Stoichiometry, herbivory and competition for nutrients: simple models based on planktonic ecosystems

Models are examined in which two prey species compete for two nutrient resources, and are preyed upon by a predator that recycles both nutrients. Two factors determine the effective relative supply of the nutrients, hence competitive outcomes: the external nutrient supply ratio, and the relative recycling of the two nutrients within the system. This second factor is governed by predator stoichiometry--its relative requirements for nutrients in its own biomass. A model with nutrient resources that are essential for the competing prey is detailed. Criteria are given to identify the limiting nutrient for a food chain of one competitor with the predator. Increased supply of this limiting nutrient increases predator density and concentration of this nutrient at equilibrium, while decreasing the concentration of a non-limiting nutrient. Changes in supply or recycling of a non-limiting nutrient affect only the concentration of that nutrient. Criteria for the invasion of a second prey competitor are presented. When different nutrients limit growth of the resident prey and the invader, increased supply or recycling of the invader's limiting nutrient assists invasion, while increased supply or recycling of the resident's limiting nutrient hinders invasion. If the same nutrient limits both resident and invader, then changes in supply and recycling have complex effects on invasion, depending on species properties. In a parameterized model of a planktonic ecosystem, green algae and cyanobacteria coexist over a wide range of nitrogen:phosphorus supply ratios, without predators. When the herbivore Daphnia is added, coexistence is eliminated or greatly restricted, and green algae dominate over a wide range of supply conditions, because the effective supply of P is greatly reduced as Daphnia rapidly recycles N.     

Parametric Analysis of a Predator–prey System Stabilized by a Top Predator

We present a complete parametric analysis of a predator–prey system influenced by a top predator. We study ecosystems with abundant nutrient supply for the prey where the prey multiplication can be considered as proportional to its density. The main questions we examine are the following: (1) Can the top predator stabilize such a system at low densities of prey? (2) What possible dynamic behaviors can occur? (3) Under which conditions can the top predation result in the system stabilization? We use a system of two nonlinear ordinary differential equations with the density of the top predator as a parameter. The model is investigated with methods of qualitative theory of ODEs and the theory of bifurcations. The existence of 12 qualitatively different types of dynamics and complex structure of the parametric space are demonstrated. Our studies of phase portraits and parametric diagrams show that a top predator can be an important factor leading to stabilization of the predator-prey system with abundant nutrient supply. Although the model here is applied to the plankton communities with fish (or carnivorous zooplankton) as the top trophic level, the general form of the equations allows applications of our results to other ecological systems.     

Not attackable or not crackable—How pre‐ and post‐attack defenses with different competition costs affect prey coexistence and population dynamics

It is well‐known that prey species often face trade‐offs between defense against predation and competitiveness, enabling predator‐mediated coexistence. However, we lack an understanding of how the large variety of different defense traits with different competition costs affects coexistence and population dynamics. Our study focusses on two general defense mechanisms, that is, pre‐attack (e.g., camouflage) and post‐attack defenses (e.g., weaponry) that act at different phases of the predator—prey interaction. We consider a food web model with one predator, two prey types and one resource. One prey type is undefended, while the other one is pre‐ or post‐attack defended paying costs either by a higher half‐saturation constant for resource uptake or a lower maximum growth rate. We show that post‐attack defenses promote prey coexistence and stabilize the population dynamics more strongly than pre‐attack defenses by interfering with the predator's functional response: Because the predator spends time handling “noncrackable” prey, the undefended prey is indirectly facilitated. A high half‐saturation constant as defense costs promotes coexistence more and stabilizes the dynamics less than a low maximum growth rate. The former imposes high costs at low resource concentrations but allows for temporally high growth rates at predator‐induced resource peaks preventing the extinction of the defended prey. We evaluate the effects of the different defense mechanisms and costs on coexistence under different enrichment levels in order to vary the importance of bottom‐up and top‐down control of the prey community.     

Feedback between size balance and consumption strongly affects the consequences of hatching phenology in size‐dependent predator–prey interactions

In many size‐dependent predator–prey systems, hatching phenology strongly affects predator–prey interaction outcomes. Early‐hatched predators can easily consume prey when they first interact because they encounter smaller prey. However, this process by itself may be insufficient to explain all predator–prey interaction outcomes over the whole interaction period because the predator–prey size balance changes dynamically throughout their ontogeny. We hypothesized that hatching phenology influences predator–prey interactions via a feedback mechanism between the predator–prey size balance and prey consumption by predators. We experimentally tested this hypothesis in an amphibian predator–prey model system. Frog tadpoles Rana pirica were exposed to a predatory salamander larva Hynobius retardatus that had hatched 5, 12, 19 or 26 days after the frog tadpoles hatched. We investigated how the salamander hatch timing affected the dynamics of prey mortality, size changes of both predator and prey, and their subsequent life history (larval period and size at metamorphosis). The predator–prey size balance favoured earlier hatched salamanders, which just after hatching could successfully consume more frog tadpoles than later hatched salamanders. The early‐hatched salamanders grew rapidly and their accelerated growth enabled them to maintain the predator‐superior size balance; thus, they continued to exert strong predation pressure on the frog tadpoles in the subsequent period. Furthermore, frog tadpoles exposed to the early‐hatched salamanders were larger at metamorphosis and had a longer larval period than other frog tadpoles. These results suggest that feedback between the predator‐superior size balance and prey consumption is a critical mechanism that strongly affects the impacts of early hatching of predators in the short‐term population dynamics and life history of the prey. Because consumption of large nutrient‐rich prey items supports the growth of predators, a similar feedback mechanism may be common and have strong impacts on phenological shifts in size‐dependent trophic relationships.     

Predation, competition, and nutrient recycling: a stoichiometric approach with multiple nutrients

A model for two competing prey species and one predator is formulated in which three essential nutrients can limit growth of all populations. Prey take up dissolved nutrients and predators ingest prey, assimilating a portion of ingested nutrients and recycling or respiring the balance. For all species, the nutrient contents of individuals vary and growth is coupled to increasing content of the limiting nutrient. This model was parameterized to describe a flagellate preying on two bacterial species, with carbon (C), nitrogen (N), and phosphorus (P) as nutrients. Parameters were chosen so that the two prey species would stably coexist without predators under some nutrient supply conditions. Using numerical simulations, the long-term outcomes of competition and predation were explored for a gradient of N:P supply ratios, varying C supply, and varying preference of the predator for the two prey. Coexistence and competitive exclusion both occurred under some conditions of nutrient supply and predator preference. As in simpler models of competition and predation these outcomes were largely governed by apparent competition mediated by the predator, and resource competition for nutrients whose effective supply was partly governed by nutrient recycling also mediated by the predator. For relatively small regions of parameter space, more complex outcomes with multiple attractors or three-species limit cycles occurred. The multiple constraints posed by multiple nutrients held the amplitudes of these cycles in check, limiting the influence of complex dynamics on competitive outcomes for the parameter ranges explored.     

Consequences of symbiosis for food web dynamics

Basic Lotka-Volterra type models in which mutualism (a type of symbiosis where the two populations benefit both) is taken into account, may give unbounded solutions. We exclude such behaviour using explicit mass balances and study the consequences of symbiosis for the long-term dynamic behaviour of a three species system, two prey and one predator species in the chemostat. We compose a theoretical food web where a predator feeds on two prey species that have a symbiotic relationships. In addition to a species-specific resource, the two prey populations consume the products of the partner population as well. In turn, a common predator forages on these prey populations. The temporal change in the biomass and the nutrient densities in the reactor is described by ordinary differential equations (ODE). Since products are recycled, the dynamics of these abiotic materials must be taken into account as well, and they are described by odes in a similar way as the abiotic nutrients. We use numerical bifurcation analysis to assess the long-term dynamic behaviour for varying degrees of symbiosis. Attractors can be equilibria, limit cycles and chaotic attractors depending on the control parameters of the chemostat reactor. These control parameters that can be experimentally manipulated are the nutrient density of the inflow medium and the dilution rate. Bifurcation diagrams for the three species web with a facultative symbiotic association between the two prey populations, are similar to that of a bi-trophic food chain; nutrient enrichment leads to oscillatory behaviour. Predation combined with obligatory symbiotic prey-interactions has a stabilizing effect, that is, there is stable coexistence in a larger part of the parameter space than for a bi-trophic food chain. However, combined with a large growth rate of the predator, the food web can persist only in a relatively small region of the parameter space. Then, two zero-pair bifurcation points are the organizing centers. In each of these points, in addition to a tangent, transcritical and Hopf bifurcation a global heteroclinic bifurcation is emanating. This heteroclinic cycle connects two saddle equilibria where the predator is absent. Under parameter variation the period of the stable limit cycle goes to infinity and the cycle tends to the heteroclinic cycle. At this global bifurcation point this cycle breaks and the boundary of the basin of attraction disappears abruptly because the separatrix disappears together with the cycle. As a result, it becomes possible that a stable two-nutrient–two-prey population system becomes unstable by invasion of a predator and eventually the predator goes extinct together with the two prey populations, that is, the complete food web is destroyed. This is a form of over-exploitation by the predator population of the two symbiotic prey populations. When obligatory symbiotic prey-interactions are modelled with Liebigs minimum law, where growth is limited by the most limiting resource, more complicated types of bifurcations are found. This results from the fact that the Jacobian matrix changes discontinuously with respect to a varying parameter when another resource becomes most limiting.Revised version: 21 July 2003     

Examination of the effects of toxicity and nutrition on a two-prey one-predator system with a metabolomics-inspired model

Mercury (Hg) sequestration by phytoplankton results in intracellular concentrations that are multiple times greater than ambient water levels, and therefore the consumption of contaminated phytoplankton by herbivorous zooplankton, such as Daphnia, and their inefficient excretion of methylmercury (MeHg) can mediate the transfer to higher trophic levels. Employing a modified version of a metabolomics-inspired Daphnia ecophysiological model, the present study introduces two prey species to a simple Lotka-Volterra predator-prey system in order to shed light on the implications for the integrity of zooplankton assemblages, when experiencing multiple prey items of different toxicity and nutritional quality. We also examine the capacity of adaptive strategies of the predator (homeostatic rigidity, energetic investments to cope with toxicity) to shape predator-prey interactions. Our analysis suggests that the degree of nutritional quality of the prey items is a predominant driver of the predator-prey relationships, shifting from prey- to predator-dominated food webs with increasing nutritional quality. Increasing prey nutritional content leads to the emergence of oscillatory behaviour, which can be further modulated by the growth rates and degree of toxicity of different prey species. Severe exposure to contamination could lead to a decline of the predator biomass with faster growth rates of low nutritional quality prey, even though the increase of its MeHg somatic quota is only modest. In stark contrast, when a prey assemblage of superior nutritional quality prevails in an environment of elevated toxicity, faster prey growth rates are conducive to higher predator biomass levels, albeit its distinctly higher internal contaminant content. Owing to the heightened somatic growth dilution, the ingestion of carbon and nutritional metabolites is significantly higher relative to the MeHg intake rates, which leads to faster net growth of the predator and thus reinforces the benefits brought about by the nutritional value of their diet. Our results suggest that the homeostatic rigidity of the predator can assist in coping with toxic exposure. With a tighter range between the minimum and optimum somatic quotas, the predator population appears to be more resilient and its decline begins at higher levels of MeHg exposure. The predator-prey system displays a greater propensity for oscillatory behaviour, with their amplitude being driven by the interplay between the degree of saturation for nutritionally beneficial metabolites, and the energetic investments allotted to cope with toxicity and/or the excretion of excess metabolic by-products. We conclude by highlighting the prospect of our modelling work to guide new directions of research, to test a multitude of hypotheses pertaining to various ecophysiological facets of predator-prey systems, and extend its use to other contexts, such as the implications of toxin-producing algae for the predator physiology.     

Minimax strategies for a predator—Prey game

Suppose prey are distributed in patches. The predator knows the fraction of patches containing 0, 1, 2,… prey, but not how many prey a particular patch contains. It searches each patch randomly, at constant speed. It leaves a patch when the intercapture times satisfy a formula designed to maximize the number of prey eaten per unit time. We show that, if the prey distribution is Poisson, the predator should stay in each patch for the same time, regardless of what happens there. Accordingly, the prey can minimize the predator's maximum intake by choosing the Poisson distribution, and the predator can maximize its minimum intake (against a “smart” prey) by choosing the constant-time strategy.     

Chaotic dynamics of a food web in a chemostat

We analyze a mathematical model of a simple food web consisting of one predator and two prey populations in a chemostat. Monod's model is employed for the dependence of the specific growth rates of the two prey populations on the concentration of the rate-limiting substrate and a generalization of Monod's model for the dependence of the specific growth rate of the predator on the concentrations of the prey populations. We use numerical bifurcation techniques to determine the effect of the operating conditions of the chemostat on the dynamics of the system and construct its operating diagram. Chaotic behavior resulting from successive period doublings is observed. Multistability phenomena of coexistence of steady and periodic states at the same operating conditions are also found.     

Effects of prey quality and availability on the life history of a trap-building predator

Although generalist predators catch a great diversity of prey species, foraging theory has mostly been concerned with quantitative aspects and neglected questions about the nutrient quality of prey. Here, we test the hypothesis that the life history of a trap-building predator is affected by both prey availability and by the nutrient quality of prey. Under controlled laboratory conditions, orb-weaving spiders ( Zygiella x-notata ) were raised from hatchlings to maturity on prey of different nutrient quality and in different amounts. Both prey nutrient quality and availability had significant but different effects on many important life history traits, such as instar duration, number of instars used in the development, body weight at maturation and development time. Prey availability was especially important for growth rates whereas prey nutrient quality had the most severe effects on juvenile survivorship and female fecundity. Furthermore, while prey of low quality tended to reduce the number of instars used in the development, prey availability induced sex-specific responses in instar numbers. Thus, both prey nutrient quality and availability may be important factors shaping the evolution of life history traits in generalist predators.     

Cascading effects of belowground predators on plant communities are density‐dependent

Soil food webs comprise a multitude of trophic interactions that can affect the composition and productivity of plant communities. Belowground predators feeding on microbial grazers like Collembola could decelerate nutrient mineralization by reducing microbial turnover in the soil, which in turn could negatively influence plant growth. However, empirical evidences for the ecological significance of belowground predators on nutrient cycling and plant communities are scarce. Here, we manipulated predator density (Hypoaspis aculeifer: predatory mite) with equal densities of three Collembola species as a prey in four functionally dissimilar plant communities in experimental microcosms: grass monoculture (Poa pratensis), herb monoculture (Rumex acetosa), legume monoculture (Trifolium pratense), and all three species as a mixed plant community. Density manipulation of predators allowed us to test for density‐mediated effects of belowground predators on Collembola and lower trophic groups. We hypothesized that predator density will reduce Collembola population causing a decrease in nutrient mineralization and hence detrimentally affect plant growth. First, we found a density‐dependent population change in predators, that is, an increase in low‐density treatments, but a decrease in high‐density treatments. Second, prey suppression was lower at high predator density, which caused a shift in the soil microbial community by increasing the fungal: bacterial biomass ratio, and an increase of nitrification rates, particularly in legume monocultures. Despite the increase in nutrient mineralization, legume monocultures performed worse at high predator density. Further, individual grass shoot biomass decreased in monocultures, while it increased in mixed plant communities with increasing predator density, which coincided with elevated soil N uptake by grasses. As a consequence, high predator density significantly increased plant complementarity effects indicating a decrease in interspecific plant competition. These results highlight that belowground predators can relax interspecific plant competition by increasing nutrient mineralization through their density‐dependent cascading effects on detritivore and soil microbial communities.     

Prey size diversity hinders biomass trophic transfer and predator size diversity promotes it in planktonic communities

Body size exerts multiple effects on plankton food-web interactions. However, the influence of size structure on trophic transfer remains poorly quantified in the field. Here, we examine how the size diversity of prey (nano-microplankton) and predators (mesozooplankton) influence trophic transfer efficiency (using biomass ratio as a proxy) in natural marine ecosystems. Our results support previous studies on single trophic levels: transfer efficiency decreases with increasing prey size diversity and is enhanced with greater predator size diversity. We further show that communities with low nano-microplankton size diversity and high mesozooplankton size diversity tend to occur in warmer environments with low nutrient concentrations, thus promoting trophic transfer to higher trophic levels in those conditions. Moreover, we reveal an interactive effect of predator and prey size diversities: the positive effect of predator size diversity becomes influential when prey size diversity is high. Mechanistically, the negative effect of prey size diversity on trophic transfer may be explained by unicellular size-based metabolic constraints as well as trade-offs between growth and predation avoidance with size, whereas increasing predator size diversity may enhance diet niche partitioning and thus promote trophic transfer. These findings provide insights into size-based theories of ecosystem functioning, with implications for ecosystem predictive models.     

Mismatch between dietary requirements for lipid by a predator and availability of lipid in prey

Growth is an important factor in predicting an organism's overall success as an adult. Understanding how abiotic and biotic factors influence body size is key to predicting how environmental changes will impact organisms and predicting optimal behaviors under varying conditions. Food items can vary widely in nutrient content and this variation can affect growth. We tested how the quantity and macronutrient content of live prey affected the growth of juvenile jumping spiders, Phiddipus audax, using 420 spiderlings raised on one of 21 diets. In addition, we measured the nutrient content of prey from the field and compared average prey nutrient content with the diet at which spiders maximized growth. Our results show that the quantity and nutrient content of prey have significant and interacting effects on the growth of an actively hunting predator. In particular, spiders grew larger in body size (tibia/patella length and posterior lateral eye width) and were heavier on diets with higher lipid content. Yet, data on the nutrient content of prey from the field shows that most potential prey have high protein and low lipid content in their bodies. This apparent mismatch between spider nutritional requirements and prey nutrient availability likely presents a challenge to spiders seeking to maximize growth in the field. Several hypotheses for how these predators overcome this challenge to reach the large body sizes observed in the field are discussed.     

Growth,Grazing, and Starvation Survival in Three Heterotrophic Dinoflagellate Species

To assess the effects of fluctuating prey availability on predator population dynamics and grazing impact on phytoplankton, we measured growth and grazing rates of three heterotrophic dinoflagellate species—Oxyrrhis marina, Gyrodinium dominans and Gyrodinium spirale—before and after depriving them of phytoplankton prey. All three dinoflagellate species survived long periods (> 10 d) without algal prey, coincident with decreases in predator abundance and cell size. After 1–3 wks, starvation led to a 17–57% decrease in predator cell volume and some cells became deformed and transparent. When re‐exposed to phytoplankton prey, heterotrophs ingested prey within minutes and increased cell volumes by 4–17%. At an equivalent prey concentration, continuously fed predators had ~2‐fold higher specific growth rates (0.18 to 0.55 d^?1) than after starvation (?0.16 to 0.25 d^?1). Maximum specific predator growth rates would be achievable only after a time lag of at least 3 d. A delay in predator growth poststarvation delays predator‐induced phytoplankton mortality when prey re‐emerges at the onset of a bloom event or in patchy prey distributions. These altered predator‐prey population dynamics have implications for the formation of phytoplankton blooms, trophic transfer rates, and potential export of carbon.     

Prey-stage preferences and functional and numerical responses of Amblyseius largoensis (Acari: Phytoseiidae) to Raoiella indica (Acari: Tenuipalpidae)

Raoiella indica Hirst (Acari: Tenuipalpidae) is a phytophagous mite that recently invaded the Western Hemisphere. This mite is a multivoltine and gregarious species that can reach very high population densities and cause significant damage to various palm species (Arecaceae). The predatory mite Amblyseius largoensis (Muma) (Acari: Phytoseiidae) has been found associated with R. indica in Florida. This study evaluated A. largoensis for potential to control R. indica by (1) determining predator preferences among developmental stages of R. indica, and (2) estimating predator functional and numerical responses to varying densities of its most preferred prey-stage. Under no-choice conditions A. largoensis consumed significantly more eggs than other stages of R. indica. In choice tests A. largoensis showed a significant preference for R. indica eggs over all other prey stages. Amblyseius largoensis displayed a type II functional response showing an increase in number of prey killed with an increase in prey population density. Consumption of prey stabilized at approximately 45 eggs/day, the level at which oviposition by the predator was maximized (2.36?±?0.11 eggs/day; mean?±?SEM). Results of this study suggest that A. largoensis can play a role in controlling R. indica populations, particularly when prey densities are low.     

Decomposing Predation: Testing for Parameters that Correlate with Predatory Performance by a Social Bacterium

Predator–prey interactions presumably play major roles in shaping the composition and dynamics of microbial communities. However, little is understood about the population biology of such interactions or how predation-related parameters vary or correlate across prey environments. Myxococcus xanthus is a motile soil bacterium that feeds on a broad range of other soil microbes that vary greatly in the degree to which they support M. xanthus growth. In order to decompose predator–prey interactions at the population level, we quantified five predation-related parameters during M. xanthus growth on nine phylogenetically diverse bacterial prey species. The horizontal expansion rate of swarming predator colonies fueled by prey lawns served as our measure of overall predatory performance, as it incorporates both the searching (motility) and handling (killing and consumption of prey) components of predation. Four other parameters—predator population growth rate, maximum predator yield, maximum prey kill, and overall rate of prey death—were measured from homogeneously mixed predator–prey lawns from which predator populations were not allowed to expand horizontally by swarming motility. All prey species fueled predator population growth. For some prey, predator-specific prey death was detected contemporaneously with predator population growth, whereas killing of other prey species was detected only after cessation of predator growth. All four of the alternative parameters were found to correlate significantly with predator swarm expansion rate to varying degrees, suggesting causal interrelationships among these diverse predation measures. More broadly, our results highlight the importance of examining multiple parameters for thoroughly understanding the population biology of microbial predation.     

Effects of light and microcrustacean prey on growth and investment in carnivory in Utricularia vulgaris

SUMMARY 1. In a 5-week enclosure experiment, we studied the effects of light (ambient light, low light) and prey availability (no prey, prey added) on growth and investment in carnivory in Utricularia vulgaris .
2. Investment in carnivory, measured as the proportion of biomass allocated to bladders, was strongly affected by our manipulations of light intensity and prey density. In the treatment with high prey density the light reduction decreased the investment in bladders from 25% to zero. The effect of prey density on investment in bladders was negative. Because prey addition increased the concentration of nutrients, especially phosphorus, we propose that the effect of the prey treatment on investment reflected altered nutrient concentrations.
3. Availability of prey increased growth and apical biomass of Utricularia . As Utricularia had very few bladders in some treatments we suggest that the effect was due to a combination of live prey trapped and increased nutrient availability from dead prey.
4. Abundance of periphyton on Utricularia and on the enclosure walls was highest in the treatments with high prey density where nutrient concentrations were highest. Thus we interpret the response of periphyton as primarily reflecting nutrient availability.     

The Feeding Behaviour of a Sit-and-Wait Predator,Ranatra dispar (Heteroptera: Nepidae): The Combined Effect of Food Deprivation and Prey Size on the Behavioural Components of Prey Capture

Previous work has shown a significant effect of hunger on the predatory behaviour in a sit-and-wait predator Ranatra dispar, the water stick insect (Bailey 1986 a). The experiments reported here were designed to investigate the combined effect of prey size and hunger on the predatory behaviour in order to identify which behavioural components are effected. It was found that the hunger level determines whether R. dispar will initially be aroused or not but the distance at which the arousal takes place is influenced by the size of the prey. This is believed to reflect the capacity and interrelation between visual and mechanoreceptor, sensory organs. The decision to strike at a prey is, although again influenced by hunger, significantly affected by prey size. The distance of the prey when the strike takes place is affected by hunger not the size of the prey. The outcome of the strike is determined by the size of the prey, not the hunger level of the predator. This is believed to reflect the relationship between strike trajectory, leg morphology and prey size. Food deprivation affects all components of predatory behaviour of R. dispar leading up to prey capture, by increasing not only distance of response but also the number of strikes, hits, and captures per unit presentation of prey. It does not affect capture efficiency which remains at about 70 to 80 %. Food deprivation also increases the range of prey sizes that R. dispar responds to and attempts to capture. The effect of food deprivation is considered to reflect a motivational change in responsiveness to particular prey stimuli usually described as a sensitization of particular stimulus-response relations rather than the food deprivation affecting the sensory mechanisms. The predatory success in relation to size of model prey suggested a hypothetical size that could be captured, irrespective of predator motivational level, which is based primarily on the relationship between the shape of the grasping leg and size of prey.     

Effects of aluminium on growth and nutrient uptake of Betula pendula seedlings

The response to aluminium concentrations was evaluated for birch seedlings ( Betula pendula Roth, formerly Betula verrucosa Ehrh.) by using a growth technique that provides stable internal concentrations of nutrients in plants. Aluminium was added as aluminium nitrate and aluminium chloride and pH was kept at 3.8±0.2 by adding HCl or NaOH. The seedlings were grown in two different series of nutrient treatments, either with near-optimum conditions (relative addition rate 25% day⁻¹) or with constant nutrient stress (relative addition rate 10% day⁻¹) before the aluminium addition. Growth reduction occurred at aluminium concentrations greater than 3 m M , and lethal effects at aluminium concentrations greater than 15 m M . In plants subjected to near-optimum conditions before aluminium addition, the internal nutrient concentrations decreased with increasing aluminium concentration for all macronutrients. The concentration of the macronutrients N, K and P decreased gradually with increasing aluminium concentration, while the concentration of Ca and Mg decreased fairly abruptly when aluminium concentrations exceeded 1 m M . The same tendency was observed in nutrient stressed birch seedlings, but the pattern was more scattered. Relative growth rate of the seedlings was not affected by a low Ca/Al ratio. In all treatments, the molar Ca/Al ratio in/on the roots was below 0.2 at the end of the experiments. As decrease in growth occurs only at high aluminium concentrations, there is no reason to suggest that aluminium in acid soils is growth limiting for natural birch stands.     

A resolution of the paradox of enrichment

Theoretical studies have shown a paradoxical destabilizing response of predator-prey ecosystems to enrichment, but there is the gap between the intuitive view of nature and this theoretical prediction. We studied a minimal predator-prey system (a two predator-two prey system) in which the paradox of enrichment pattern can vanish; the destabilization with enrichment is reversed, leading to stabilization (a decrease in the amplitude of oscillation of population densities). For resolution of the paradox, two conditions must be met: (1) the same prey species must be preferred as a dietary item by both predator species, creating the potential for high exploitative competition between the predator species, and (2), while both predators are assumed to select their diet in accordance with optimal diet utilization theory, one predator must be a specialist and the other a generalist. In this system, the presence of a less profitable prey species can cause the increase in population oscillation amplitudes associated with increasing enrichment to be suppressed via the optimal diet utilization of the generalist predator. The resulting stabilization is explained by the mitigating effect of the less profitable prey showing better population growth with increasing enrichment on the destabilization underlying the specialist predator and prey relation, thus resolving the paradox of enrichment.