The global susceptibility of coastal forage fish to competition by large jellyfish

Abstract

Competition between large jellyfish and forage fish for zooplankton prey is both a possible cause of jellyfish increases and a concern for the management of marine ecosystems and fisheries. Identifying principal factors affecting this competition is therefore important for marine management, but the lack of both good quality data and a robust theoretical framework have prevented general global analyses. Here, we present a general mechanistic food web model that considers fundamental differences in feeding modes and predation pressure between fish and jellyfish. The model predicts forage fish dominance at low primary production, and a shift towards jellyfish with increasing productivity, turbidity and fishing. We present an index of global ecosystem susceptibility to shifts in fish–jellyfish dominance that compares well with data on jellyfish distributions and trends. The results are a step towards better understanding the processes that govern jellyfish occurrences globally and highlight the advantage of considering feeding traits in ecosystem models.

1. Introduction

During the last few decades, the ecology of pelagic cnidarians and ctenophores has attracted increasing attention and has raised public concerns about their impact on our societies [1]. This was sparked by spectacular cases where jellyfish have proliferated, causing extensive economic damage [2,3] and dramatic changes of the local ecosystem structure [4–7] with alternate ecosystem states [7,8]. The species responsible for these changes are almost exclusively large, feeding-current feeding types [2,9], and we refer to these types as ‘jellyfish’ throughout this study.

Jellyfish are generally considered unwanted or harmful and can cause direct damage to tourism, infrastructure and fishing gear [2]. They also have more indirect impacts on ecosystem functioning, as certain jellyfish and forage fish (small pelagic zooplanktivorous fish) feed at a similar trophic level [4–6,8,10,11]. Additionally, many jellyfish can be locally important predators on the younger life stages of fish [3,12]. Competition is notoriously difficult to prove [12] but environmentally induced changes in the ability of jellyfish to compete with fish are likely a cause of jellyfish proliferation and can have large negative impacts on both ecology and economy. Forage fish are not only targets of important fisheries, but are also the main prey for high-value predatory fish, as well as for many seabirds and marine mammals [3]. Thus, a better understanding of the factors governing the competition between fish and jellyfish is important to predict patterns in jellyfish abundance and distribution. In particular, changes in competitive interactions may be responsible for the observed shift towards jellyfish dominance in certain ecosystems affected by climatic and anthropogenic pressures [3,13].

Despite recent advances in mapping global jellyfish distributions, blooms and temporal variation [1,14,15], most studies are on a local scale, and have revealed a host of environmental and anthropogenic factors promoting jellyfish (reviewed in [16]), including overfishing of fish [13], eutrophication [17], reduced water clarity [18,19], changing oxygen availability [15], changes of benthic substrate [20] and introduction of alien species [21]. The large variety of both environmental conditions and species compositions across ecosystems makes it hard to identify general mechanisms that can be scaled up to the global level. To understand global patterns in jellyfish distribution and impact on forage fish in both time and space, we need to focus on fundamental properties transcending taxa and systems.

A fundamental difference between forage fish and jellyfish is in how they feed. While the visual feeding mode of fish is very efficient under good visual conditions, their clearance rate decreases with decreasing visibility, whereas the tactile feeding of jellyfishes does not [19,22,23]. Turbid conditions, owing to high phytoplankton biomass or terrestrial run-off, generate low light penetration in the water column and therefore tend to favour jellyfish over fish communities, as has been shown in Norwegian fiord systems [18]. A close correlation between optical conditions and forage fish biomass has also been found in the Black Sea [24], where extensive jellyfish blooms have coincided with crashes in forage fish populations.

In addition, whereas many predators are primarily dependent on forage fish for prey, jellyfish are typically consumed opportunistically by a broad range of predators [25,26], including fish [12]. Thus, forage fish may be subject to tighter trophic control than jellyfish and are often targets of important commercial fisheries [3]. Food web structure, exploitation and feeding ecology may thus cause jellyfish to be dominant in pelagic ecosystems heavily affected by eutrophication, high water turbidity and fishing, as it has been suggested by other modelling studies [23,27].

The overall ecological role of jellyfish in marine ecosystems is not yet well understood, but we do have a fairly good understanding of cnidarian and ctenophore autecology, including physiological traits such as elemental composition, allometric scaling of vital rates and locomotion [28–30], life-history (e.g. [31]) and feeding traits [28,32]. Here, we make use of this information to build a model of the fish–jellyfish competitive interaction by using mechanistic descriptions of processes at the individual level, to gain insights into the response of the system to changes in the environment. Basing the model on mechanisms that are common across all environments and taxa allows us to make it general enough to be applied in a global setting. The aim is to investigate to what extent feeding traits in fish and jellyfish populations can describe competition for food and explain some of the observed global patterns in jellyfish occurrence.

As the focus is on trophic interactions between large jellyfish species and fish populations, additional factors such as temperature effects on population growth and intraguild predation of fish and jellyfish during ontogeny are not explicitly addressed here, although the sensitivity of our results to temperature changes is considered.

2. Material and methods

(a). System formulation

Our food web model describes competitive interactions between a small pelagic forage fish (F, representing species such as anchovy, sprat or the like) and a cruising feeding-current feeding jellyfish (J, representing medusae such as Aurelia aurita, or ctenophores such as Mnemiopsis leidyi), competing for zooplankton prey (figure 1a). The coexistence of jellyfish and fish in the food web is dependent on both environmental conditions (primary production, light) and individual parameters, and changes in either may define different food web configurations where fish and jellyfish do not coexist (figure 1b,c). We consider two size groups of mesozooplankton (Z_l and Z_s), to allow for differences in selectivity for prey size between fish and jellyfish. Our food web contains a predator fish (P, representing larger pelagic predators, fish such as tuna, cod, etc.) that predates upon forage fish, but not on jellyfish.

Figure 1.

Idealized food webs describing (a) jellyfish and fish competition for zooplankton resources. The coexistence of all species in the food web depends on organism traits and environmental conditions, and changes in either of these may produce different food web configurations dominated by either (b) fish or (c) jellyfish. Primary production supports the food web and may also impact fish predation through changes in turbidity.

We let the food web be forced by primary production R (g C m⁻³ d⁻¹) that is converted into mesozooplankton biomass with transfer efficiency T_Z (dimensionless) [33]. We furthermore assume global assimilation efficiency f (dimensionless), and a production ratio between small and large zooplankton z (dimensionless). In the population model, we convert carbon mass to individuals using the body carbon mass w_i (g C ind⁻¹) of an individual of species i (electronic supplementary material, tables S1 and S2).

The food web is then represented by five coupled differential equations:

2.1a

2.1b

2.1c

2.1d

2.1e

where β_i,j is the clearance rate of predator i on prey j (m³ ind⁻¹ d⁻¹) and m_i, ∂_i and y_i are, respectively, the specific respiration rate, natural mortality and fishing mortality on species i (all in units of d⁻¹). Note that this model formulation does not include direct trophic interactions (i.e. predation) between the jellyfish and the fish.

Although jellyfish can effectively feed on fish early life stages [12], and sometimes may control forage fish recruitment [34], we think that such cases are strongly dependent on local jellyfish populations being very abundant at both the time and place of spawning. In addition, many forage fish have nursery or spawning sites that are separate from the pelagic, and the extent of jellyfish predation on forage fish larvae or eggs is largely species specific. For these reasons, we think that at the scale we apply our model (large marine ecosystems) and for the generality of our results, those interactions are of secondary importance with respect to competition for food.

(b). Mechanistic description of feeding interactions

(i). Fish

We assume a fish swimming through the water with velocity v_i (m d⁻¹). The fish scans the surrounding water for prey within an average visual range (m), and a limited visual field defined by the visual half angle θ_i (°). On encounter, prey is captured with a probability A_ij, yielding the following clearance rate:

2.2

where v_j denotes the swimming velocity of the prey (m d⁻¹). The visual range depends on the light regime, the optical properties of the water, prey size, colour and shape, and on characteristics of the predator eyes. Here, we use a model of visual range by [22]

2.3

where r_ij,Z is the visual range at depth Z, c is the beam attenuation coefficient (m⁻¹), C_j is the inherent prey contrast, a_j is the image area of the prey (m²), is a compound visual processing parameter [35], I is the irradiance (µE photons m⁻² s⁻¹) just below the surface, K_d is the light attenuation coefficient (m⁻¹) and K_e is the half-saturation constant for the visual system of the predator (µE photons m⁻² s⁻¹). was estimated for each depth interval using a numerical solver, and then averaged over depth Z_max (m) to yield the depth-averaged visual range:

2.4

(ii). Jellyfish

We consider a large feeding-current feeding jellyfish. Although the morphology of feeding structures and method of capture varies enormously, jellyfish of this type all swim continuously, displacing water in a cross-sectional area with a diameter equal to the maximum width of the animal and perpendicular to the swimming direction [28]. A certain proportion of this water passes through the capture apparatus, where prey is filtered out of the water with a certain efficiency. Thus, the clearance rate will be proportional to the velocities of prey and predator (v_i and v_j), the cross-sectional area of the animal and the filtering efficiency S [28]:

2.5

where L_i (m) is the maximum diameter of the jellyfish in the plane perpendicular to the swimming direction. The filtering efficiency S combines the probability of capture with the fraction of displaced water coming into contact with the capture surfaces.

(c). Parameter estimation and model evaluation

Many of the parameters considered in our model are size dependent. However, including ontogenetic development would require a more complex, physiologically structured model. Instead, we parametrize the model using a specific reference size for each model population. Species-specific parameters are calculated from carbon content using group-specific allometric relationships (electronic supplementary material, table S2), and a comparison of the resulting clearance rates with observations verifies that the model yields realistic rates (see the electronic supplementary material, figures S3 and S4). When solved numerically, the model (equation (2.1)) converges towards a steady state. Six non-trivial and biologically meaningful equilibria can be derived analytically, all but one (figure 1a) being food web configurations with one or more missing species.

The global patterns of competition between forage fish and jellyfish in terms of productivity and optical conditions are explored by applying the model to the Large Marine Ecosystems (LMEs, see §2d), at a 0.5°-grid resolution. We exclude Arctic and Antarctic regions, because of a lack of reliable data on primary production and turbidity in those regions. We limit our analysis to the LMEs because jellyfish bloom occurrences are better documented there, allowing comparisons between predictions and observations.

A Monte Carlo scheme is used in each grid point to evaluate model results over a range of the biological parameters describing the mechanistic interactions (equations (2.1)–(2.5)). As we employ a mechanistic description of the feeding interactions with a set of physiological and individual specific parameters, this methodology is a simple way to account for both species and trait diversity, as well as for the uncertain nature of the ecosystems when subject to seasonality and year-to-year variability. The Monte Carlo procedure draws a random set of parameters from a uniform distribution assigned around the values of each mechanistic parameter ±25%. Because of the computational cost of solving the visual range (equation (2.4)), those parameters are not included in the procedure and the value of calculated for each data point is treated as a parameter. The Monte Carlo simulations are performed for each month of 4 years (2003–2006), using 500 random parameter sets in each realization. We then calculate the viability of fish and jellyfish in each grid point by counting the event of positive values for forage fish (F* > 0) and jellyfish (J* > 0) groups over the total number of random sets (N_tot = 24 000). From these probabilities, we calculate in each grid point the Ecosystem Susceptibility Index (ESI):

2.6

This index measures the probabilities of the different food web configurations, and it takes values between ESI = 100 when the model never predicts a viable forage fish population (while jellyfish are present, figure 1c) and ESI = −100 when forage fish are always present and no jellyfish can be sustained in the food web (figure 1b). An index value around zero generally means that fish and jellyfish are present with equal probability. Alternatively, it can also arise from not having either, but in our application this case is rare. The index is a measure of how much the environment favours the jellyfish over the fish, and accounts for the sensitivity of the food web towards perturbations in environment or species composition that might push the system towards jellyfish domination.

(d). Model forcing

The model is forced with satellite data on primary production (R), light availability (I) and light attenuation coefficient (K_d).

Primary production R consists of 4 years (2003–2006) of monthly averaged data (mg C m⁻² d⁻¹; [36]), and we assume that these values are representative of the production in the upper (0-Z_max) layer.

A climatology of monthly average solar radiation (Watt m⁻²; [37]) is used to calculate the irradiance (µE photons m⁻² s⁻¹) in equation (2.3) by applying a conversion factor accounting for the visible fraction and daylight length. Four years of global data (2003–2006) on light extinction coefficient from satellite observations [38] are used to assign the values of K_d in equation (2.3).

(e). Temperature effect

Several studies have indicated that vital rates like respiration, pulsation frequency or growth rate of locally adapted jellyfish are often unaffected by temperature [39,40]. By contrast, respiration rates of local fish and copepods are affected by latitudinal ambient temperature differences [41,42]. Thus, we investigate the effect of temperature on the results when we apply a Q₁₀ of 1.8 [41,42] on the respiration rates of fish and copepods (, , and in equation (2.1)), e.g. = 1.8^{(25°C–15°C)/10}, and then calculate the change in ESI relative to a reference temperature value of 15°C, e.g. ΔESI = ESI_25°C − ESI_15°C. Note that generally temperature is also expected to affect growth rates via increased activity, however, it is difficult to apply the same scaling on growth rates within the specific mechanistic formulation on feeding rates used in our model. Indeed, we lack information on how temperature affects fish swimming speed, prey capture and sensing and hence, as we can only account for the effect of temperature on respiration rates of fish and copepods, we do not use temperature effects in our global simulations, but instead investigate the sensitivity of our estimated ESI to this important factor.

3. Results

(a). Global results

The model predicts distinct patterns in the ESI (figure 2c), with high probability of coexistence of forage fish and jellyfish in most areas (electronic supplementary material, figure S6). Higher ESI occurs in regions with high levels of primary production, especially in areas that are also close to major watersheds and consequently have high turbidity, e.g. in the Baltic Sea and more generally in several coastal areas (such as in the Benguela current, Patagonian shelf and East China Sea). By contrast, we observe low scores in oligotrophic regions (e.g. in the eastern Mediterranean). Surface irradiance does not seem to have a very large impact on the generated patterns.

Figure 2.

(a) Trends in jellyfish populations in the Large Marine Ecosystems (reproduced with permission from [14]). Colours represent areas with increasing trends and low uncertainty (red), increasing trend and high uncertainty (yellow), stable or fluctuating biomass (green), decreasing trend (blue) or no data (grey). (b) Global occurrences of coastal jellyfish blooms (red lines; reproduced with permission from [3]). (c) ESI for the Large Marine Ecosystems, as generated by our model. Positive values indicate that jellyfish are more likely to be present than forage fish, negative numbers the opposite.

Few regions are strongly dominated by either fish or jellyfish (ESI < −80 or ESI > 80). Instead, most areas of the LMEs have ESI scores in the −20 to +20 range, meaning that coexistence of fish and jellyfish is predicted. Regions where neither fish nor jellyfish are predicted are rare (electronic supplementary material, figure S6a). Hence, environmental perturbations that can affect the competitive interactions in the model (whether natural or anthropogenic) are not expected to significantly change the food web structure in those areas. Other regions are predicted to favour either fish or jellyfish to a moderate extent (−80 < ESI < −20 or 20 < ESI < 80). These areas are the ones predicted to be sensitive to environmental perturbations affecting the competitive interaction between fish and jellyfish, and include the California, Humboldt and Benguela current systems, as well as the East Bering, Baltic and eastern US continental shelf seas and the Gulf of Oman.

(b). Community structure

The global patterns can be understood by looking at the equilibrium of the model for changes of primary production and fishing mortalities. The model shows a succession of species invasions with increasing primary production and light attenuation (figure 3a). At low production, R, only the zooplankton trophic level can be sustained in the food web, while successive higher trophic levels can be present as primary production increases. The model predicts that forage fish populations are sustainable when primary production is R > ∼30 g C m⁻² yr⁻¹, with predator fish entering the system almost immediately after this threshold, i.e. when the forage fish biomass is F* ≈ 3.5 × 10⁻² g C m⁻². The forage fish is then controlled by the predator and both fish groups, as well as zooplankton, increase until jellyfish can enter the system, at R ≈ 90 g C m⁻² yr⁻¹. The biomass of jellyfish exceeds that of their forage fish competitors at R > ∼100 g C m⁻² yr⁻¹, and thereafter increases linearly with primary production.

Figure 3.

Food web structure at increasing primary production. (a) Equilibrium biomasses of predator fish (blue), forage fish (light blue), jellyfish (red), large zooplankton (green) and small (yellow) zooplankton, at increasing primary production, and fishing mortalities (y_F and y_P) of 0.5 yr⁻¹. (b) Values of ESI at increasing primary production, using a total of 500 random parameter sets. (c) ESI anomaly at different temperatures and primary production. The anomaly is the difference between ESI values at 25°C (dashed dark line), 20°C (dashed grey line), 10°C (dotted grey line), 5°C (dotted dark line) and the reference ESI at 15°C. For this figure, we assume a relationship between primary production and light attenuation K_d = 3.257 × 10⁻⁹ × R + 0.05952, based on regression of our satellite data on R and K_d (bootstrap method, p < 0.001, R² = 0.1537).

There is a large range of R in which all groups can be present in the food web, and where jellyfish generally dominate the biomass. This is the region where ESI ≈ 0 (figure 3b) and further increases in R in this region increases biomasses of forage fish and jellyfish, but not predator fish. This is due to decreases in fish visual range caused by the increased turbidity associated with high R, in combination with the competition from jellyfish. The gradual decrease in predation pressure allows forage fish to increase initially, but the effects of decreased light availability and competition eventually cause the extinction of the fish (F and P) from the food web, at R ≈ 930 g C m⁻² yr⁻¹. In the absence of jellyfish, fish are present over the entire range of primary production even with values as high as 2000 g C m⁻² yr⁻¹. It is the combined effects of erosion of fish feeding ability and the competition with jellyfish for zooplankton that can drive fish to extinction.

The ESI score is affected by temperature changes (figure 3c). As temperature increases, respiration of fish increases, and more zooplankton is needed to sustain forage fish, thus changing the threshold values of primary production for fish entry and extinction (figure 3a). Thus, with our simple description of temperature effects, we obtain that the direction of ESI change with changes in temperature depends on the level of primary production, but that for most primary production values, ESI increases with increasing temperature, and vice versa.

These results are robust to changes in fishing pressure on forage fish (y_F, equation (2.1)), although thresholds for the entry and eventual elimination of fish from the food web are shifted, so that the region of R where fish thrive expands (contracts) with decreasing (increasing) fishing mortality on forage fish. Thus, both fishing mortality and primary production can drive changes in the model food web structure, and four distinct coexistence regions can be identified (figure 4): an extremely oligotrophic region where fish cannot be sustained (figure 4A), a moderately oligotrophic region that supports fish but not jellyfish (figure 4B), a large intermediate region with coexistence of fish and jellyfish (figure 4C) and a eutrophic region where fish are competitively excluded and jellyfish are present (figure 4D). Transition from state B to C does not depend on fishing mortality on the forage fish. This is because in this region fishing mortality mainly has an impact in regulating the abundance of the top predator as in all predator–prey systems of this kind. In the absence of the predator fish, this transition will depend on the level of fishing mortality. Moreover, increasing fishing mortality always regulates the extent of the coexistence regions (figure 4) and, in general, the structure of the food web depends on a nonlinear relationship between fishing mortality and primary production. Hence it is difficult to identify the importance and thresholds of these drivers when taken in isolation.

Figure 4.

Regions of coexistence at different values of primary production and forage fish fishing mortality. For any given point, the model predicts the presence of neither fish nor jellyfish (A), the presence of fish but not jellyfish (B), coexistence of both fish and jellyfish (C) or jellyfish only (D). The threshold of forage fish entry is sensitive towards fishing, whereas the jellyfish entry threshold is not.

4. Discussion

We show that high productivity and trophic control, in combination with fishing pressure and reduced water clarity can combine to drive a simple ecosystem towards increased jellyfish biomass and eventually competitive exclusion of the (forage) fish. At low and intermediate levels of primary production and turbidity, and for a large range of the parameter values, the occurrence of large increases in jellyfish populations and competitive exclusion of fish are unlikely in our model. Indeed, over a wide range of parameters, coexistence of fish and jellyfish (ESI ≈ 0) is quite robust to changes in parameter values that could arise due to, e.g. climate, fishing, species invasion and other environmental change. Even including the drastic effects of temperature in changing the respiration rates of fish and zooplankton, we obtain a variability of ESI within 20% in non-oligotrophic regions, suggesting continued high levels of coexistence in regions where we calculate ESI ≈ 0.

Our descriptions of the feeding interactions are to a large extent based on simple mechanistic descriptions of processes occurring at the individual level. The formulations employed are general for each life form included in the model. However, the specific parameters used in the expressions can be species-specific. For example, fish species have different light sensitivities or swimming speeds, and all zooplankton species are not equal in size or conspicuousness. The Monte Carlo method employed swipes over a large range of species-specific parameters, making our results robust to changes in the species composition.

Therefore, in regions where our idealized food web is representative of real conditions, we predict that drastic jellyfish outbreaks and ecosystem takeovers are unlikely to occur at low and intermediate productivity, although localized blooms are possible. On the contrary, in highly productive eutrophic regions, especially those influenced by terrestrial run-off, we predict that jellyfish are not only more likely to occur, but also that small perturbations and increased fishing are more likely to push ecosystems towards jellyfish dominance and forage fish crashes. This is important because these are also the regions that support the largest net-based fisheries in the world [3].

Jellyfish population sizes are highly variable in both time and space, due to the ability of jellyfish to aggregate (e.g. [43]) and respond rapidly to favourable conditions [9]. The ESI (figure 2c) should not be interpreted as a measure of relative abundance, but rather as an indicator of the vulnerability of the ecosystem to perturbations that may favour jellyfish populations overall or promote local blooms. Note that high ESI does not mean that an area is in fact dominated by jellyfish, but rather that the equilibrium between fish and jellyfish is more vulnerable to changes in environmental conditions that may lead to jellyfish dominance. Likewise, intermediate ESI scores in very oligotrophic environments reflect the absence of both jellyfish and fish (electronic supplementary material, figure S6), and those regions would at least initially become fish dominated if primary production were to increase. In spite of these reservations, it is nevertheless relevant to compare the global patterns in ESI to observations of jellyfish.

Recently, a few studies have investigated jellyfish patterns on a global level [3,14,15]. Of these, Lucas et al. [15] used available data to assemble global biomass maps of jellyfish, showing that ctenophores and cnidarians are ubiquitous in the world's oceans. Robinson et al. [3] presented data on jellyfish bloom occurrence and their adverse effects on fisheries to show that there is considerable overlap between the world's largest fisheries and coastal jellyfish blooms (figure 2b). Finally, Brotz et al. [14] used various sources of information to detect trends in jellyfish populations in coastal ecosystems (figure 2a).

A qualitative comparison between the ESI and the jellyfish population trends (figure 2a) and frequent blooms of jellyfish (figure 2b) reveals an overall good correspondence. Almost all LMES where jellyfish have been increasing (figure 2a), have areas with high ESI (figure 2c), with the exceptions of northeast Australia and the Mediterranean Sea. Similarly, bloom occurrences (figure 2b) also largely correspond to regions with high ESI, again except for the Mediterranean Sea. We note that in the Mediterranean Sea, our model is likely missing some fundamental processes (e.g. hydrographical features or temperature effects) as this is a region where jellyfish blooms are often reported, even though primary production is low.

Temperature is important for the life history of many (especially cnidarian) jellyfish [16]. As an example, the timing and magnitude of the release of scyphozoan ephyrae from benthic polyps is highly temperature dependent in many cases [16,31]. However, the direction and magnitude of this temperature effect on life history is variable between organisms and areas [16,31], and in addition, our model is not able to capture life history and ontogenetic growth.

In our model, ESI generally increases with increasing temperature (figure 3b) and decreases with decreasing temperature, although the magnitude and direction of this change is dependent on the level of primary production and light attenuation. Other studies have found a link between increased temperature and jellyfish proliferations in some cases [16,44], and the lack of this driver in our global model may account for some of the discrepancy between model results and observations. Temperature change may partially explain the mismatch in the oligotrophic eastern Mediterranean Sea, because it can produce large changes in food web structure in oligotrophic regions in our model (figure 3c).

Despite the very simplified structure of our model and the limits in the number of processes that we can resolve, the ESI score appears to compare generally well with available observations—which are themselves not perfect. Moreover, the predictions of zooplankton, fish and jellyfish biomasses are consistent with those reported by Oguz & Gilbert [7] using long time series in the Black Sea (see the electronic supplementary material, table S5).

Changes in turbidity initially only negatively affects the predator fish (P), while the biomass of forage fish increases. Similarly, fishing mortality on forage fish does not immediately affect forage fish biomass prior to their disappearance, but instead decreases the biomass of their predators. This lack of an immediate biomass response of a prey species is universal to Lotka–Volterra-type models like this one [27]. However, this does not mean that the forage fish are unaffected. Their production does indeed decrease, but this is compensated by a decrease in the predator biomass. When we run the model without predator fish, forage fish biomass does indeed decrease with increasing fishing mortality, and we would argue that overfishing on forage fish often occurs after the depletion of predatory fish stocks, i.e. ‘fishing down the food web’ [8,45]. Trophic control on forage fish is a key feature in our model and is supported by many observations of trophic cascades in fish ecosystems [7,8,46,47]. Moreover, the predicted sudden replacement of fish by jellyfish when this trophic control breaks is similar to what has been observed in some systems [6,8].

Jellyfish predation on the younger stages of fish is an important process in many systems, whereas there is little evidence of the opposite [3]. Most large, blooming jellyfish prey on fish eggs and/or larvae to some extent, although the magnitude of this is very variable. Intraguild predation by jellyfish on young stages of forage fish may negatively affect recruitment to the fish stocks in some cases, provided that there is a significant overlap in distributions and timing, as well as sufficiently large abundances of jellyfish. Here, we have focused on competition regulated by the environment and neglected intraguild predation. Hence, our results can be considered conservative, as this process is expected to reinforce the ability of jellyfish to replace fish at high zooplankton densities. However, to properly estimate the relevance of this process in regulating fish dynamics, a different approach using, for example, physiologically structured population models would probably be needed.

A critical assumption in our model is the lack of trophic control on jellyfish. An increasing amount of studies indicate that jellyfish are not exclusively ‘dead ends’ in the food web, but are in fact predated opportunistically by many predatory fish [25]. However, our model mainly describes large jellyfish that apparently have few specialized predators, but are rather consumed opportunistically (e.g. [25,26]). This results in a weak trophic coupling and in low control of jellyfish biomasses by these predators. Consistent with other studies [3], we assume that jellyfish can have a large impact on lower trophic levels but do not transfer energy further up in the food web very efficiently.

Many important forage fish, such as anchovies, menhaden and sardine are also able to filter-feed [48]. This could potentially cause predation efficiency of forage fish in our model to be underestimated. A forage fish with the carbon weight assumed in our model corresponds to a fish of approximately 8 cm in length and a maximum gape size diameter of 1.19 cm [49]. If we calculate the visual area for the forage fish feeding on the large zooplankton, we get a diameter minimum of 1.25 cm (0.72 cm for the small zooplankton). We conclude that including filter feeding for forage fish in our model would not change the results as minimum visual range is comparable to the gape size.

The interaction between visual feeding and the water turbidity describes a mechanism where bottom up forcing directly affects key traits of organisms at higher trophic levels. This highlights the importance of describing organism traits and not just biomasses in ecosystem models. Models developed on fundamental traits are general, and allow applications across different ecosystems as long as the interactions based on a mechanistic description of proximate factors are still valid. This is particularly important to describe jellyfish ecology across ecosystems, since the lack of long time series of jellyfish populations makes it hard to construct good statistical models of jellyfish populations on a global scale.

Mechanistic models of the relative profitability of jellyfish and fish feeding modes have been studied before [23], and the relationship between system production and turbidity is similar to previous modelling studies for the Baltic Sea [27]. However, to the best of our knowledge, this is the first mechanistic model of fish and jellyfish competition that has been applied on a global scale.

Authors' contributions

All authors contributed in conceiving the study. N.A.S.-M. performed modelling work, with the help of P.M. N.A.S.-M. and P.M. collected data. N.A.S.-M., P.M. and T.K. analysed model output. N.A.S.-M. wrote the first draft of the manuscript, and all authors contributed substantially to revisions. The solutions of the model equilibria are available upon request to the main author.

Competing interests

We have no competing interests.

Funding

The Centre for Ocean Life is supported by the Villum Foundation.