Biodiversity in model ecosystems, I: coexistence conditions for competing species

This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper, we study the coexistence of competing species at the fixed point of population dynamic equations. For many simple models, this imposes a limit on the width of the productivity distribution, which is more severe the more diverse the ecosystem is (1994, Theor. Popul. Biol. 45, 227-276). Here we review and generalize this analysis, beyond the "mean-field"-like approximation of the competition matrix used in previous works, and extend it to structured food webs. In all cases analysed, we obtain qualitatively similar relations between biodiversity and competition: the narrower the productivity distribution is, the more species can stably coexist. We discuss how this result, considered together with environmental fluctuations, limits the maximal biodiversity that a trophic level can host.     

Species assembly in model ecosystems, I: Analysis of the population model and the invasion dynamics

Recently we have introduced a simplified model of ecosystem assembly (Capitán et al., 2009) for which we are able to map out all assembly pathways generated by external invasions in an exact manner. In this paper we provide a deeper analysis of the model, obtaining analytical results and introducing some approximations which allow us to reconstruct the results of our previous work. In particular, we show that the population dynamics equations of a very general class of trophic-level structured food-web have an unique interior equilibrium point which is globally stable. We show analytically that communities found as end states of the assembly process are pyramidal and we find that the equilibrium abundance of any species at any trophic level is approximately inversely proportional to the number of species in that level. We also find that the per capita growth rate of a top predator invading a resident community is key to understand the appearance of complex end states reported in our previous work. The sign of these rates allows us to separate regions in the space of parameters where the end state is either a single community or a complex set containing more than one community. We have also built up analytical approximations to the time evolution of species abundances that allow us to determine, with high accuracy, the sequence of extinctions that an invasion may cause. Finally we apply this analysis to obtain the communities in the end states. To test the accuracy of the transition probability matrix generated by this analytical procedure for the end states, we have compared averages over those sets with those obtained from the graph derived by numerical integration of the Lotka-Volterra equations. The agreement is excellent.     

Examining the potential effects of species aggregation on the network structure of food webs

One of the key measures that have been used to describe the topological properties of complex networks is the “degree distribution”, which is a measure that describes the frequency distribution of number of links per node. Food webs are complex ecological networks that describe the trophic relationships among species in a community, and the topological properties of empirical food webs, including degree distributions, have been examined previously. Previously, the “niche model” has been shown to accurately predict degree distributions of empirical food webs, however, the niche model-generated food webs were referenced against empirical food webs that had their species grouped together based on their taxonomic and/or trophic relationships (aggregated food webs). Here, we explore the effects of species aggregation on the ability of the niche model to predict the total- (sum of prey and predator links per node), in- (number of predator links per node), and out- (number of prey links per node) degree distributions of empirical food webs by examining two food webs that can be aggregated at different levels of resolution. The results showed that (1) the cumulative total- and out-degree distributions were consistent with the niche model predictions when the species were aggregated, (2) when the species were disaggregated (i.e., higher resolution), there were mixed conclusions with regards to the niche model's ability to predict total- and out-degree distributions, (3) the model's ability to predict the in-degree distributions of the two food webs was generally inadequate. Although it has been argued that universal functional form based on the niche model could describe the degree distribution patterns of empirical food webs, we believe there are some limitations to the model's ability to accurately predict the structural properties of food webs.     

Biodiversity maintenance in food webs with regulatory environmental feedbacks

Although the food web is one of the most fundamental and oldest concepts in ecology, elucidating the strategies and structures by which natural communities of species persist remains a challenge to empirical and theoretical ecologists. We show that simple regulatory feedbacks between autotrophs and their environment when embedded within complex and realistic food-web models enhance biodiversity. The food webs are generated through the niche-model algorithm and coupled with predator-prey dynamics, with and without environmental feedbacks at the autotroph level. With high probability and especially at lower, more realistic connectance levels, regulatory environmental feedbacks result in fewer species extinctions, that is, in increased species persistence. These same feedback couplings, however, also sensitize food webs to environmental stresses leading to abrupt collapses in biodiversity with increased forcing. Feedback interactions between species and their material environments anchor food-web persistence, adding another dimension to biodiversity conservation. We suggest that the regulatory features of two natural systems, deep-sea tubeworms with their microbial consortia and a soil ecosystem manifesting adaptive homeostatic changes, can be embedded within niche-model food-web dynamics.     

Species assembly in model ecosystems, II: Results of the assembly process

In the companion paper of this set (Capitán and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitán et al. (2009). This model is based on the construction of an assembly graph containing all viable configurations of the community, and the definition of a Markov chain whose transitions are the transformations of communities by new species invasions. In the present paper we provide an exhaustive numerical analysis of the model, describing the average time to the recurrent state, the statistics of avalanches, and the dependence of the results on the amount of available resource. Our results are based on the fact that the Markov chain provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables as well as the time variation of these magnitudes during succession, in an exact manner. Since the absorption times into the recurrent set are found to be comparable to the size of the system, the end state is quickly reached (in units of the invasion time). Thus, the final ecosystem can be regarded as a fluctuating complex system where species are continually replaced by newcomers without ever leaving the set of recurrent patterns. The assembly graph is dominated by pathways in which most invasions are accepted, triggering small extinction avalanches. Through the assembly process, communities become less resilient (e.g., have a higher return time to equilibrium) but become more robust in terms of resistance against new invasions.     

Body size and food web structure: testing the equiprobability assumption of the cascade model

The cascade model successfuly predicts many patterns in reported food webs. A key assumption of this model is the existence of a predetermined trophic hierarchy; prey are always lower in the hierarchy than their predators. At least three studies have suggested that, in animal food webs, this hierarchy can be explained to a large extent by body size relationships. A second assumption of the standard cascade model is that trophic links not prohibited by the hierarchy occur with equal probability. Using nonparametric contingency table analyses, we tested this ”equiprobability hypothesis” in 16 published animal food webs for which the adult body masses of the species had been estimated. We found that when the hierarchy was based on body size, the equiprobability hypothesis was rejected in favor of an alternative, ”predator-dominance” hypothesis wherein the probability of a trophic link varies with the identity of the predator. Another alternative to equiprobabilty is that the probability of a trophic link depends upon the ratio of the body sizes of the two species. Using nonparametric regression and liklihood ratio tests, we show that a size-ratio based model represents a significant improvement over the cascade model. These results suggest that models with heterogeneous predation probabilities will fit food web data better than the homogeneous cascade model. They also suggest a new way to bridge the gap between static and dynamic food web models. Received: 3 February 1999 / Accepted: 26 October 1999     

The effects of mixotrophy on the stability and dynamics of a simple planktonic food web model

Recognition of the microbial loop as an important part of aquatic ecosystems disrupted the notion of simple linear food chains. However, current research suggests that even the microbial loop paradigm is a gross simplification of microbial interactions due to the presence of mixotrophs-organisms that both photosynthesize and graze. We present a simple food web model with four trophic species, three of them arranged in a food chain (nutrients-autotrophs-herbivores) and the fourth as a mixotroph with links to both the nutrients and the autotrophs. This model is used to study the general implications of inclusion of the mixotrophic link in microbial food webs and the specific predictions for a parameterization that describes open ocean mixed layer plankton dynamics. The analysis indicates that the system parameters reside in a region of the parameter space where the dynamics converge to a stable equilibrium rather than displaying periodic or chaotic solutions. However, convergence requires weeks to months, suggesting that the system would never reach equilibrium in the ocean due to alteration of the physical forcing regime. Most importantly, the mixotrophic grazing link seems to stabilize the system in this region of the parameter space, particularly when nutrient recycling feedback loops are included.     

Biodiversity lessens the risk of cascading extinction in model food webs

Due to the complex interactions between species in food webs, the extinction of one species could lead to a cascade of further extinctions and hence cause dramatic changes in species composition and ecosystem processes. We found that the risk of additional species extinction, following the loss of one species in model food webs, decreases with the number of species per functional group. For a given number of species per functional group, the risk of further extinctions is highest when an autotroph is removed and lowest when a top predator is removed. In addition, stability decreases when the distribution of interaction strengths in the webs is changed from equal to skew (few strong and many weak links). We also found that omnivory appears to stabilize model food webs. Our results indicate that high biodiversity may serve as an insurance against radical ecosystem changes.     

Geographical variation in food web structure in Nepenthes pitcher plants

Abstract. 1. Relative to Nepenthes species in West Malaysia near the evolutionary centre of the genus, outlying species of Nepenthes in the Seychelles, Sri Lanka and Madagascar have fewer species of both prey and predator living in them, fewer and smaller guilds of species, much apparently empty niche space, less complex food webs, and a greater connectance. The ratios of prey to predators, and of connectance (C₁) to the total number of trophic types present remain approximately constant.
2. Differences between the food webs appear to be related in a complex way to the size of the country and its degree of spatial and temporal isolation, the size of the local species pool capable of colonizing the pitchers, and the number of Nepenthes species present. However, the maximal length of food chains in the richest and most complex food webs is probably limited by energetic constraints or environmental predictability.
3. The data may illustrate how food webs change to become more complex, both by the addition of new guilds of species and the addition of species to existing guilds, while at the same time certain properties of the food web are kept approximately constant.     

The impact of nonlinear functional responses on the long-term evolution of food web structure

We investigate the long-term web structure emerging in evolutionary food web models when different types of functional responses are used. We find that large and complex webs with several trophic layers arise only if the population dynamics is such that it allows predators to focus on their best prey species. This can be achieved using modified Lotka-Volterra or Holling/Beddington functional responses with effective couplings that depend on the predator's efficiency at exploiting the prey, or a ratio-dependent functional response with adaptive foraging. In contrast, if standard Lotka-Volterra or Holling/Beddington functional responses are used, long-term evolution generates webs with almost all species being basal, and with additionally many links between these species. Interestingly, in all cases studied, a large proportion of weak links result naturally from the evolution of the food webs.     

Integrating internal and external dispersal in metacommunity assembly: preliminary theoretical analyses

Internal dispersal, which occurs among local communities within a metacommunity, and external dispersal, which supplies immigrants from outside the metacommunity, can both have a major impact on species diversity. However, few studies have considered the two simultaneously. Here I report preliminary computer-simulation results to suggest that internal and external dispersal can interact to influence species richness. Specifically, the results show that internal dispersal did not affect species richness under frequent external dispersal, whereas it enhanced richness in local communities while decreasing richness in metacommunities under infrequent external dispersal. Conversely, external dispersal influenced species richness in local communities more greatly in the absence of internal dispersal than in its presence, while external dispersal did not affect richness in metacommunities regardless of internal dispersal. Furthermore, internal and external dispersal interactively determined the importance of community assembly history in generating and maintaining variation in local community structure. Overall, these results suggest that the two dispersal types can reciprocally provide the context in which each affects species diversity and therefore that their effects cannot be understood in isolation of the other.Electronic Supplementary Material Supplementary material is available for this article at Tadashi Fukami is the recipient of the ninth Denzaburo Miyadi Award.     

Macroecological patterns and niche structure in a new marine food web

The integration of detailed information on feeding interactions with measures of abundance and body mass of individuals provides a powerful platform for understanding ecosystem organisation. Metabolism and, by proxy, body mass constrain the flux, turnover and storage of energy and biomass in food webs. Here, we present the first food web data for Lough Hyne, a species rich Irish Sea Lough. Through the application of individual-and size-based analysis of the abundance-body mass relationship, we tested predictions derived from the metabolic theory of ecology. We found that individual body mass constrained the flux of biomass and determined its distribution within the food web. Body mass was also an important determinant of diet width and niche overlap, and predator diets were nested hierarchically, such that diet width increased with body mass. We applied a novel measure of predator-prey biomass flux which revealed that most interactions in Lough Hyne were weak, whereas only a few were strong. Further, the patterning of interaction strength between prey sharing a common predator revealed that strong interactions were nearly always coupled with weak interactions. Our findings illustrate that important insights into the organisation, structure and stability of ecosystems can be achieved through the theoretical exploration of detailed empirical data.     

Community convergence in a simple microbial food web

Previous studies of communities implicate many potential mechanisms that can create alternate stable states. These include density-dependent foraging behavior, size refuges reached by early colonists, environmental feedback following disturbance, and different initial densities of intraguild predators. Previous work shows that alternate states of varying stability can occur in food webs containing the intraguild predators Blepharisma americanum and Tetrahymena vorax. Differences in colonization history could create the alternate states, consisting of dominance by either Blepharisma or Tetrahymena, but it was unclear whether results depended on effects of initial density or only on changes in the resource base. We manipulated initial densities of both species to determine if density effects alone could create alternate stable states. Convergence of these communities over time indicated that differences in initial density did not create alternate stable states. By default, other factors influenced by colonization history, such as resource availability, may produce alternate states. Models of alternate stable-state phenomena should incorporate differences in resource availability in addition to direct competitive and predatory interactions to provide a more complete depiction of the causes of differences in community composition in otherwise similar habitats.     

Emergence of non-random structure in local food webs generated from randomly structured regional webs

Previous studies have shown that high-resolution, empirical food webs possess a non-random network structure, typically characterized by uniform or exponential degree distributions. However, the empirical food webs that have been investigated for their structural properties represent local communities that are only a subset of a larger pool of regionally coexisting species. Here, we use a simple model to investigate the effects of regional food web structure on local food webs that are assembled by two simple processes: random immigration of species from a source web (regional food web), and random extinction of species within the local web. The model shows that local webs with non-random degree distributions can arise from randomly structured source webs. A comparison of local webs assembled from randomly structured source webs with local webs assembled from source webs generated by the niche model shows that the former have higher species richness at equilibrium, but have a nonlinear response to changing extinction rates. These results imply that the network structure of regional food webs can play a significant role in the assembly and dynamics of local webs in natural ecosystems. With natural landscapes becoming increasingly fragmented, understanding such structure may be a necessary key to understanding the maintenance and stability of local species diversity.     

Multi-objective optimization of an ecological assembly model

The aim of the present work is to use multi-objective evolutionary algorithms (MOEA) to parameterise an ecological assembly model based on Lotka–Volterra dynamics. In community assembly models, species are introduced from a pool of species according to a sequence of invasion. By manipulating the assembly sequences, we look at the structure of the final communities obtained by a multi-objective process where the goal is to optimize the productivity of the final communities. The MOEA must also meet the constraint that the communities constructed in this fashion have a specified connectance. The Non-dominated Sorting Algorithm (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2) were employed to optimize sequences according to the multi-objective optimization problem. The results show that the assembly process using optimized sequences generated different community structure than those generated via random sequences. First, the assembled communities are much more productive than those obtained from random sequences. We show that this increase of productivity is due to the degree distribution of the community food web, which was reshaped by the optimization process. In addition, using identical regional species pools the MOEAs were able to generate communities of different expected connectances. These results demonstrate the effectiveness of NSGA-II and SPEA2 for optimizing parameters in ecological models.     

Community assembly along a species pool gradient: implications for multiple-scale patterns of species diversity

Various ecological processes influence patterns of species diversity at multiple spatial scales. One process that is potentially important but rarely considered is community assembly. I assembled model communities using species pools of differing size to examine how the history of community assembly may affect multi-scale diversity patterns. The model contained three scales at which diversity could be measured: local community, metacommunity, and species pool. Local species saturation occurred, as expected from the competition and predation built in the model. However, local communities did not become resistant to invasions except when the species pool was very small. Depending on dispersal rate and trophic level, the larger the species pool, the harder it was to predict which species invades which local community at a given time. Consequently, local-community dissimilarity maintained by assembly history increased linearly with pool size, even though local diversity was decoupled from pool size. These results have two implications for multi-scale diversity patterns. First, assembly history may provide an explanation for scale-dependent relationships between local and regional diversity: assembly causes the relationship to be curvilinear at one scale (local community), while linear at another (metacommunity). Second, assembly history influences how -diversity is partitioned into - and -diversity: assembly causes the relative contribution of to increase with pool size. Overall, this study suggests that community assembly history interacts with species pool size to regulate multi-scale patterns of species diversity.     

Adaptive omnivory and species coexistence in tri-trophic food webs

The commonness of omnivory in natural communities is puzzling, because simple dynamic models of tri-trophic systems with omnivory are prone to species extinction. In particular, the intermediate consumer is frequently excluded by the omnivore at high levels of enrichment. It has been suggested that adaptive foraging by the omnivore may facilitate coexistence, because the intermediate consumer should persist more easily if it is occasionally dropped from the omnivore's diet. We explore theoretically how species permanence in tri-trophic systems is affected if the omnivore forages adaptively according to the "diet rule", i.e., feeds on the less profitable of its two prey species only if the more profitable one is sufficiently rare. We show that, compared to systems where omnivory is fixed, adaptive omnivory may indeed facilitate 3-species persistence. Counter to intuition, however, facilitation of 3-species coexistence requires that the intermediate consumer is a more profitable prey than the basal resource. Consequently, adaptive omnivory does not facilitate persistence of the intermediate consumer but enlarges the persistence region of the omnivore towards parameter space where a fixed omnivore would be excluded by the intermediate consumer. Overall, the positive effect of adaptive omnivory on 3-species persistence is, however, small. Generally, whether omnivory is fixed or adaptive, 3-species permanence is most likely when profitability (=conversion efficiency into omnivores) is low for basal resources and high for intermediate consumers.     

Zooplankton interactions with toxic phytoplankton: Some implications for food web studies and algal defence strategies of feeding selectivity behaviour, toxin dilution and phytoplankton population diversity

This study focuses on the interactions between toxic phytoplankton and zooplankton grazers. The experimental conditions used are an attempt to simulate situations that have, so far, received little attention. We presume the phytoplankton community to be a set of species where a population of a toxic species is intrinsically diverse by the presence of coexisting strains with different toxic properties. The other species in the community may not always be high-quality food for herbivorous zooplankton. Zooplankton populations may have developed adaptive responses to sympatric toxic phytoplankton species. Zooplankton grazers may perform a specific feeding behaviour and its consequences on fitness will depend on the species ingested, the effect of toxins, and the presence of mechanisms of toxin dilution and compensatory feeding. Our target species are a strain of the dinoflagellate Alexandrium minutum and a sympatric population of the copepod Acartia clausi. Mixed diets were used with two kinds of A. minutum cells: non-toxic and toxic. The flagellate Rhodomonas baltica and the non-toxic dinoflagellate Alexandrium tamarense were added as accompanying species. The effect of each alga was studied in separate diets. The toxic A. minutum cells were shown to have negative effects on egg production, hatching success and total reproductive output, while, in terms of its effect on fitness, the non-toxic A. minutum was the best quality food offered. R. baltica and A. tamarense were in intermediate positions. In the mixed diets, copepods showed a strong preference for toxic A. minutum cells and a weaker one for A. tamarense cells, while non-toxic A. minutum was slightly negatively selected and R. baltica strongly negatively selected. Although the level of toxins accumulated by copepods was very similar, in both the diet with only toxic A. minutum cells and in the mixed diet, the negative effects on fitness in the mixed diet could be offset by toxin dilution mechanisms. The implications of these findings are the fact that mesozooplankton may not play an important role in phytoplankton blooms development. Phytoplankton endotoxin production does not seem to be an evolutionary stable strategy as a defence against some herbivores.     

The predatory Chironomidae of an iron-rich stream: feeding ecology and food web structure

Abstract. 1. Three species of Tanypodinae (Chironomidae) were found in an acid and iron-rich stream in southern England. Maximum abundance was achieved in summer and they were sparse at other times. Individuals were aggregated on the stream bed and were overrepresented in accumulations of leaf litter.
2. The diets of all three species consisted of a mixture of prey (prominently detritivorous chironomid larvae) and detritus. More detritus and fewer prey were taken in winter than in summer.
3. When comparing large tanypod species with small and, intraspecifically, late instars with early, the proportion of guts containing prey increased with increasing body size.
4. Stonefly larvae were more prominent in the diet of Zavrelimyia barbatipes (Kieffer) in summer than in winter but for the other two species the reverse was true. A bigger proportion of Trissopelopia longimana (Staeger) guts contained prey in early summer than in August whereas more Macropelopia goetghebueri (Kieffer) guts contained prey in August. This was apparently a consequence of seasonal differences in the distribution of body size among the populations of these two species.
5. The stream contains two further common predators, Plectrocnemia conspersa (Curtis) and Sialis fuliginosa Pict. These are important predators of tanypod larvae but might also compete with them since they severely deplete populations of prey taken in common.
6. Analysis of the food-web in Broadstone Stream reveals remarkably high values of connectance (C and C_max) and of species richness times connectance (SC_max). Such characteristics are theoretically associated with fragile and dynamically unstable food webs, and may be found in 'constant' environments. There is also an apparently unusual prevalence of omnivory in the community.     

Effects on ecosystem resilience of biodiversity, extinctions, and the structure of regional species pools

Resilience is a general concept that aims to help understand how ecosystems respond to disturbances such as extinctions and invasions. Here, we propose a measure of one aspect of resilience, R _X , which is one minus the expected change in functional diversity (X) caused by a species extinction or addition. We show how two components of biodiversity, species richness and functional diversity, and the structure of regional species pools affect this measure. Variation in species richness and in functional diversity have opposite effects on R _X . Speciose assemblages generally have higher R _X than depauperate ones, whereas functionally diverse assemblages have low R _X relative to functionally depauperate ones. The effect of an extinction on R _X reflects this tradeoff. In our analyses, extinctions usually cause only a small decrease in both functional diversity and R _X . However, extinctions sometimes cause a large reduction in functional diversity and then tend to increase R _X . Regional assemblages containing all rather unique species tend to result in speciose assemblages with relatively low R _X and in low richness assemblages with relatively high R _X . The opposite is true of regional assemblages containing functionally similar species. Information about the processes that structure regional assemblages will therefore increase understanding of ecosystem resilience. Generally, these results suggest that management for biodiversity may not always result in management for resilience.