Dispersal delays, predator-prey stability, and the paradox of enrichment

It takes time for individuals to move from place to place. This travel time can be incorporated into metapopulation models via a delay in the interpatch migration term. Such a term has been shown to stabilize the positive equilibrium of the classical Lotka-Volterra predator-prey system with one species (either the predator or the prey) dispersing. We study a more realistic, Rosenzweig-MacArthur, model that includes a carrying capacity for the prey, and saturating functional response for the predator. We show that dispersal delays can stabilize the predator-prey equilibrium point despite the presence of a Type II functional response that is known to be destabilizing. We also show that dispersal delays reduce the amplitude of oscillations when the equilibrium is unstable, and therefore may help resolve the paradox of enrichment.     

Imperfect optimal foraging and the paradox of enrichment

We show that the paradox of enrichment can be theoretically resolved in a flexible predator–prey system in which the predator practices imperfect optimal foraging. A previous study showed that perfect optimal foraging can mitigate increases in the amplitude of population oscillations associated with enrichment, but it did not show a stabilization pattern. Our results show that imperfect optimal foraging can stabilize the system and resolve the paradox of enrichment under nonequilibrium dynamics. Furthermore, the degree of stabilization with enrichment was stronger when the imperfection of optimal foraging was larger.     

Implications of resting eggs of zooplankton for the paradox of enrichment

In this study, we numerically investigated to what extent introducing resting-egg dynamics would stabilize simple Daphnia–algae consumer–resource models. In the models, the density of viable resting eggs was explicitly expressed, and we assumed that zooplankton produced resting eggs seasonally or in response to food deficiency and that resting eggs hatched seasonally. The models predicted that, although the paradox of enrichment was not completely resolved (i.e., the system was destabilized by eutrophication), we found the following conditions under which the stabilizing effects of resting eggs would be significantly large: (1) resting eggs are produced seasonally (rather than in response to food deficiency), (2) the annual average allocation ratio to resting eggs is large, and (3) the annual average hatching rate of resting eggs is low. The results suggest that resting-egg dynamics can significantly reduce the paradox of enrichment within the biologically meaningful parameter space and contribute to the stability of plankton community dynamics.     

The effects of haloclines on the vertical distribution and migration of zooplankton

While the influence of horizontal salinity gradients on the distribution and abundance of planktonic organisms in estuaries is relatively well known, the effects of vertical salinity gradients (haloclines) are less well understood. Because biological, chemical, and physical conditions can vary between different salinity strata, an understanding of the behavioral response of zooplankton to haloclines is crucial to understanding the population biology and ecology of these organisms. We studied four San Francisco Bay copepods, Acartia (Acartiura) spp., Acartia (Acanthacartia) spp., Oithona davisae, and Tortanus dextrilobatus, and one species of larval fish (Clupea pallasi), in an attempt to understand how and why zooplankton respond to haloclines. Controlled laboratory experiments involved placing several individuals of each species in two 2-m-high tanks, one containing a halocline (magnitude varied between 1.4 and 10.0 psu) and the other without a halocline, and recording the location of each organism once every hour for 2-4 days using an automated video microscopy system. Results indicated that most zooplankton changed their vertical distribution and/or migration in response to haloclines. For the smaller taxa (Acartiura spp., Acanthacartia spp., and O. davisae), this behavior took the form of accumulating in or below the halocline, while the effects on the larger species (C. pallasi and T. dextrilobatus) were more subtle. C. pallasi yolk sac and 3- to 6-day-old larvae seemed to pause or remain in the halocline during their diel migration, while 14- to 17-day-old larvae appeared to avoid the halocline by remaining in deeper, more saline water. There were very few statistically significant effects of haloclines on the vertical distribution of T. dextrilobatus. Subsequent mortality experiments with Acartiura spp., Acanthacartia spp. and T. dextrilobatus indicated that the behavioral changes seen in the halocline studies were not associated with any salinity-induced mortality per se, although more subtle affects of physiological stress could not be ruled out. These results point to a high degree of flexibility in vertical migration behavior within a given species as well as large variation between species. Such behavioral flexibility is likely to be very important in allowing planktonic organisms generally, and estuarine organisms in particular, to maintain or alter position relative to currents, food, and predators.     

The stability of ecosystems: A brief overview of the paradox of enrichment

In theory, enrichment of resource in a predator-prey model leads to destabilization of the system,thereby collapsing the trophic interaction,a phenomenon referred to as "the paradox of enrichment". After it was first pro posed by Rosenzweig (1971), a number of subsequent studies were carried out on this dilemma over many decades. In this article, we review these theoretical and experimental works and give a brief overview of the proposed solutions to the paradox. The mechanisms that have been discussed are modifications of simple predator -prey models in the presence of prey that is inedible, invulnerable, unpalatable and toxic. Another class of mechanisms includes an incorporation of a ratio-dependent functional form,inducible defence of prey and density-dependent mortality of the predator. Moreover, we find a third set of explanations based on complex population dynamics including chaos in space and time. We conclude that,although any one of the various mechanisms proposed so far might potentially prevent destabilization of the predator-prey dynamics following enrichment, in nature different mechanisms may combine to cause stability, even when a system is enriched. The exact mechanisms,which may differ among systems,need to be disentangled through extensive field studies and laboratory experiments coupled with realistic theoretical models.     

Diel vertical migrations of zooplankton in a shallow, fishless pond: a possible avoidance-response cascade induced by notonectids

1. Day (noon) and night (midnight) vertical distributions of zooplankton and phytoplankton in the water column (1.5 m) of a Vermont pond were determined on two consecutive days from 470 mL water samples taken at three depths (0.1, 0.5 and 1.0 m) at three sites. There was little variation across depths in temperature, dissolved oxygen concentration and phytoplankton. All individuals of each zooplankton species (a small copepod, Tropocyclops extensus and six rotifers) were counted. 2. A three-way ANOVA on the zooplankton data showed no effect of date or time of day on the abundance of any species. Significant diel shifts in vertical distribution (depth × time-of-day interactions) were found for T. extensus (nauplii, as well as copepodites and adults) and Polyarthra remata, but not for Hexarthra mira, Keratella cochlearis, Anuraeopsis fissa, Ascomorpha ovalis and Plationus patulus. Tropocyclops extensus showed a pronounced, typical diel vertical migration, avoiding the surface and occurring most abundantly near the bottom during the day. Polyarthra remata showed an equally pronounced, reverse diel vertical migration, avoiding the bottom and being most abundant near the surface during the day. 3. The diurnal descent of Tropocyclops is interpreted as an avoidance response to Buenoa macrotibialis, a notonectid which feeds on this copepod at the surface during the day but not at night. The diurnal ascent of Polyarthra is thought to be an avoidance response to Tropocyclops, which strongly suppresses this rotifer in field enclosures and laboratory vessels. Thus, these out-of-phase migrations may be coupled and represent a behavioural cascade initiated by Buenoa. 4. At night, Tropocyclops and Polyarthra both were uniformly distributed across depths. This is believed to reflect the absence of appreciable depth-related variation in temperature, algal food resources (biovolume of cryptomonads and chrysophyte flagellates) and predation risk at this time. 5. The five rotifer species that did not exhibit diel vertical migrations may be less susceptible to Tropocyclops predation than Polyarthra.     

富食悖论研究进展

Michael Rosenzweig于1971年首次提出＂富食悖论＂这一概念：在简单的被捕食者-捕食者系统中,随着营养物质供应的增加,系统变得不再稳定,并产生大振幅波动,最终导致系统内的物种灭亡。然而,许多实验结果并不支持Rosenzweig的理论。综述＂富食悖论＂的定义、理论和实验研究,同时综述各种解释实际与理论之间矛盾的机制,最后探讨＂富食悖论＂的研究前景。     

Interplay between the paradox of enrichment and nutrient cycling in food webs

Nutrient cycling is fundamental to ecosystem functioning. Despite recent major advances in the understanding of complex food web dynamics, food web models have so far generally ignored nutrient cycling. However, nutrient cycling is expected to strongly impact food web stability and functioning. To make up for this gap, we built an allometric and size structured food web model including nutrient cycling. By releasing mineral nutrients, recycling increases the availability of limiting resources for primary producers and links each trophic level to the bottom of food webs. We found that nutrient cycling can provide a significant part of the total nutrient supply of the food web, leading to a strong enrichment effect that promotes species persistence in nutrient poor ecosystems but leads to a paradox of enrichment at high nutrient inputs. The presence of recycling loops linking each trophic level to the basal resources weakly affects species biomass temporal variability in the food web. Recycling loops tend to slightly dampen the destabilising effect of nutrient enrichment on consumer temporal variability while they have opposite effects for primary producers. By considering nutrient cycling, this new model improves our understanding of the response of food webs to nutrient availability and opens perspectives to better link studies on food web dynamics and ecosystem functioning.     

Towards a correct description of zooplankton feeding in models: Taking into account food-mediated unsynchronized vertical migration

Complex nature of foraging behaviour of zooplankton makes it difficult to describe adequately zooplankton grazing in models with vertical space. In mean-field models (based on systems of PDEs or coupled ODEs), zooplankton feeding at a given depth is normally computed as the product of the local functional response and the zooplankton density at this depth. Such simplification is often at odds with field observations which show the absence of clear relationship between intake rates of organisms and the ambient food density. The observed discrepancy is generic and is often caused by fast non-synchronous vertical migration of organisms with different nutrition status. In this paper, we suggest a simple way of incorporating unsynchronized short-term vertical migration of zooplankton into the mean-field modelling framework. We compute grazing of zooplankton in each layer depending on feeding activity of organisms in the layer. We take into account grazing impact of animals which are in the active phase of foraging cycle at the given moment of time but neglect the impact of animals which are in the non-active phase of the cycle (e.g. digesting food). Unsynchronized vertical migration determines the vertical distribution of actively feeding animals in layers depending on vertical distribution of food. In this paper, we compare two generic plankton models: (i) a model based on ‘classical’ grazing approach and (ii) a model incorporating food-mediated unsynchronized vertical migration of zooplankton. We show that including unsynchronized food-mediated migration would make the behaviour of a plankton model more realistic. This would imply a significant enhancement of ecosystem's stability and some additional mechanisms of regulation of algal blooms. In the system with food-mediated unsynchronized vertical migration, the control of phytoplankton by herbivorous becomes possible even for very large concentrations of nutrients in the water (formally, when the system's carrying capacity tends to infinity).     

Statistical quantification of the effect of thermal stratification on patterns of dispersion in a freshwater zooplankton community

The vertical distribution of crustacean zooplankton species was examined during 2000 in Windermere, Cumbria. Patterns of dispersion were evaluated quantitatively using two different approaches. Firstly, Morisita’s index was used to test whether patterns of dispersion differed significantly from a state of randomness and, secondly, the relative distribution of zooplankton individuals between the epilimnion and hypolimnion was investigated, for a series of standardised vertical profiles of organism density. All six of the dominant species of planktonic crustaceans showed aggregated patterns of dispersion throughout the year. For most species, patterns of dispersion were affected by the onset and breakdown of thermal stratification in the lake. The degree of aggregation in the vertical plane, measured using Morisita’s index, increased when the lake became thermally stratified. Furthermore, for most species, there was a positive association between the degree of vertical differentiation in abundance across the thermocline, and the degree of temperature differentiation in the stratified water column. The results of the present analysis provide quantitative evidence for the phenomenon known as ‘zooplankton stratification’ and for temporal variation in patterns of zooplankton dispersion.     

An <Emphasis Type="Italic">in situ</Emphasis> method for the investigation of vertical distributions of zooplankton in lakes: test of a two-compartment enclosure

Two-section enclosures were designed for the investigation of the effect of various physicochemical and biological factors on vertical distribution of zooplankton in situ. The framework of the enclosure was a cylindrical polyethylene column without any partitions inside, in which the isolation of animals in different sections after in situ exposure was achieved by pinching the flexible central part of the column. Enclosures were tested at the brackish stratified meromictic Lake Shira (Russia, Khakasia). The absence of fish and carnivorous zooplankton in the lake suggests that the vertical distribution of zooplankton is mainly determined by physicochemical gradients in the water column. Experiments and field observations demonstrated that all age and size groups of Arctodiaptomus salinus and Brachionus plicatilis strongly avoided surface layers during the daylight. The escape of zooplankton from the anoxic hypolimnion was less active. Statistically significant avoidance was observed only for copepodites C4–C5 and females of A. salinus. The relatively simple construction of the columns and easy handling during the experiment were the factors that favoured the use of this device to perform in situ basic tests of the effect of different factors on the vertical distribution of zooplankton.     

Towards a solution of the plankton paradox: the importance of physiology and life history

Phytoplankton communities reveal an astonishing biodiversity, whereas classical competition theory seems to suggest that only a few competing species can survive. Recently we suggested a new solution to this plankton paradox. In theory, at least, competition between multiple species can generate complex dynamics that can support a large number of species. How likely is it then, in reality, that competitive chaos indeed promotes biodiversity? To obtain some insight, we simulated multispecies competition according to five different physiological scenarios. For random species parameters, biodiversity was generally low. Assuming plausible physiological trade‐offs, the simulations revealed switches back and forth between equilibrium and nonequilibrium dynamics, and a higher biodiversity. An extremely high biodiversity, with sometimes more than 100 species on three resources, was observed in simulations that assumed a cyclic relation between competitive abilities and resource contents. We conclude that physiological and life‐history patterns have a major impact on the likelihood of nonequilibrium dynamics and on the biodiversity of plankton communities.     

On the stability of equilibria in metabolic feedback systems

A sufficient criterion for the stability of the equilibrium of a metabolic feedback system will be constructed.     

Discounting the freedom to choose: implications for the paradox of choice

Organisms prefer to make their own choices. However, emerging research from behavioral decision making sciences has demonstrated that there are boundaries to the preference for choice. Specifically, many decision makers find an extensive array of choice options to be aversive, often leading to negative emotional states and poor behavioral outcomes. This study examined the degree to which human participants discounted hypothetical rewards that were (a) delayed, (b) probabilistic, and (c) chosen from a large array of options. The present results suggest that the "paradox of choice" effect may be explained within a discounting model for individual patterns of decision making.     

哺乳动物基因组靶向修饰阳性细胞富集的报告载体系统研究进展

基因组靶向修饰技术对基因功能研究、基因治疗以及转基因育种研究都具有重要的意义和价值。近年来发展起来的人工核酸酶如ZFNs、TALENs和CRISPR/Cas9等的应用大大提高了基因组靶向修饰的效率。但是由于核酸酶表达载体转染效率、核酸酶表达效率及活性以及基因组被打靶后的修复效率等因素在一定程度上制约着基因组靶向修饰阳性细胞的获得。因此富集和筛选基因组靶向修饰阳性细胞是一个亟待解决的问题。报告载体系统可以间接地反映核酸酶的工作效率并有效富集核酸酶修饰的阳性细胞,进而提高基因组靶向修饰阳性细胞的富集和筛选效率。本文主要针对由非同源末端连接(Non-homologous end joining,NHEJ)和单链退火(Single-strand annealing,SSA)两种修复机制分别介导的报告载体系统的原理和应用进行了详细的介绍,以期为以后的相关研究提供借鉴和参考。     

Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson–Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date — repeatedly described as more evolutionarily stable than expected — so this skewness should be accounted for when investigating evolutionary dynamics in the wild.     

Damaging UV radiation and invertebrate predation: conflicting selective pressures for zooplankton vertical distribution in the water column of low DOC lakes

In nature most organisms have to manage conflicting demands of food gathering, predator avoidance, and finding a favorable abiotic environment (oxygen, temperature, etc.) in order to maximize their fitness. In the vertical water column of lakes with high solar ultraviolet radiation (UV) and invertebrate predators, zooplankton face two particularly strong and conflicting selective pressures. During daylight hours invertebrate predators often induce an upward vertical migration of zooplankton prey while potentially damaging UV forces a downward migration. We used 2.2 m long columns suspended vertically in a lake to conduct 2×2 factorial experiments to examine patterns of depth selection behavior by zooplankton in the presence and absence of both the invertebrate predator Chaoborus and UV. We hypothesized that Chaoborus and UV both affect the distribution of zooplankton and a combination of both factors would lead to a narrowing of depth distribution. We found that when Chaoborus were present zooplankton tended to be distributed at shallower depths in the columns, while in the presence of UV they exhibited a deeper distribution. Chaoborus themselves were always found near the bottom of the columns regardless of the UV treatment. Simultaneous exposure to predators and UV resulted in a peak of zooplankton (especially Daphnia catawba) distribution at intermediate depths. In a significant number of cases, depth range was narrowed in response to Chaoborus, UV, or both.     

冬小麦根系各种参数垂直分布实验研究

本文根据田间实测资料研究了冬小麦根系各种参数(长度、重量、活性表面和根径)的垂直分布。结果表明,在所观测地区的土壤条件下,冬小麦根系的长度、重量、表面积和体积随深度呈指数分布,而累积根系的长度、重量和表面积随深度呈双曲线型分布。根据作者的观测资料和国内外其它观测资料分析研究表明,对于不同土壤,根区各层土壤中累计根重及根长的百分比随相对深度的变化都符合下列双曲线函数形式:这一研究结果可为根系生态研究和作物对水分吸收的模拟工作提供参考。     

Attenuation of the vertical flux of copepod fecal pellets under Arctic sea ice: evidence for an active detrital food web in winter

A variable fraction of fecal pellets produced in the epipelagic layer is intercepted and retained before reaching the bottom. We assessed fecal pellet retention in the ice-covered Beaufort Sea in early February by comparing the shape and size-frequency distribution of pellets collected by a sediment trap moored at 210 m to that produced in vitro. Appendicularian ellipsoidal and copepod cylindrical pellets made up 75 and 24% of the flux (165 μg C m⁻² day⁻¹). In contrast, production (135 μg C m⁻² day⁻¹) was dominated by cylindrical pellets (93%). The vertical flux of cylindrical pellets at 210 m was attenuated by 70%. Pellets >120 μm in width, represented 42% of the production, but were not detected in the trap. Retention most likely resulted from coprorhexic feeding by copepods such as Metridia longa. Our observations suggest that the detritivore food web prevailing under the ice of the Arctic Ocean in winter is dominated by appendicularians feeding on pellets fragmented by copepods.     

Effects of omnivorous filter‐feeding fish and nutrient enrichment on the plankton community and water transparency of a tropical reservoir

1. The major aim of this study was to test the hypothesis that nutrient enrichment and the introduction of the Nile tilapia (Oreochromis niloticus), an exotic omnivorous filter‐feeding fish, operate interdependently to regulate plankton communities and water transparency of a tropical reservoir in the semi‐arid northeastern Brazil. 2. A field experiment was performed for 5 weeks in 20 enclosures (9.8 m³) to which four treatments were randomly allocated: tilapia addition (F), nutrient addition (N), tilapia and nutrient addition (F + N) and a control treatment with no tilapia or nutrient addition (C). A two‐way repeated measures anova was undertaken to test for time, tilapia and nutrient effects and their interactions on water transparency, total phosphorus and total nitrogen concentrations, phytoplankton biovolume and zooplankton biomass. 3. Nutrient addition had no effect except on rotifer biomass, but there were significant fish effects on the biomass of total zooplankton, copepod nauplii, rotifers, cladocerans and calanoid copepods and on the biovolume of total phytoplankton, large algae (GALD ≥ 50 μm), Bacillariophyta and Zygnemaphyceae and on Secchi depth. In addition, we found significant interaction effects between tilapia and nutrients on Secchi depth and rotifers. Overall, tilapia decreased the biomass of most zooplankton taxa and large algae (diatoms) and decreased water transparency, while nutrient enrichment increased the biomass of rotifers, but only in the absence of tilapia. 4. In conclusion, the influence of fish on the reservoir plankton community and water transparency was significant and even greater than that of nutrient loading. This suggests that biomanipulation of filter‐feeding tilapias may be of importance for water quality management of eutrophic reservoirs in tropical semi‐arid regions.