Introduction

About 75% of all freshwater fish species on earth are found in the tropics (van der Sleen and Albert 2021). Large tropical rivers in particular are home to exceptional levels of fish species richness, the origin of which have been related to their size (McGarvey and Terra 2016; Rolls et al. 2018), habitat heterogeneity (Heino 2011; Rabosky 2020), and the persistence and stability of tropical biomes, leading to the accumulation of species over millions of years (Albert and Reis 2011; Cassemiro et al. 2023). Such an accumulation of species can however only occur if species can coexist for sufficient periods of time to lower extinction rates relative to speciation rates. Niche differentiation has traditionally been used to study species coexistence, but for many tropical freshwater fish distinct niches are hard to define. In the Amazon basin, for example, feeding specializations are clearly present (e.g. Zuanon and Ferreira 2008), but many species groups appear to exhibit substantial, if not complete, habitat and dietary overlap (e.g. Goulding et al. 1988). It can be expected that such overlap, on the longer term, will reduce diversity without the presence of mechanisms that prevent, or slow, competitive exclusion. However, the mechanisms facilitating coexistence in tropical rivers remain poorly understood.

Many tropical rivers experience a large annual flood pulse, causing inundation of floodplains that can last from several weeks to several months each year, depending on local topography (Adamson et al. 2009; Goulding et al. 2003; Junk et al. 1989). In her seminal work, Lowe-McConnell (1987) already hypothesized that the annual flood pulse could be a crucial factor that prevents competitive exclusion in tropical rivers, and thus for biodiversity maintenance. The premise is that during the flooding season, fish have access to lateral floodplains (Fig. 1a), which provide an abundance of allochthonous food sources, including invertebrates, fruits and seeds (e.g. Chapman 2001; Goulding 1980; Kubitzki and Ziburski 1994; Poulsen et al. 2004). The super-abundance of allochthonous resources may drastically reduce competition between fish species during the high-water season. Moreover, predation pressure is likely low during the flooding season, as inundated plants and trees can provide abundant shelter and fish densities are very low given the extreme expansion of the aquatic ecosystem. During the low-water season, on the other hand, food availability is low and diet flexibility and fat reserves built up during the floods may prevent starvation (Correa and Winemiller 2014; Goulding et al. 1988). During the time of lowest water level, fish are packed in main river channels and oxbow lakes, where predation pressure is high (Crampton 2011). It is hypothesized that if highly competitive species become more abundant during the high-water season, they will experience proportionally more predation during the low-water season, preventing them from becoming dominant (Lowe-McConnell 1987).

Fig. 1
figure 1

Generalized profile of a tropical river and associated floodplains (a), which in the Amazon, Mekong and Congo, for example, commonly experience a 4–6 month flooding season. Intra-annual variability in surface area and food availability (b) in the models with a flood pulse (black solid line) and without a flood pulse (black dotted line). Example of trophic interactions included in our model simulations (c, d). The food chain in our models included a single primary resource, 13 consumer and 7 predator species; circular arrows for predator species indicate cannibalism. Note that mean annual surface area and total annual food availability is the same in both models, but that this remains constant throughout the year in the models without a flood pulse (b,c), and varies across the year in the models that include an annual flood pulse (b, d)

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Species coexistence in fluctuating environments, such as driven by rainfall seasonality in semi-arid environments, has been a subject of study for many decades and a large body of theoretical work has proposed mechanisms that could promote coexistence in such environments, including storage effects and relative nonlinearity (e.g. Chesson 1994, 2000; Chesson et al. 2004; Holt 2008; Sakavara et al. 2018). Yet, few studies have focussed on species coexistence in pulsing tropical rivers. Understanding the role of the flood pulse for sustaining fish diversity in tropical rivers is of critical importance because deforestation (Lima et al. 2014; Xu et al. 2022), climate change (Zulkafli et al. 2016), and the construction of large hydropower dams (Winemiller et al. 2016) are currently causing accelerated flood pulse change across the tropics.

Although the mechanisms hypothesized by Lowe-McConnell (1987) are known from general theoretical and experimental work (e.g. as “frequency dependent exploitation by generalist enemies”; see recent review in Hawlena et al. 2022), they have not been widely considered in the current debate on the impacts of hydrological change in tropical rivers. Partially, this is because empirical tests of these mechanisms are highly impractical under field conditions. We therefore developed a theoretical model that includes some key features relevant for tropical riverine fish communities, such as predicable annual flooding regimes and a strong dependence on allochthonous energy input. In our models, species within a trophic guild exploit the same limited resource, but differ strongly in competitive strength. We simulated millions of species interactions and recorded species population development and coexistence over time, using scenarios with and without an annual flood pulse. We also included scenarios without predators in order to examine the effect of the flood pulse on interspecific competition only. Our main aim was to assess whether and how the flood pulse could lower competitive exclusion and promote species coexistence.

Methods

General model description

We simulated a basic aquatic food web, where species within a trophic guild exploit the same limited resources, but differ in competitive strength (i.e. in their ability to acquire resources), with the competitive strength of the “best” competitor being 50 times larger than the “worst” competitor. Our model works like a tournament (Fig. 2), where trophic interactions are randomly drawn, but the chance that a species will interact (and could acquire food) is based on: (i) its population size, (ii) the abundance of its food source, and (iii) its competitive strength. We thus calculated how likely it is that each of the possible trophic interactions would occur at a given moment. For example, it is more likely, at a given time, that an individual of a highly competitive species with a large population size (i.e. many individuals) will acquire an abundant food source, than an individual of a less competitive species with a small population size (i.e. few individuals) and/or feeding on a less abundant food source. Based on these probabilities, a single interaction was drawn at each time step. Each individual species could interact until: (i) it is saturated (i.e. all individuals are full), (ii) it spent its available energy for food acquisition, or (iii) its food source is depleted. If no interactions are possible, the model will move to the next time step, here chosen to represent a month. We simulated an arbitrary chosen number of 2400 months, using scenarios with and without an annual flood pulse and recorded biomass development of simulated fish populations and competitive exclusion. The R-script containing the full model is included as supplementary material; all parameters included in the model are given in Table S1.

Fig. 2
figure 2

Schematic flow chart of basic model components. At each iteration, a single trophic interaction is randomly drawn from the pool of all possible interactions (here only three are shown for simplicity). The probability that a specific interaction is drawn is a function of the density of a species and its food as well as its competitive strength (P = predator, C = consumers, R = allochthonous resource). An interaction can lead to a successful outcome (food is found and eaten) or not (hunt/search did not lead to food acquisition), the probability of which is density dependent. Regardless of its success, all interactions cost energy (“Interaction energy costs”). If successful, food can be assimilated and used for population growth if none of the listed situations apply: species is saturated, food source has been depleted, or a species spent it available energy for food acquisition. Changes in biomass (loss due to interaction costs and predation; and gain though food consumption) affect the interaction probabilities for the next iteration. If no more trophic interactions (i.e. iterations) are possible, the model will move to the next time step, here chosen to represent a month (Fig. 1b)

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Trophic interactions

For simplicity reasons and to keep calculating time low, our model included one primary food source and 20 fish species: 13 herbivore species (called “consumers” hereafter) and 7 predatory species (called “predators” hereafter). The predators are generalists and can consume all other species including smaller individuals of the same species (i.e. cannibalism), whereas the consumers can only feed on the primary food source, which represents the primary productivity of floodplain forests. Thus, the possible interactions in the model are resource-consumer, predator–consumer, and predator-predator interactions (Fig. 1c, d). For all possible interactions an “interaction strength” (I) is calculated as:

$$I={B}_{food}*{B}_{species}*comp*int$$
(1)

With, Bfood being the biomass of the food source, which corresponds to the primary resource for consumers and a prey species for predators, and Bspecies is the biomass of the consumer or predator species. Comp is the competitive strength of the consumer or predator; int (0 or 1) indicates whether the species interaction is possible (e.g. consumer eating resource; value = 1) or not (e.g. consumer eating a predator; value = 0). Based on these interaction strengths, a single interaction was drawn. The probability of each possible interaction to be selected was proportional to the interaction strength (i.e. interactions with a higher interaction strength have a higher chance of being drawn). Next, the drawn interaction can be successful or unsuccessful, based on the density of the prey species. For example, predation is more likely to be successful on a prey species with a large population size compared to a prey species with a small population size (Fig. 2). To calculate density, the biomass of the fish populations was first transformed to an estimate of the number of (adult) individuals using the length–weight relationship:

$$W=0.0249*S{L}^{3.008}$$
(2)

In this equation, W is the weight of an individual fish. The values 0.0249 and 3.008 are acquired for a generalized fish from the Amazon basin, using the mean of data for 398 species (Froese and Pauly 2021). Based on data from 1288 species from the Amazon basin, the mean standard length (SL) for the consumer fish species was set to 15 cm, whereas the mean SL for the predator fish species was set to 18 cm (Froese and Pauly 2021). The calculated individual weight (W) can then be used to calculate the number of individuals (n) using the current biomass (B) of a species:

$$n=B/W$$
(3)

From the Eqs. 2 and 3, the density of a species (D) was calculated:

$$D=n/A$$
(4)

With A representing the area (in m2) of available habitat in that month, being variable in scenarios with an annual flood pulse and constant in scenarios without a flood pulse (Fig. 1b). Success rates were arbitrarily set at 100% at a density of 1 fish per m2 and decrease proportionally as prey species density decreases. For example, the chance of a successful hunt by a predator is 50% when the density of the prey species is 0.5 fish per m2.

Population growth

After a successful interaction, a species’ biomass increased based on the biomass eaten and a fixed trophic efficiency. If a predator is larger than its prey, it will eat the body weight of the prey. However, predatory fish species can have morphological constraints, such as gape size, that limit the maximum size of prey species they can consume (Mihalitsis and Bellwood 2017). Therefore, if the individual weight of the predator is the same as the individual weight of the prey in the model, which can occur in our simulations when a predator eats another predator, the predator will eat 50% of its own body weight (i.e. representing a smaller-sized individual). If the interaction is between a consumer and the food source, the consumer will eat 50% of its own body weight.

In our model, each species’ interaction also costs energy, representing for example, the energy required for food acquisition, which is included arbitrarily in the model as a loss of 0.1 g for the predator or consumer, no matter the success of the interaction. We chose a limit of 0.5% loss of the population biomass of the species for each modelled month for food acquisition. Thus, a species with a population size of 5 kg has (0.005 * 5 kg =) 25 g to spend on interactions, which means that the species can partake in 250 interactions for food acquisition. Per modelled month, species can consume a maximum amount of food equal to 2% of their population biomass at the start of the month before being saturated. After each interaction, the available energy for interactions, and maximum intake of the interacting species are updated, to correct for the cost of the interaction and the biomass that is eaten, respectively.

Mortality in the model can occur due to predation, but also due to density-dependent “background” mortality. This density-dependent mortality occurs, for example, because of density-dependent diseases and intraspecific competition (e.g. Ward et al. 2006). To determine the density-dependent mortality in the model, the density of the species is first calculated (see Eqs. 2–4). Next, mortality (m) is calculated using:

$$m= {m}_{min}+(\frac{ {m}_{max}- {m}_{min}}{{D}_{max}}*D)$$
(5)

With mmin representing a minimum background mortality (set at a value of 0.5% in our simulations), mmax representing the maximum mortality (set at a value of 12% in our simulations), and Dmax the maximum density of 1. Thus, if a species has a density of 1 fish per m2, this species would experience a mortality rate of 12%, which means that 12% of the species’ biomass will be lost due to natural mortality before the next month in the model. If D is larger than Dmax, D is set to a value of 1.

We did not include resource-dependent mortality (i.e. starvation effects during the low-water season in scenarios with a flood pulse) since many tropical fish appear to have a high resilience to periods of low food availability because of the fat reserves that were build-up during the high-water season (Araujo-Lima and Goulding 1997; Goulding 1980).

Modelled scenarios

We ran the model for 2400 months, using two basic scenarios: with and without an annual flood pulse. The flood pulse is included in the model through intra-annual changes in food availability and surface area. Over a year, this flood pulse constitutes 6 months of low water and 6 months of rising/falling/high water. In the flood pulse scenarios, the maximum area was 10 ha during the peak of the flooding season, decreasing to a minimum area of 1 ha during the dry season (Fig. 1b). We thus assume a tenfold increase in the available area for the fish species in the model during the flooding period. In the scenario with no flood pulse, the area was set at a fixed level of 3 ha, which is the average water height in a flood pulse year. As the available primary food source in the model was set at 0.8 kg per ha per month, the intra-annual division of available food differs between the model scenarios with a flood pulse versus without a flood pulse (Fig. 1b). In the model scenario with a flood pulse, this food availability fluctuates together with the fluctuation in water height over the months. However, the total annual food availability is the same in both scenarios. We also ran our model simulation with only consumer species. Although predatory species are a major component of aquatic food webs in the tropical rivers, we included these scenarios to examine the effect of the flood pulse on interspecific competition only, thus excluding the effect of top-down control. All four model scenarios (with and without predators in combination with or without a flood pulse) were ran ten times.

Sensitivity analyses

Sensitivity analyses were performed to assess the effect of different parameter settings on the outcome of the model simulation. For each parameter, the value of the model used was increased by 50% and decreased by 50%, and we recorded the effect thereof on population biomass of the consumer and predator species as well as on extinction rates (Table S2). We only used the scenario with the flood pulse and with both predators and consumers in the sensitivity analysis, which was run three times. All analyses were performed in R.

Results

In the scenarios with a regular annual flood pulse, consistently lower extinction rates occurred compared to the scenarios without a flood pulse (Figs. 3 and 4). Specifically, in the scenarios with an annual flood pulse, none of the species (in the scenario with only consumer species) and 0–5% of the species (in the scenario with both consumer and predator species) were outcompeted and went extinct, whereas in the scenario without a flood pulse, these extinction rates were 30.8–38.5% and 5–15%, respectively. We also found that in the model scenario without a flood pulse the biomass of highly competitive consumers was much higher than that of the consumers with relatively low competitive strength (Figs. 3 and 4). In the models that included a flood pulse, the difference in population biomass of “strong” and “weak” competitor species was much less pronounced. This is clearest in the scenarios without predatory species (Fig. 3a). Interestingly, extinction rates were zero for predator species, and their biomass development was very similar, regardless of the presence of absence of a flood pulse (Figs. 3 and 4). Although most parameters in the model were arbitrary chosen, sensitivity analyses indicated that their individual effect on model outcomes were small (Table S2).

Fig. 3
figure 3

Examples of model outcomes including only consumer species (a, b), or both consumer and predator species (c, d), with and without a flood pulse. Each line shows biomass development for an individual species; black stars indicate time of a species exclusion; arrows on the right sides indicates the difference in biomass between the species with the highest and the lowest biomass

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Fig. 4
figure 4

Mean population biomass by the end of the simulation (mean of ten runs; species ranked from low to high abundance) and cumulative extinction during each simulation (each run as separate line) using scenarios with and without a flood pulse, and without (a) or with predator species (b)

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Discussion

We found that the presence of a regular annual flood pulse can lower competitive exclusion and promote fish species coexistence. These findings are related to the flood-pulse driven changes in both food availability and mortality during the year. In the scenarios without flood pulse, the “strongest” competitors continue to grow to a population size that allows them to eat nearly all of the available food each month, ultimately outcompeting the “weaker” competitors (Fig. 3a, c). In contrast, the presence of a flood pulse allows all species to acquire at least some of the available resources during the high-water season. During these months, food is so abundant for the consumer species that not all resources were consumed in our simulations (Fig. S1). Empirical evidence indeed suggests that food availability may not be a limiting factor for fish growth in the flooding season. Herbivorous and omnivorous species sampled in the flooding seasons in the Amazon basin commonly have full stomach content, while in the dry season empty stomachs are frequently encountered (e.g. Correa and Winemiller 2014; Goulding et al. 1988; Soares et al. 1986).

A similar mechanism operates for mortality, as both the natural (i.e. background) mortality and the mortality due to predation in the model are density-dependent. More competitive species, that become more abundant, also experience increased mortality. Yet in the model with a flood pulse, this process is accentuated by the limited area during the dry season (causing even stronger population control of competitive species). Our assumption is that predator species are generalists and will switch to the most abundant prey, a behaviour that has been observed in several species (McPhee et al. 2015; Warburton et al. 1998). Both generalist predators (e.g. Kuang and Chesson 2010; Roughgarden and Feldman 1975) and natural enemies (causing density-dependent mortality; Connell 1971; Janzen 1970) have been long understood to profoundly affect the outcomes of interactions between species. However, in our model simulations, predators have an additive effect and the flood pulse can also promote species coexistence in the absence of top-down controls (Fig. 3a, b).

The models without a flood pulse resulted in higher total fish biomass compared to the models with a flood pulse (Figs. 3 and 4). This suggests that although flood pulses may promote species coexistence, it reduces total fish abundance. Such an outcome is unlikely in reality. In the Amazon basin for example, profound change of the flood pulse after dam construction in the Uatumã river led to floodplain truncation and mortality of floodplain trees (Assahira et al. 2017; Schongart et al. 2021). Such changes will likely lower allochthonous energy input and hence the biomass of dependent fish species on the longer term. Interestingly, little difference was found in population biomass or extinction rate for predator species between scenarios with and without a flood pulse (even though the modelled species differed strongly in competitive strength; Figs. 3 and 4). This result is a consequence of the strong self-regulation in modelled predator species, whereby more competitive predator species have a high probability to catch prey, but the resulting increase in population biomass also increases biomass loss through intraguild predation and cannibalism. Such self-regulation has been documented in many predator fish species (e.g. Frankiewicz et al. 1999; Hart 2002; Smith and Reay 1991), including fish in tropical rivers (Luz-Agostinho et al. 2008; Pereira et al. 2017; Piana et al. 2006).

Our model includes several assumptions and limitations. One of the main assumptions is that all species are generalists and that all consumers share a single resource. Yet, diet specializations, resource partitioning, and diet flexibility are widely occurring in tropical freshwaters, and for some species this has been related to the hydrological cycle (e.g. Azevedo et al. 2022; Barros et al. 2017; Correa and Winemiller 2014; Melo et al. 2019; Neves et al. 2018, 2021; Zuanon and Ferreira 2008). Nonetheless, it has also been found that many species share the available food sources at any given time, regardless of diet switching during the year (e.g. Correa et al. 2011; Goulding et al. 1988). Here, we show that the flood pulse can promote species coexistence, even when niche differentiation is absent and competitive differences between species are large.

Another limitation of our model is that it includes only two trophic guilds, whereas many more tropic guilds exist in tropical riverine ecosystems. Trophic guilds can easily be added to our basic model, but even though it could make the model more realistic, it will also greatly increase its complexity and we do not expect it will quantitatively change our results. Nonetheless, our simulations are a simplification and other factors that may contribute to species coexistence, such as feeding specializations (Zuanon and Ferreira 2008) and potential storage effects (Chesson et al. 2004; Hauser and Benedito 2012), were not included. Lastly, for many of the parameters in the model, such as density-dependent natural mortality, an arbitrary value was chosen. Although some parameter values were based on literature, many of the parameter settings (Table S1) could be unrealistic. However, our sensitivity analyses indicated that model output is relatively robust to changes in parameter settings (Table S2).

A comparative study found higher species richness in riverine ecosystems with a regular, predictable flood pulse compared to rivers with irregular flooding regimes (Jardine et al. 2015). Such empirical findings are consistent with the outcomes of our simulations. If, as our results show, the flood pulse is an important mechanism for the maintenance of fish diversity in tropical rivers, then flood pulse change could drive species extinctions. Observations in tropical rivers indicate that hydrological change following dam construction can indeed negatively affect fish diversity (Agostinho et al. 2008; Araujo et al. 2013; Baird and Hogan 2023; Keppeler et al. 2022; Sa-Oliveira et al. 2015). Such changes could follow from the mechanisms discussed above and/or from other factors such as blockage of migration routes (Hurd et al. 2016; Ziv et al. 2012) and reduced reproduction success (Baird and Hogan 2023; Röpke et al. 2022). Interestingly, some species can dramatically increase in abundance in the reservoirs created by hydropower dams (Cella-Ribeiro et al. 2017; Monaghan et al. 2020), which is in line with the outcomes of our model simulations when a regular flood pulse was absent. Changes in food availability or water transparency in the reservoir may however, also underlie such increases.

Tropical rivers likely face inevitable hydrological change due to increasing land-use intensity, ongoing climate change, and the continued development of hydropower production. While our models only compare two extreme scenarios—recurrent (identical) flood pulses versus the complete absence thereof—hydrological change will be in the form of an intermediate scenario. Assessing the impact of different change scenarios (i.e. in frequency, timing and magnitude of flooding) was beyond the scope of our study. Nonetheless, our model, albeit simplistic and generic, could serve as a basis for more specific and comprehensive population models that include the sensitivity of fish populations to flooding regimes. The absence of such models is currently limiting our ability to predict the consequences of hydrological change for fish communities, as well as our ability to define safe operating margins for hydrological engineering (i.e. how much can be deviated from natural flooding regimes before fish populations collapse). This knowledge gap is pressing as fish production in tropical rivers provides nutrition to more than 150 million people (Sabo et al. 2017). Declines in the abundance and diversity of tropical freshwater fish can thus have a large impact and threaten the well-being of people already susceptible to poverty (Lima et al. 2020). Understanding the relationships between the flood pulse and fish diversity and abundance in tropical rivers is therefore an urgent research priority.