Fluctuating Environments and Phytoplankton Community Structure: A Stochastic Model

Spatial heterogeneity in organism and resource distributions can generate temporal heterogeneity in resource access for simple organisms like phytoplankton. The role of temporal heterogeneity as a structuring force for simple communities is investigated via models of phytoplankton with contrasting life histories competing for a single fluctuating resource. A stochastic model in which environmental and demographic stochasticity are treated separately is compared with a model with deterministic resource variation to assess the importance of stochasticity. When compared with the deterministic model, the stochastic model allows for coexistence over a wider range of parameter values (or life-history types). The model suggests that demographic stochasticity alone is far more important in increasing the possibility of coexistence than environmental stochasticity alone. However, the combined effects of both types of stochasticity produce the largest likelihood of coexistence. Finally, the influence of relative nutrient levels and nutrient pulse frequency on these results is addressed. We relate our findings to variable environment theory with evidence for both relative nonlinearity and the storage effect acting in this model. We show for the first time that temporal dynamics generated by demographic stochasticity may operate like the storage effect at particular spatial scales.     

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.     

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.     

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.     

Probability of Mitochondrial Lineage Extinction in Female Offspring,Modern and Paleolithic: Branching Process Analysis

We evaluate the probability of extinction of the female offspring of two populations of women: the one Paleolithic, the other that of Italy today. In both cases it is assumed that possible extinction arises exclusively on account of limitations in the degree of fertility and/or an imbalance in the sex-ratio of the population. The value is obtained as the probability that a Branching Process describing the evolution of the offspring by a progenitor degenerates to a “Blank Generation,” that is, a generation without women. Mathematically, it derives from a solution between 0 and 1 of a linear equation whose coefficients are the probabilities that a single progenitor breeds various integer numbers of daughters. We evaluated such probabilities by consulting literature. The probability of branch extinction is also the probability of extinction of progenitor’s mitochondrial lineage.     

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.     

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.     

Difference Inadaptive Dispersal Ability Can Promote Species Coexistence in Fluctuating Environments

Theories and empirical evidence suggest that random dispersal of organisms promotes species coexistence in spatially structured environments. However, directed dispersal, where movement is adjusted with fitness-related cues, is less explored in studies of dispersal-mediated coexistence. Here, we present a metacommunity model of two consumers exhibiting directed dispersal and competing for a single resource. Our results indicated that directed dispersal promotes coexistence through two distinct mechanisms, depending on the adaptiveness of dispersal. Maladaptive directed dispersal may promote coexistence similar to random dispersal. More importantly, directed dispersal is adaptive when dispersers track patches of increased resources in fluctuating environments. Coexistence is promoted under increased adaptive dispersal ability of the inferior competitor relative to the superior competitor. This newly described dispersal-mediated coexistence mechanism is likely favored by natural selection under the trade-off between competitive and adaptive dispersal abilities.     

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.     

A Compartmental Model for Activity-Dependent Dendritic Spine Branching

Dendritic spines are small, mushroom-like protrusions from the arbor of a neuron in the central nervous system. Interdependent changes in the morphology, biochemistry, and activity of spines have been associated with learning and memory. Moreover, post-mortem cortices from patients with Alzheimer’s or Parkinson’s disease exhibit biochemical and physical alterations within their dendritic arbors and a reduction in the number of dendritic spines. For over a decade, experimentalists have observed perforations in postsynaptic densities on dendritic spines after induction of long-term potentiation, a sustained enhancement of response to a brief electrical or chemical stimulus, associated with learning and memory. In more recent work, some suggest that activity-dependent intraspine calcium may regulate the surface area of the spine head, and reorganization of postsynaptic densities on the surface. In this paper, we develop a model of a dendritic spine with the ability to partition its transmission and receptor zones, as well as the entire spine head. Simulations are initially performed with fixed parameters for morphology to study electrical properties and identify parameters that increase efficacy of the synaptic connection. Equations are then introduced to incorporate calcium as a second messenger in regulating continuous changes in morphology. In the model, activity affects compartmental calcium, which regulates spine head morphology. Conversely, spine head morphology affects the level of local activity, whether the spines are modeled with passive membrane properties, or excitable membrane using Hodgkin–Huxley kinetics. Results indicate that merely separating the postsynaptic receptors on the surface of the spine may add to the diversity of circuitry, but does not change the efficacy of the synapse. However, when the surface area of the spine is a dynamic variable, efficacy of the synapse may vary continuously over time.     

Mechanisms of Side Branching and Tip Splitting in a Model of Branching Morphogenesis

Recent experimental work in lung morphogenesis has described an elegant pattern of branching phenomena. Two primary forms of branching have been identified: side branching and tip splitting. In our previous study of lung branching morphogenesis, we used a 4 variable partial differential equation (PDE), due to Meinhardt, as our mathematical model to describe the reaction and diffusion of morphogens creating those branched patterns. By altering key parameters in the model, we were able to reproduce all the branching styles and the switch between branching modes. Here, we attempt to explain the branching phenomena described above, as growing out of two fundamental instabilities, one in the longitudinal (growth) direction and the other in the transverse direction. We begin by decoupling the original branching process into two semi-independent sub-processes, 1) a classic activator/inhibitor system along the growing stalk, and 2) the spatial growth of the stalk. We then reduced the full branching model into an activator/inhibitor model that embeds growth of the stalk as a controllable parameter, to explore the mechanisms that determine different branching patterns. We found that, in this model, 1) side branching results from a pattern-formation instability of the activator/inhibitor subsystem in the longitudinal direction. This instability is far from equilibrium, requiring a large inhomogeneity in the initial conditions. It successively creates periodic activator peaks along the growing stalk, each of which later on migrates out and forms a side branch; 2) tip splitting is due to a Turing-style instability along the transversal direction, that creates the spatial splitting of the activator peak into 2 simultaneously-formed peaks at the growing tip, the occurrence of which requires the widening of the growing stalk. Tip splitting is abolished when transversal stalk widening is prevented; 3) when both instabilities are satisfied, tip bifurcation occurs together with side branching.     

Estimation in a Continuous State Space Branching Process

In some biological studies it is impossible to count the total number of individuals, but the size of the population can be measured by it's weight or volume. The probability of extinction of such populations is an interesting parameter, e.g. in modelling of epidemics. In this paper, the estimation of extinction probability and the moments of the offspring distribution is studied and the asymptotic properties of the estimators are discussed.     

Sporadic Disturbances in Fluctuating Coral Reef Environments: El Nino and Coral Reef Development in the Eastern Pacific

The disastrous effects of the intense 1982–83 El Niño-SouthernOscillation (ENSO) bring new insight into the long-term developmentof eastern Pacific coral reefs. The 1988–83 ENSO sea surfacewarming event caused extensive reef coral bleaching (loss ofsymbiotic zooxanthellae), resulting in up to 70–95% coralmortality on reefs in Costa Rica, Panama, Colombia and Ecuador.In the Galapagos Islands (Ecuador), most coral reefs experienced>95% coral mortality. Also, several coral species experiencedextreme reductions in population size, and local and regionalextinctions. The El Niño event spawned secondary disturbances,such as increased predation and bioerosion, that continue toimpact reef-building corals. The death of Pocillopora colonieswith their crustacean guards eliminated coral barriers now allowingthe corallivore Acanthaster planci access to formerly protectedcoral prey. Sea urchins and other organisms eroded disturbedcorals at rates that exceed carbonate production, potentiallyresulting in the elimination of existing reef buildups. In otherreefbuilding regions following extensive, catastrophic coralmortality, rapid recovery often occurs through the growth ofsurviving corals, recruitment of new corals from nearby sourcepopulations, and survival of consolidated reef surfaces. Inthe eastern Pacific, however, the return of upwelling conditionsand the survival of coral predators and bioeroders hamper coralreef recovery by reducing recruitment success and eroding coralreef substrates. Thus, coral reef growth that occurs betweendisturbance events is not conserved. Repeated El Niñodisturbances, which have occurred throughout the recent geologichistory of the eastern Pacific, prevent coral communities fromincreasing in diversity and limit the development and persistenceof significant reef features. The poor development of easternPacific coral reefs throughout Holocene and perhaps much ofPleistocene time may result from recurrent thermal disturbancesof the intensity of the 1982–83 El Niño event.     

Effects of Fluctuating Temperature on Germination and Emergence of Seeds in Different Moisture Environments

Seeds of calabrese and carrot were sown in soil at differentmoisture contents or were germinated in polyethylene glycolsolution of equivalent water potential. The seeds were alsosubjected to temperature environments which were either constant,altering at 12 h intervals, or changing smoothly and continuouslyin a daily cycle. The environments had similar mean temperatures,similar accumulated numbers of day-degrees, and the changing-temperatureenvironments had similar upper and lower temperature limits.In soil, at low and moderate moisture stress, seedlings of bothcrops emerged faster in the changing-temperature environmentsthan at constant temperature; at high moisture stress, emergenceoccurred only in the changing temperature environments. In osmoticsolutions, germination (radicle emergence) of calabrese seedswas faster in changing-temperature environments, but germinationof carrot seeds was unaffected by the temperature treatments.The results indicate that interaction between moisture stressand temperature environment is important and that results ofexperiments run at both constant moisture stress and constanttemperature together may not relate directly to the field situation.     

Evolutionary Branching in a Finite Population: Deterministic Branching vs. Stochastic Branching

Adaptive dynamics formalism demonstrates that, in a constant environment, a continuous trait may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called “evolutionary branching.” Most previous analyses of evolutionary branching have been conducted in an infinitely large population. Here, we study the effect of stochasticity caused by the finiteness of the population size on evolutionary branching. By analyzing the dynamics of trait variance, we obtain the condition for evolutionary branching as the one under which trait variance explodes. Genetic drift reduces the trait variance and causes stochastic fluctuation. In a very small population, evolutionary branching does not occur. In larger populations, evolutionary branching may occur, but it occurs in two different manners: in deterministic branching, branching occurs quickly when the population reaches the singular point, while in stochastic branching, the population stays at singularity for a period before branching out. The conditions for these cases and the mean branching-out times are calculated in terms of population size, mutational effects, and selection intensity and are confirmed by direct computer simulations of the individual-based model.     

Developmental Stability of DROSOPHILA MELANOGASTER under Artificial and Natural Selection in Constant and Fluctuating Environments

Populations of Drosophila melanogaster in constant 25° and fluctuating 20/29° environments showed increases in developmental stability, indicated by decreases in bilateral asymmetry of sterno-pleural chaeta number. In both environments, rates of decrease in asymmetry were greater under natural selection (control lines) than under artificial stabilizing selection. Overall mean asymmetry was greater in the fluctuating environment.—There was no evidence that decreased asymmetry was due to heterozygosity, and the decline in asymmetry was not explained by the decline in chaeta number in the lines under only natural selection. However, the decline was consistent with changes in total phenotypic variance and environmental variance.—The divergence between lines after 39 generations of selection was seen in differences in asymmetry and also in the genotype-environment interaction expressed in cross-culturing experiments.     

A Developmental Model for Branching Morphogenesis of Lake Cress Compound Leaf

Lake cress, Rorippa aquatica (Brassicaceae), is a semi-aquatic plant that exhibits a variety of leaf shapes, from simple leaves to highly branched compound leaves, depending on the environment. Leaf shape can vary within a single plant, suggesting that the variation can be explained by a simple model. In order to simulate the branched structure in the compound leaves of R. aquatica, we implemented reaction-diffusion (RD) patterning onto a theoretical framework that had been developed for serration distribution in the leaves of Arabidopsis thaliana, with the modification of the one-dimensional reaction-diffusion domain being deformed with the spatial periodicity of the RD pattern while expanding. This simple method using an iterative pattern could create regular and nested branching patterns. Subsequently, we verified the plausibility of our theoretical model by comparing it with the experimentally observed branching patterns. The results suggested that our model successfully predicted both the qualitative and quantitative aspects of the timing and positioning of branching in growing R. aquatica leaves.