magnitude of the hindcast total consumer biomass differed significantly between biogeochemical provinces (ANOVA, F(1, 2906) = 7.854, p value < 0.05, Fig. 8d). Comparing the consumer biomass before (1998–2012) and during (2013–2016) the occurrence of the Blob, all biogeochemical provinces in the northeastern Pacific, except the Alaska coastal downwelling (ALSK) and Central American coast (CAMR), exhibited a significant total consumer biomass decrease (ANOVA, F(1, 151) = 155.443, p value < 2×10-16) under the scenario with and without MHWs. Under the “without MHW” scenario, total consumer biomass in the North Pacific tropical gyre (NPTG) biogeochemical provinces, followed by the California current (CCAL+OCAL biogeochemical provinces), was hindcast to decline the most amongst the provinces when comparing before, during and after the Blob (Fig. 8d). Under the “with MHWs” scenario and with a resistance capacity setting of α=0.2, all biogeochemical provinces were hindcast to have an additional biomass decrease during and after the Blob. This additional biomass decrease ranged from 0.9 % to 5 % and from 1.4 % to 5.1 % during and after the Blob, with an average decrease of 2.7 % ± 0.4 % and 3.1 % ± 0.3 %, respectively (Fig. 8d). In particular, the California current and the Alaska coastal downwelling provinces were most affected by the MHW, with additional biomass decreases of 5 % and 3.8 % relative to the “without MHW” scenario, during and after the Blob.

The impact of the Blob on various trophic levels was similar to the global pattern, with a rapid reaction (in terms of biomass loss) observed at lower TLs and higher TLs exhibiting a delayed response (Fig. S8). Considering the influence of MHWs from 2013 to 2016 using the “with MHWs” scenario and α=0.2 resistance capacity, there was a hindcast biomass reduction of 6.8 % ± 0.7, 6.3 % ± 0.6 and 4.3 % ± 0.3 for low, medium and high TLs, respectively, when compared to the reference period of 1998 to 2009. Compared to pre-event conditions, by 2021, aside from low TLs, medium and high TLs gave no sign of recovery from the Blob MHW event.

Trophic dynamics of the biomass spectra in the northeastern Pacific were hindcast to be impacted by the Blob (Fig. S9). The trophodynamic indicators flow kinetic and trophic efficiency increased and decreased, respectively, in the model. Under the scenario “without MHW”, the average hindcast flow kinetic of the biomass spectra in the northeastern Pacific increased by 0.6 % ± 0.2, while the transfer efficiency decreased by 0.7 % ± 0.2 in the period 2013–2016 relative to 1998–2009. Consideration of the MHW under the “with MHWs” scenario exacerbated the increase in flow kinetic and decrease in trophic efficiency significantly by 0.7 % and 0.4 %, respectively (t test p value < 0.05).

Over the past two decades, MHWs have led to increased mortality rates and significant alterations in the functioning and structure of ecosystems (Smith et al., 2023; Wernberg et al., 2013, 2016). Our modelling analysis suggests that, without accounting for MHWs and their ecological effects, the decline in global-scale biomass associated with climate change may have been significantly underestimated. We show that MHWs have exacerbated the impacts of long-term climate change, impacting trophodynamic parameters such as the flow kinetic and transfer efficiency in ecosystems, which is congruent with studies by Arimitsu et al. (2021), Gomes et al. (2024) and Smith et al. (2023). These perturbations in ecosystem functioning result in biomass loss through food webs. Although MHW temperature anomalies have mostly lasted for weeks to months only, we emphasise that the resulting ecosystem perturbations last for a longer time (decades) and influence long-term biomass change (Fig. 8; Babcock et al., 2019; Cheung and Frölicher, 2020; Guibourd de Luzinais et al., 2024). Finally, the intensity and duration of MHWs have influenced the magnitude of the perturbation in ecosystem functioning (Oliver et al., 2021; Smith et al., 2023). We have highlighted the fact that the intensity and duration of MHWs have continuously increased since the beginning of the 21st century (Fig. 3), leading to a sharp biomass decrease over the hindcast period (Fig. 4). Such short-term biomass decreases have strengthened the impacts of long-term climate change (Cheung and Frölicher, 2020; Collins et al., 2019).

At a global scale, over the whole time series and in different MHW resistance capacity scenarios, high TL biomass experienced greater impacts from MHWs and was not able to recover to pre-perturbation levels as effectively as the low and medium TL biomass. The gap in biomass recovery was most apparent in tropical and upwelling biomes, where the hindcast biomass of high TLs consistently decreased over time. The time needed for the biomass to return to pre-perturbed levels was related to the rate of biomass turnover, which was also dependent on the speed of biomass flows. This turnover decreased with trophic level and was low for organisms at the top of the food chain (Gascuel et al., 2008; du Pontavice et al., 2020; Schoener, 1983). Thus, the high frequency of MHWs in recent years may be greater than the time that high TLs need to recover from the impacts of individual MHWs; this could contribute to the continued decline in high-TL biomass.

In our modelling approach, trophodynamic changes were assessed through transfer efficiency (TE) and flow kinetics. TE (dimensionless) is defined as the fraction of energy transferred from one trophic level (TL) to the next and summarises all the losses in the trophic network (Jennings et al., 2002; Libralato et al., 2008; Lindeman, 1942; Niquil et al., 2014; Pauly and Christensen, 1995; Schramski et al., 2015; Stock et al., 2017). It is an emergent property of marine ecosystems and an essential parameter in many applications of marine ecology, such as estimating biomass flux in production models (e.g. Carozza et al., 2016; du Pontavice et al., 2021; Gascuel et al., 2011; Jennings et al., 2008; Tremblay-Boyer et al., 2011). Unlike previous applications of EcoTroph at an annual timescale (du Pontavice et al., 2021, 2023), where changes in transfer efficiency reflected long-term changes in species assemblages, having a transfer efficiency that evolved on a biweekly basis (14 d) allowed us to take into account metabolic fluctuations over a shorter period. The temperature during MHWs increases the basal metabolism (catabolism) of marine organisms (Grimmelpont et al., 2023; Minuti et al., 2021), thus reducing the energy available for anabolic processes that can only occur once catabolic needs are met (Eddy et al., 2021). The estimation of transfer efficiency only considers anabolic processes (Eddy et al., 2021); hence, this balance between catabolism and anabolism is how MHWs could disrupt transfer efficiency on a biweekly scale. The flow kinetics expressed in TL yr⁻¹ quantifies the speed of the trophic flux, i.e. the rate of biomass transfer from lower trophic levels to higher ones, due to predation and/or ontogenesis (Gascuel et al., 2008; du Pontavice et al., 2020). This rate is inversely proportional to the biomass residence time (BRT; du Pontavice et al., 2020), which is the average time a unit of biomass spends moving from one TL to the next higher one through predation (Gascuel et al., 2008; Schramski et al., 2015). This flow kinetics can be measured by the production / biomass ratio (P / B; Gascuel et al., 2008), which is used in many ecosystem models, particularly Ecopath with Ecosim (EwE; Christensen and Pauly, 1992).

MHWs disrupt the metabolism of individuals and, on a larger scale, impact the entire ecosystem with trophodynamic changes throughout the trophic network (Fig. S9; Arimitsu et al., 2021; Collins et al., 2019; Gomes et al., 2024; Smith et al., 2023). However, due to their different physical characteristics depending on the ecosystems and the varying functioning of these ecosystems, they do not induce the same structural and functional changes, leading to different biomass losses. Tropical ecosystems are composed of species with low transfer efficiency (TE, low ratio between stored energy and ingested energy), with significant energy losses that increase with temperature (Brown et al., 2004; du Pontavice et al., 2020; Schramski et al., 2015). To compensate for this low efficiency, predation activity is high, resulting in rapid biomass transfers between prey and predators (biomass flow; du Pontavice et al., 2020). In these ecosystems, communities (which may be dominated by short-lived and fast-growing species) are generally living at the upper end of their thermal preferences (Begon and Townsend, 2021; Pinsky et al., 2019; Vinagre et al., 2016). They experience thermal stress associated with MHWs, leading to substantial mortality across the trophic network, with a higher proportion occurring in lower trophic levels regardless of the intensity of the MHWs as low TLs tend to have lower thermal limits than high TLs (Guibourd de Luzinais et al., 2024). MHWs scarcely affect transfer efficiency (TE), with an estimated average decrease of 0.05 % between 1998 and 2021 because the metabolism of species is already very high (du Pontavice et al., 2020). However, MHWs exacerbate prey mortality rates, resulting in proportionally higher predation rates, i.e. biomass remains for a shorter time at each trophic level, corresponding to an acceleration of biomass flow (estimated at 1 % on average between 1998 and 2021). Given the relatively high number of MHW days (Fig. 3; Hobday et al., 2018; Marin et al., 2021; Oliver et al., 2018), these modifications to biomass flow are “persistent” and involve significant biomass losses.

In temperate ecosystems, biomass is transferred more slowly between trophic levels, with less loss (higher trophic efficiency; du Pontavice et al., 2020; Eddy et al., 2021). In EcoTroph-Dyn, temperate communities experience thermal stress and mortality only during high-intensity MHWs (Guibourd de Luzinais et al., 2024). MHWs affect the metabolic efficiency of species by increasing basal metabolism and respiration-related losses, which decreases TE across the trophic spectrum, estimated in our simulations at an average of 0.2 % between 1998 and 2021. These higher metabolic demands lead to an increase in predation activity, which, combined with lower mortality (compared to tropical waters), reduces the biomass residence time at each trophic level in the food chain, i.e. a slight acceleration of the speed of biomass flow between each trophic level (estimated in our simulations at an average of 0.3 % between 1998 and 2021). Since MHWs in these ecosystems are characterised by significant temperature anomalies but over relatively short durations (Fig. 3; Frölicher et al., 2018; Oliver et al., 2018), these modifications to biomass flow are “temporary” and involve lower biomass losses.

Finally, in upwelling ecosystems, communities are characterised by low transfer efficiencies with high biomass residence times, indicating slow biomass transfers between prey and predators (du Pontavice et al., 2020). MHWs cause thermal stress and moderate mortality in these ecosystems (Guibourd de Luzinais et al., 2024). They lead to a decrease in the metabolic efficiency of species (estimated in our simulations at an average of 0.03 % between 1998 and 2021), along with an increase in predation activity, moderately impacting the rate of biomass flows in the ecosystem (estimated in our simulations at an average of 0.3 % between 1998 and 2021). The MHWs occurring in these ecosystems are of high intensity and last relatively long (an average of 23 d yr⁻¹ between 1998 and 2021). One might expect more significant impacts than in tropical environments; however, this was not the case. This could potentially be explained by (i) the high productivity of these ecosystems, which supports a highly biodiverse food web (Largier, 2020; Pauly and Christensen, 1995; Rykaczewski and Checkley, 2008; Ryther, 1969), leading to better resilience to environmental changes and extreme temperature events (Bernhardt and Leslie, 2013); and (ii) the specific functioning of these ecosystems with cool water rising from depth to the surface, which tends to reduce the number of MHW days compared to the adjacent open ocean (Varela et al., 2021). More generally, it has been highlighted that ocean warming does not affect coastal regions with upwelling in the same way as the open ocean (Varela et al., 2021).

Generally, in our simulations, higher temperatures and frequent mortality events promoted the emergence of species and the growth of populations, adapted to warm waters, both characterised by rapid growth and short lifespans (Beukhof et al., 2019; du Pontavice et al., 2020). This phenomenon was observed, for example, during the Blob event in the California ocean and California coastal current (OCAL and CCAL) provinces, with an increase of tropical species that usually live much farther south, such as tuna, sailfish and marlin (Cavole et al., 2016).

The specific examination of the Blob allowed us to elucidate how this MHW differentially affected the biogeochemical provinces (Longhurst, 2007; Reygondeau et al., 2013) and influenced their long-term responses. According to our simulations (Fig. 8), the biomass in the affected oceanic regions had not returned to the reference levels (1998–2009) by 2021. Following the MHW, all biogeochemical regions experienced significant biomass losses (ANOVA, p value < 0.05), although with varying magnitudes. Differences in exposure to the intensity and duration of temperature anomalies can potentially explain these differences in responses. For example, the coastal part of the California current and the subarctic gyres of the northeastern Pacific were subject to lower anomalies of different durations (Varela et al., 2021). In addition, differences in the structure and functioning of trophic networks may also have contributed to the variation in responses to MHWs between provinces (Morgan et al., 2019; Peterson et al., 2017; Ruzicka et al., 2012). The biogeochemical zones have different compositions of pelagic communities that may respond differently to MHWs (Peterson et al., 2017). For instance, the Gulf of Alaska saw its planktonic community shift towards smaller plankton and zooplankton, resulting in a loss in the nutritional quality and quantity of the forage portion of the pelagic community for their predators, highlighting the disruption of biomass flow (Arimitsu et al., 2021; Piatt et al., 2020; Suryan et al., 2021). In contrast, in the California current biogeochemical region, the MHW was associated with a substantial increase in the abundance of pyrosomes, which implied a limitation of energy flow moving towards higher trophic levels (Gomes et al., 2024). This was not necessarily the case for the oceanic part of the California current. These different changes in the composition and abundance of the lower trophic levels are represented in EcoTroph-Dyn by changes in the amount of energy flowing through the food web. EcoTroph-Dyn also takes into account the differences in trophodynamic characteristics (e.g. transfer efficiency, flow kinetics) between biogeochemical zones. For example, communities in the Gulf of Alaska are more efficient than those in the Californian current (du Pontavice et al., 2020), and the energy entering the food web was less disrupted than in the California current, which may explain the greater impact of the MHW on the California current.

We have developed an innovative approach to modelling marine ecosystems, linking trophic ecology with MHW hindcast to assess their ecological impacts on a seasonal timescale and at a global scale. Despite its apparent simplicity and the reduced number of parameters, EcoTroph-Dyn is part of the family of “complete ecosystem models and dynamic system models” (Plagányi, 2007) as it represents all trophic levels, from primary producers to top predators. It merges individual “species” into categories defined solely by their trophic level and describes ecosystems through a continuous distribution of biomass (trophic biomass spectrum), from primary producers to top predators. EcoTroph-Dyn does not account for specific climate effects on individual species and populations. The model assumes that variations in environmental conditions will lead to new biomass transfer dynamics in theoretical ecosystems at equilibrium. EcoTroph-Dyn meets the criteria described by Link (2010) to be considered a plausible representation of marine ecosystems. These criteria include the following: (i) the biomass values of all functional groups must cover 5 to 7 orders of magnitude, (ii) there must be a 5 % to 10 % decrease in biomass density (on a logarithmic scale) for each unit increase in trophic level, (iii) specific biomass production values (P / B) must never exceed specific biomass consumption values (C / B) and (iv) the ecotrophic efficiency (EE) for each group must be less than 1. Additionally, the model relies on empirically obtained equations (Gascuel et al., 2008; du Pontavice et al., 2020) and has demonstrated its ability to replicate the effects of fishing and climate change on marine ecosystems (e.g. du Pontavice et al., 2021, 2023; Tremblay-Boyer et al., 2011).

To discuss the validity of our hindcasts, we focussed on the most studied MHW (the Blob) in the literature with available quantitative data (e.g. Arimitsu et al., 2021; Bond et al., 2015; Cavole et al., 2016; Cheung and Frölicher, 2020; Gomes et al., 2024; Piatt et al., 2020; Suryan et al., 2021). The historical biomass change simulations from our “with MHWs” simulations and the α=0.2 scenarios showed the same biomass evolution per trophic group as the observational data based on species biomass surveys (Suryan et al., 2021). However, our historical simulations estimated lower biomass and also showed a smaller biomass decrease compared to observed data (Suryan et al., 2021). This would indicate a possible underestimation of biomass and ecosystem response to MHWs by EcoTroph-Dyn. The underestimation of ecological responses to MHWs is likely caused by the choice of a lower α value that lowers the sensitivity of the ecosystem to MHWs. To reduce the uncertainty over the α value, future studies could calibrate it for specific regions using observational data of MHW impacts on marine ecosystems' biomass.

Our simulations of biomass changes, according to the “with MHWs” and α=0.2 scenarios, also fell within the range of historical biomass simulations reported by studies using other approaches to represent ecosystem functioning (e.g. the species-based Dynamic Bioclimate Envelope Model (DBEM) by Cheung and Frölicher (2020) and Ecotran, an extension of the popular Ecopath modelling framework by Gomes et al. (2024); see Fig. 9). Additionally, we projected that the trophodynamic kinetic parameter of biomass flow increased by 3 % in the “with MHWs” and α=0.2 scenarios, which is consistent with the estimates highlighted by Gomes et al. (2024) (3.7 %). Finally, the decreases in trophodynamic transfer efficiency parameters highlighted in EcoTroph-Dyn with the Blob case study correspond to previous estimates (e.g. Arimitsu et al., 2021), showing a reduction in the availability and quality of food in the food web. It is worth noting that historical simulations obtained using a smaller (larger) α led to an underestimation (overestimation) of biomass losses and changes in biomass flow parameters relative to the estimates of Cheung and Frölicher (2020) and Gomes et al. (2024).

One of the main uncertainties in modelling MHWs in EcoTroph-Dyn is the assumption of the resilience of the biomass spectrum to MHWs, i.e. parameter α. It is important to note that the α values applied in this study were chosen arbitrarily, albeit reasonably, and were able to capture a broad range of potential responses to MHWs. It would therefore have been valuable to test EcoTroph-Dyn against other MHWs in the world ocean in order to acquire better estimates of the α parameter and more reliable results regarding the consequences of MHWs. However, to date, few MHWs are as well studied as the Blob, limiting these analyses. As discussed in Guibourd de Luzinais et al. (2024), given the diversity of ecosystem functioning, there is no reason why communities in different ecosystems, biogeochemical regions or trophic levels should have the same capacity to resist MHWs. Thus, we encourage future studies to use various observational data on the impacts of MHWs across the ocean (if available) to better estimate the α parameter as a function of different ecosystems, biogeochemical regions or trophic levels in order to reduce the uncertainties in projections.

Here, we focussed solely on the direct impacts of MHWs occurring during the year's warmest month via thermal stress, resulting in species mortality (Oliver et al., 2021; Smith et al., 2023). However, MHWs in other seasons can also have consequences on populations by affecting a specific stage of the life cycle of certain species (Crickenberger and Wethey, 2018; Oliver et al., 2021; Smith and Thatje, 2013). For example, MHWs that stress adult breeders can lead to a decrease in reproductive investment and, consequently, fewer, smaller and lower quality gametes (e.g. Shanks et al., 2020), resulting in a loss of abundance and biomass of some species (Johansen et al., 2021). While taking seasonality into account will increase the number of detected extreme events, some may not have ecological consequences (Oliver et al., 2021; Smith et al., 2023). Thus, our approach can be seen as conservative and may underestimate the impact of MHWs. Nevertheless, we detected MHWs with potentially significant ecological impacts. Studying MHWs occurring in seasons other than summer would involve considering the phenological effects of MHWs. However, since the EcoTroph-Dyn model does not directly represent this phenological aspect of marine organisms, future studies can apply other approaches that explicitly represent seasonal processes such as spawning and migration to elucidate the effects of phenology.

Furthermore, uncertainties in our results arise from the environmental drivers of EcoTroph-Dyn. In our current investigation, EcoTroph-Dyn was driven by satellite data. For the NPP forcing variable, we implemented the EPPLEY-VGMP algorithm (Behrenfeld and Falkowski, 1997; Morel, 1991), which, like other algorithms such as CbPM and CAFE, derives NPP from satellite-derived estimates of Chl a and SST. First, in this study, we did not consider the “with” and “without” MHWs scenarios for NPP. Acknowledging that MHWs generally increase NPP at high latitudes while decreasing it at low latitudes (Arteaga and Rousseaux, 2023; Bouchard et al., 2017; Le Grix et al., 2022; LeBlanc et al., 2020), we may have overestimated MHW impacts on ecosystem functioning at high latitudes and underestimated their impact at low latitudes. Furthermore, the variability and uncertainty in the estimation of the NPP by satellites directly affects the reliability of our results. In EcoTroph-Dyn, as well as in other marine ecosystem models, ocean primary production (and its related phytoplankton biomass) plays a crucial role in both sustaining and constraining the biomass of higher trophic levels (e.g. Blanchard et al., 2012; Carozza et al., 2016; Cheung et al., 2011; Jennings and Collingridge, 2015). However, there exists significant variability in NPP estimation among satellite NPP algorithms (Milutinović and Bertino, 2011; Westberry et al., 2023). These discrepancies are particularly pronounced over continental shelves and oligotrophic gyres, primarily due to variations in model parameterisation and growth rate representation (Milutinović and Bertino, 2011; Westberry et al., 2023). Second, in this study, in order to propose a suitable representation of the world ocean, we use an interpolation method to reconstruct an incomplete NPP time series. The interpolation was constrained by the minimum and maximum satellite data values of the NPP observed over their respective time series to ensure reliable interpolation and reduce potential bias. Third and lastly, in this study, we duplicated the NPP monthly values to enable the EcoTroph-Dyn to run with 15 d time steps. This duplication may have smoothed marine ecosystem responses to the historical changes in marine environment; however, it has not changed trends and the conclusions of our results. Consequently, elucidating the sources of the current uncertainty associated with satellite-derived NPP and refining these estimates pose significant challenges in comprehending the responses of marine food webs to MHWs.

Moreover, EcoTroph-Dyn does not account explicitly for species; thus, we could only assess aggregated food web responses to MHWs. The model projected that the aggregated response across species is expected to be negative, although it is known that some species would exhibit positive effects from MHW occurrence (Cavole et al., 2016; Smith et al., 2023; Suryan et al., 2021; Wernberg et al., 2016). To be cautious, we considered various loss rate scenarios to obtain a complete range of responses from marine ecosystems. Running the aforementioned five MHW-induced loss rate scenarios, we found that the aggregated resistance capacities α had a significant (ANOVA, p value < 2×10-16) and large effect. All scenarios are consistent with each other, with an increasing biomass loss over marine ecosystems with decreasing resistance capacities (increasing α). Even though the global impact of MHWs is negative, species-explicit modelling could improve our understanding of how various impacts of climate change and species-level responses will affect trophodynamics and ecosystem structure and function.

In our study, we highlighted the specific impacts of MHWs on ecosystem structure and function, particularly through the case study of the MHW known as “the Blob” (the longest and strongest period of abnormal temperature ever recorded (Collins et al., 2019; Oliver et al., 2021)). The anomalously low wind during the 2013–2014 winter induced the anomalously weak Ekman transport of colder water from the north and, coupled with anomalously low air–sea heat exchange, triggered the Blob (Bond et al., 2015). Furthermore, these processes as well as the El Niño Southern Oscillation (ENSO) have already contributed to the increased average duration and intensity of MHWs in the northeastern Pacific Ocean. Given that projections for the 21st century indicate that ENSO events will increase in intensity and frequency (Holbrook et al., 2020; Oliver et al., 2021), events such as the Blob are expected to occur more frequently (Holbrook et al., 2020; Oliver et al., 2021). This underscores the need for ongoing research to better understand how MHWs disrupt ecosystems. Finally, throughout the 21st century, ecosystem responses will depend on the ability of communities to adapt to the long-term increase in ocean temperature and their ability to withstand short-term extreme temperatures (Johansen et al., 2021). Therefore, to enhance our understanding of how marine ecosystems will respond to climate change, future studies should focus on potential scenarios of adaptive responses to future climate and associated MHWs. The EcoTroph-Dyn model is a tool to understand the ecological consequences of MHWs at global and local scales and to project their impacts under future scenarios. However, the model focuses on aggregated energy flows between trophic groups, while ecological responses to MHWs of species in each group may vary substantially. Some species may acclimatise or adapt to MHWs. Consideration of the potential acclimatisation/adaptation in the model requires the development of specific adaptation scenarios and model settings in addition to the model settings presented here.