Phytoplankton Succession in Recurrently Fluctuating Environments

Coastal marine systems are affected by seasonal variations in biogeochemical and physical processes, sometimes leading to alternating periods of reproductive growth limitation within an annual cycle. Transitions between these periods can be sudden or gradual. Human activities, such as reservoir construction and interbasin water transfers, influence these processes and can affect the type of transition between resource loading conditions. How such human activities might influence phytoplankton succession is largely unknown. Here, we employ a multispecies, multi-nutrient model to explore how nutrient loading switching mode might affect phytoplankton succession. The model is based on the Monod-relationship, predicting an instantaneous reproductive growth rate from ambient inorganic nutrient concentrations whereas the limiting nutrient at any given time was determined by Liebig’s Law of the Minimum. When these relationships are combined with population loss factors, such as hydraulic displacement of cells associated with inflows, a characterization of a species’ niche can be achieved through application of the R* conceptual model, thus enabling an ecological interpretation of modeling results. We found that the mode of reversal in resource supply concentrations had a profound effect. When resource supply reversals were sudden, as expected in systems influenced by pulsed inflows or wind-driven mixing events, phytoplankton were characterized by alternating succession dynamics, a phenomenon documented in inland water bodies of temperate latitudes. When resource supply reversals were gradual, as expected in systems influenced by seasonally developing wet and dry seasons, or annually occurring periods of upwelling, phytoplankton dynamics were characterized by mirror-image succession patterns. This phenomenon has not been reported previously in plankton systems but has been observed in some terrestrial plant systems. These findings suggest that a transition from alternating to “mirror-image” succession patterns might arise with continued coastal zone development, with crucial implications for ecosystems dependent on time-sensitive processes, e.g., spawning events and migration patterns.     

Optimal Recombination Rate in Fluctuating Environments

The optimal recombination rate which maximizes the long-term geometric average of the population fitness is studied for a two-locus haploid model, assuming that the fitnesses of genotypes AB, Ab, aB and ab are 1 + s(t), 1 - s(t), 1 - s(t), and 1 + s(t), respectively, where s(t) follows various stationary stochastic processes with the average zero. With positive recombination, the polymorphism is stably maintained at both loci. After an initial transient phase, the dynamics are reduced to one dimension, and are analyzed for weak selection limit, strong selection limit, and selection with two state Markovian jump. Results are: (1) If the environmental fluctuation has a predominant periodic component, ropt is approximately inversely proportional to the period irrespective of selection intensity. (2) If the fluctuation is a superposition of many periodic components, the one with the longest period is the most effective in determining ropt because the genetic dynamics cannot track very quick fluctuations (low pass filter effect). (3) If the power spectrum density is decreasing with the frequency, as in pink, or 1/f noises, ropt is small when selection is weak, and increases with the selection intensity. Numerical calculation of the genetic dynamics of a recombination modifier supports all these predictions for the evolutionarily stable recombination rate.     

Changes in Individual Allometry Can Lead to Species Coexistence without Niche Separation

The principle of competitive exclusion is a fundamental tenet of ecology. Commonly used competition models predict that at most only one species per limiting resource can coexist in the same environment at steady state; hence, the upper limit to species diversity depends only on the number of limiting resources and not on the rates of resource supply. We demonstrate that such model behavior is the result of both the growth and biomass turnover functions being proportional to the population biomass. We argue that at least the growth function should be a nonlinear, concave downward function of biomass. This form for the growth function should arise simply because of changes in the allometry of individuals in the population. With this change in model structure, we show that any number of species can coexist at an asymptotically stable steady state, even where there is only one limiting resource. Furthermore, if growth increases nonlinearly with biomass, the steady-state resource concentration and hence the potential for biodiversity increases as the resource supply rate increases. Received 31 August 2001; accepted 10 April 2002.     

Nematode Reproduction in Environments of Fluctuating Aeration

Reproduction of Aphelenchus avenae, reared on Rhizoctonia solani growing on steamed wheat seeds and Caenorhabditis sp., reared on a mixed bacterial culture grown on oatmeal, was significantly reduced at 5% oxygen and inhibited at 4% oxygen and below. Aeration ranging from atmospheric air (21%) to 10% oxygen had no effect on reproduction. Close interval (5 days or less) fluctuations, between high and low oxygen concentrations, inhibited population buildup of Hemicycliophora arenaria on tomato in soil, and of A. avenae and Caenorhabditis sp. in vitro. In soil tests with H. arenaria exposed to 12 hr of nitrogen every three days (in air) inhibited the rate of buildup compared to controls maintained in continuous air. With the in vitro studies, as little as 4 hr nitrogen every 3 days (stored in air) significantly influenced the population numbers.     

Phytoplankton Assemblage Characteristics in Recurrently Fluctuating Environments

Annual variations in biogeochemical and physical processes can lead to nutrient variability and seasonal patterns in phytoplankton productivity and assemblage structure. In many coastal systems river inflow and water exchange with the ocean varies seasonally, and alternating periods can arise where the nutrient most limiting to phytoplankton growth switches. Transitions between these alternating periods can be sudden or gradual and this depends on human activities, such as reservoir construction and interbasin water transfers. How such activities might influence phytoplankton assemblages is largely unknown. Here, we employed a multispecies, multi-nutrient model to explore how nutrient loading switching mode might affect characteristics of phytoplankton assemblages. The model is based on the Monod-relationship, predicting an instantaneous growth rate from ambient inorganic nutrient concentrations whereas the limiting nutrient at any given time was determined by Liebig’s Law of the Minimum. Our simulated phytoplankton assemblages self-organized from species rich pools over a 15-year period, and only the surviving species were considered as assemblage members. Using the model, we explored the interactive effects of complementarity level in trait trade-offs within phytoplankton assemblages and the amount of noise in the resource supply concentrations. We found that the effect of shift from a sudden resource supply transition to a gradual one, as observed in systems impacted by watershed development, was dependent on the level of complementarity. In the extremes, phytoplankton species richness and relative overyielding increased when complementarity was lowest, and phytoplankton biomass increased greatly when complementarity was highest. For low-complementarity simulations, the persistence of poorer-performing phytoplankton species of intermediate R*s led to higher richness and relative overyielding. For high-complementarity simulations, the formation of phytoplankton species clusters and niche compression enabled higher biomass accumulation. Our findings suggest that an understanding of factors influencing the emergence of life history traits important to complementarity is necessary to predict the impact of watershed development on phytoplankton productivity and assemblage structure.     

Linking Dispersal and Immigration in Multidimensional Environments

Many problems in ecology require the estimation of rates of dispersal of individuals or propagules across physical boundaries. Such problems arise in invasion ecology, forest dynamics, and the neutral theory of biodiversity. In a forest plot, for example, one might ask what proportion of the seed rain originates from outside the plot. A recent study presented analytical approximations that relate the rate of immigration across a boundary to plot geometry and to the parameters of a dispersal kernel in one- and two-dimensional environments. In this study, we provide a more rigorous derivation of these expressions and we derive a more general expression that applies in environments of arbitrary dimension. We discuss potential applications of the one-, two-, and three-dimensional results to ecological problems.     

Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as, for instance, the fluctuations in ribosome copy numbers for a gene regulatory network. While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze. In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment''s effect onto the network into a new model. More technically, we show how such fluctuating extrinsic components (e.g., chemical species) can be marginalized in order to obtain this decoupled model. We derive its corresponding process- and master equations and show how stochastic simulations can be performed. Using several case studies, we demonstrate the significance of the approach.     

Establishment Probability in Fluctuating Environments: A Branching Process Model

We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.     

Evolution under Fluctuating Environments Explains Observed Robustness in Metabolic Networks

A high level of robustness against gene deletion is observed in many organisms. However, it is still not clear which biochemical features underline this robustness and how these are acquired during evolution. One hypothesis, specific to metabolic networks, is that robustness emerges as a byproduct of selection for biomass production in different environments. To test this hypothesis we performed evolutionary simulations of metabolic networks under stable and fluctuating environments. We find that networks evolved under the latter scenario can better tolerate single gene deletion in specific environments. Such robustness is underlined by an increased number of independent fluxes and multifunctional enzymes in the evolved networks. Observed robustness in networks evolved under fluctuating environments was “apparent,” in the sense that it decreased significantly as we tested effects of gene deletions under all environments experienced during evolution. Furthermore, when we continued evolution of these networks under a stable environment, we found that any robustness they had acquired was completely lost. These findings provide evidence that evolution under fluctuating environments can account for the observed robustness in metabolic networks. Further, they suggest that organisms living under stable environments should display lower robustness in their metabolic networks, and that robustness should decrease upon switching to more stable environments.     

The Evolution of Canalization and Evolvability in Stable and Fluctuating Environments

Using a multilinear model of epistasis we explore the evolution of canalization (reduced mutational effects) and evolvability (levels of additive genetic variance) under different forms of stabilizing and fluctuating selection. We show that the total selection acting on an allele can be divided into a component deriving from adaptation of the trait mean, a component of canalizing selection favoring alleles that epistatically reduce the effects of other allele substitutions, and a component of conservative selection disfavoring rare alleles. While canalizing selection operates in both stable and fluctuating environments, it may not typically maximize canalization, because it gets less efficient with increasing canalization, and reaches a balance with drift, mutation and indirect selection. Fluctuating selection leads to less canalized equilibria than stabilizing selection of comparable strength, because canalization then becomes influenced by erratic correlated responses to shifting trait adaptation. We conclude that epistatic systems under bounded fluctuating selection will become less canalized than under stabilizing selection and may support moderately increased evolvability if the amplitude of fluctuations is large, but canalization is still stronger and evolvability lower than expected under neutral evolution or under patterns of selection that shift the trait in directions of positive (reinforcing) epistasis.     

Energetic Constraints on Species Coexistence in Birds

The association between species richness and ecosystem energy availability is one of the major geographic trends in biodiversity. It is often explained in terms of energetic constraints, such that coexistence among competing species is limited in low productivity environments. However, it has proven challenging to reject alternative views, including the null hypothesis that species richness has simply had more time to accumulate in productive regions, and thus the role of energetic constraints in limiting coexistence remains largely unknown. We use the phylogenetic relationships and geographic ranges of sister species (pairs of lineages who are each other’s closest extant relatives) to examine the association between energy availability and coexistence across an entire vertebrate class (Aves). We show that the incidence of coexistence among sister species increases with overall species richness and is elevated in more productive ecosystems, even when accounting for differences in the evolutionary time available for coexistence to occur. Our results indicate that energy availability promotes species coexistence in closely related lineages, providing a key step toward a more mechanistic understanding of the productivity–richness relationship underlying global gradients in biodiversity.     

Species Coexistence and Periodicity in Host-Host-Pathogen Models

Models for the transmission of an infectious disease in one and two host populations with and without self-regulation are analyzed. Many unusual behaviors such as multiple positive equilibria and periodic solutions occur in previous models that use the mass-action (density-dependent) incidence. In contrast, the models formulated using the frequency-dependent (standard) incidence have the behavior of a classic endemic model, since below the threshold, the disease dies out, and above the threshold, the disease persists and the infectious fractions approach an endemic equilibrium. The results given here reinforce previous examples in which there are major differences in behavior between models using mass-action and frequency-dependent incidences.     

Evolutionary Consequences of Dispersal Ability in Cactus-feeding Insects

Although gene flow is an important determinant of evolutionary change, the role of ecological factors such as specialization in determining migration and gene flow has rarely been explored empirically. To examine the consequences of dispersal ability and habitat patchiness on gene flow, migration rates were compared in three cactophagous longhorn beetles using coalescent analyses of mtDNA sequences. Analyses of covariance were used to identify the roles of dispersal ability and habitat distribution in determining migration patterns. Dispersal ability was a highly significant predictor of gene flow (p< 0.001), and was more important than any other factor. These findings predict that dispersal ability may be an import factor shaping both microevolutionary and macroevolutionary patterns; this prediction is borne out by comparisons of species diversity in cactus-feeding groups.     

How Microbes Can Achieve Balanced Growth in a Fluctuating Environment

A microbial colony needs several essential nutrients in order to grow. Moreover, the colony requires these nutrients in fixed combinations, which are dictated by the chemical composition of its biomass. Unfortunately, ambient availabilities of the various nutrients vary all the time. This poses the question of how microbes can achieve balanced growth.The present solution to this problem is novel in that the allocation of molecular building blocks among assimilatory machineries within the cell is regarded as dynamic. This paper shows that allocation can be adapted so as to achieve balanced growth, nearly regardless of environmental conditions. Moreover, it is shown that a feedback mechanism, which monitors internal stores, is able to achieve this allocation.     

Crown Architecture and Species Coexistence in Plant Communities

The relationships between crown architecture and species coexistencewere studied using the diffusion model and the canopy photosynthesismodel for multi-species plant communities. The present paperdeals with two species having different crown shapes [conic-canopyplant (CCP) and spheroidal-canopy plant (SCP)], for variousinitial mean sizes at the establishment stage and physiologicalparameter values (photosynthetic rate, etc.). Recruitment processeswere not incorporated into the model, and thus simulations weremade for the effects on the pattern of species coexistence ofeither sapling competition starting from different sapling banksor competition in single-cohort stands with little continualestablishment of species until a stand-replacement disturbance.The following predictions were derived: (1) SCPs can establishlater/slowly in the lower canopy layer even if they are overtoppedby a CCP which established first/rapidly; (2) if SCPs establishedfirst/rapidly and occupy the upper canopy layer, a CCP can rarelyestablish later/slowly in the lower canopy layer; (3) smallest-sizedCCPs can persist well in the lowermost canopy layer overtoppedby a SCP, suggesting a waiting strategy of CCP's saplings inthe understorey of a crowded stand; (4) even if CCPs establishedfirst/rapidly and occupy the upper canopy layer, an SCP canestablish later/slowly in the lower canopy layer. Therefore,the species diversity of SCPs which established first/rapidlyand occupy the upper canopy layer limits the number of CCP specieswhich can establish later/slowly. In contrast, the species diversityof CCPs which established first/rapidly and occupy the uppercanopy layer does not affect the number of SCP species whichcan establish later/slowly. The combination of initial sizesof a CCP and an SCP at the establishment stage (i.e. establishmenttiming) affects the segregation of vertical positions in thecanopy between the two species with different crown shape, andnot only species-specific physiological traits but also crownarchitecture greatly affects the coexistence pattern betweenspecies with different crown architectures. The theoreticalpredictions obtained here can explain coexistence patterns foundin single-cohort conifer-hardwood boreal and sub-boreal forests,pointing to the significance of crown architecture for speciescoexistence. Diffusion equation model; canopy photosynthesis model; conifer-hardwood boreal/sub-boreal forest; sapling establishment; vertical foliage profile     

Competition of Multiple Species in Advective Environments

We study the effect of changes in flow speed on competition of an arbitrary number of species living in advective environments, such as streams and rivers. We begin with a spatial Lotka–Volterra model which is described by n reaction–diffusion–advection equations with Danckwerts boundary conditions. Using the dominant eigenvalue \(\lambda \le 0\) of the diffusion–advection operator subject to boundary conditions, we reduce the model to a system of ordinary differential equations. We impose a “transitive arrangement” of the competitors in terms of their interspecific coefficients and growth rates, which means that in the absence of advection, we have the following situation: for all \(1\le i<j\le n\), species i out-competes species j, while species j has higher intrinsic growth rate than species i. Changing advection speed in the original spatial model corresponds to changing the value of \(\lambda \) in the spatially implicit model. Considering the cases of the odd and even n separately, we obtain explicit intervals of the values of \(\lambda \) that allow all n species to be present in the habitat (coexistence interval). Stability of this equilibrium is shown for \(n\le 4\).     

Identifying Environmental Conditions to Promote Species Coexistence: An Example with the Native Barrens Topminnow and Invasive Western Mosquitofish

Coexistence of a native and invasive species may be possible at certain conditions along an environmental gradient where the individual responses of each species are maximally apart. Water temperature may differentially affect the growth of a native cool-water species like the Barrens topminnow, Fundulus julisia, and an originally warm-water adapted western mosquitofish, Gambusia affinis, who is a recent invader in Barrens Plateau region of middle Tennessee. We measured the specific growth rate (SGR) of the two species separately in laboratory aquaria at 10, 15, 20 and 25 °C, representing a range of temperatures that occur in topminnow habitats throughout the year. Both species grew faster with increasing temperature and SGRs were highest at 25 °C. The interspecific difference in SGR was maximized at 15 °C. At this temperature, mean growth rate of topminnows was 0.78% per day, more than twice that of mosquitofish (0.38% per day). These results suggest that cool springhead habitats with a near-constant thermal environment of 15 °C throughout the year may provide a growth advantage to the Barrens topminnow over the mosquitofish. Other environmental, density-dependent, or behavioral factors not examined here may act along with temperature to mediate the coexistence of the topminnow and mosquitofish.