Use of Agent-Based Modeling To Explore the Mechanisms of Intracellular Phosphorus Heterogeneity in Cultured Phytoplankton

There can be significant intraspecific individual-level heterogeneity in the intracellular P of phytoplankton, which can affect the population-level growth rate. Several mechanisms can create this heterogeneity, including phenotypic variability in various physiological functions (e.g., nutrient uptake rate). Here, we use modeling to explore the contribution of various mechanisms to the heterogeneity in phytoplankton grown in a laboratory culture. An agent-based model simulates individual cells and their intracellular P. Heterogeneity is introduced by randomizing parameters (e.g., maximum uptake rate) of daughter cells at division. The model was calibrated to observations of the P quota of individual cells of the centric diatom Thalassiosira pseudonana, which were obtained using synchrotron X-ray fluorescence (SXRF). A number of simulations, with individual mechanisms of heterogeneity turned off, then were performed. Comparison of the coefficient of variation (CV) of these and the baseline simulation (i.e., all mechanisms turned on) provides an estimate of the relative contribution of these mechanisms. The results show that the mechanism with the largest contribution to variability is the parameter characterizing the maximum intracellular P, which, when removed, results in a CV of 0.21 compared to a CV of 0.37 with all mechanisms turned on. This suggests that nutrient/element storage capabilities/mechanisms are important determinants of intrapopulation heterogeneity.     

A modeling exercise to show why population models should incorporate distinct life histories of dispersers

Dispersal is an important form of movement influencing population dynamics, species distribution and gene flow between populations. In population models, dispersal is often included in a simplified manner by removing a random proportion of the population. Many ecologists now argue that models should be formulated at the level of individuals instead of the population level. To fully understand the effects of dispersal on natural systems, it is therefore necessary to incorporate individual-level differences in dispersal behavior in population models. Here, we parameterized an integral projection model, which allows for studying how individual life histories determine population-level processes, using bulb mites, Rhizoglyphus robini, to assess to what extent dispersal expression (frequency of individuals in the dispersal stage) and dispersal probability affect the proportion of successful dispersers and natal population growth rate. We find that allowing for life-history differences between resident phenotypes and disperser phenotypes shows that multiple combinations of dispersal probability and dispersal expression can produce the same proportion of leaving individuals. Additionally, a given proportion of successful dispersing individuals result in different natal population growth rates. The results highlight that dispersal life histories, and the frequency with which disperser phenotypes occur in the natal population, significantly affect population-level processes. Thus, biological realism of dispersal population models can be increased by incorporating the typically observed life-history differences between resident phenotypes and disperser phenotypes, and we here present a methodology to do so.     

Microscale Heterogeneity Explains Experimental Variability and Non-Linearity in Soil Organic Matter Mineralisation

Soil respiration represents the second largest CO₂ flux from terrestrial ecosystems to the atmosphere, and a small rise could significantly contribute to further increase in atmospheric CO₂. Unfortunately, the extent of this effect cannot be quantified reliably, and the outcomes of experiments designed to study soil respiration remain notoriously unpredictable. In this context, the mathematical simulations described in this article suggest that assumptions of linearity and presumed irrelevance of micro-scale heterogeneity, commonly made in quantitative models of microbial growth in subsurface environments and used in carbon stock models, do not appear warranted. Results indicate that microbial growth is non-linear and, at given average nutrient concentrations, strongly dependent on the microscale distribution of both nutrients and microbes. These observations have far-reaching consequences, in terms of both experiments and theory. They indicate that traditional, macroscopic soil measurements are inadequate to predict microbial responses, in particular to rising temperature conditions, and that an explicit account is required of microscale heterogeneity. Furthermore, models should evolve beyond traditional, but overly simplistic, assumptions of linearity of microbial responses to bulk nutrient concentrations. The development of a new generation of models along these lines, and in particular incorporating upscaled information about microscale processes, will undoubtedly be challenging, but appears to be key to understanding the extent to which soil carbon mineralization could further accelerate climate change.     

Environmental Heterogeneity, Animal Disturbances, Microsite Characteristics, and Seedling Establishment in a Quercus havardii Community

In restoration experiments it is imperative to consider the study of mechanisms of how species are maintained and preserved in a system. This paper reports on the results of a field experiment examining the growth and survival of seedlings of Schizachyrium scoparium, a dominant perennial bunchgrass member of the Quercus havardii (sand shinnery oak) communities of semiarid western Texas, on mounds of displaced soil produced by Sylvilagus auduboni (rabbit). The central question posed is: does environmental heterogeneity created by small mammals influence seedling survival and growth? The specific questions addressed are: (1) Does seedling survival, growth, and nutrient uptake vary when grown on mounds, off-mound soils, and artificially created mounds?; (2) What is the influence of the microbial and litter components of mound soils on seedling survival?; and (3) In communities where animal disturbances create environmental heterogeneity and may impact seedling establishment, is it possible to artificially create mounds that could serve a similar function? Results show that characteristics of mound soils increase seedling survival, shoot and root biomass, root length, number of tillers, mycorrhizal infection, and nutrient uptake more in plants grown on mounds than off mounds. Both the microbial and litter components of mound soils are essential components of this effect. Artificial mounds generated from soils associated with the herbaceous community were more similar to intact rabbit mounds than artificial mounds generated from soils associated with the oaks. The results indicate that rabbits produce rich patches (both nutrient and microbial) favorable to the growth of seedlings of the dominant bunchgrass, and point to the potential importance of rabbit disturbances in shaping the dynamics of this plant community. Thus, rabbit-generated disturbances produce environmental heterogeneity in the sand shinnery oak community, similar to that produced by harvester ants in this community as shown by an earlier study. Small animal activity that results in soil displacement, and influences soil characteristics, may indirectly contribute to the persistence of certain plant species within a community. Thus, disturbances may well operate in semiarid communities to produce nutrient and microbe rich microsites which may function to maintain diversity.     

Combined effects between temporal heterogeneity of water supply,nutrient level,and population density on biomass of four broadly distributed herbaceous species

Temporal heterogeneity of water supply affects grassland community productivity and it can interact with nutrient level and intraspecific competition. To understand community responses, the responses of individual species to water heterogeneity must be evaluated while considering the interactions of this heterogeneity with nutrient levels and population density. We compared responses of four herbaceous species grown in monocultures to various combinations of water heterogeneity, nutrient level, and population density: two grasses (Cynodon dactylon and Lolium perenne), a forb (Artemisia princeps), and a legume (Trifolium repens). Treatment effects on shoot and root biomass were analyzed. In all four species, shoot biomass was larger under homogeneous than under heterogeneous water supply. Shoot responses of L. perenne tended to be greater at high nutrient levels. Although root biomass was also larger under homogeneous water supply, effects of water heterogeneity on root biomass were not significant in the grasses. Trifolium repens showed marked root responses, particularly at high population density. Although greater shoot and root growth under homogeneous water supply appears to be a general trend among herbaceous species, our results suggested differences among species could be found in the degree of response to water heterogeneity and its interactions with nutrient level and intraspecific competition.     

Chemotactic response of marine micro-organisms to micro-scale nutrient layers

The degree to which planktonic microbes can exploit microscale resource patches will have considerable implications for oceanic trophodynamics and biogeochemical flux. However, to take advantage of nutrient patches in the ocean, swimming microbes must overcome the influences of physical forces including molecular diffusion and turbulent shear, which will limit the availability of patches and the ability of bacteria to locate them. Until recently, methodological limitations have precluded direct examinations of microbial behaviour within patchy habitats and realistic small-scale flow conditions. Hence, much of our current knowledge regarding microbial behaviour in the ocean has been procured from theoretical predictions. To obtain new information on microbial foraging behaviour in the ocean we have applied soft lithographic fabrication techniques to develop 2 microfluidic devices, which we have used to create (i) microscale nutrient patches with dimensions and diffusive characteristics relevant to oceanic processes and (ii) microscale vortices, with shear rates corresponding to those expected in the ocean. These microfluidic devices have permitted a first direct examination of microbial swimming and chemotactic behaviour within a heterogeneous and dynamic seascape. The combined use of epifluorescence and phase contrast microscopy allow direct examinations of the physical dimensions and diffusive characteristics of nutrient patches, while observing the population-level aggregative response, in addition to the swimming behaviour of individual microbes. These experiments have revealed that some species of phytoplankton, heterotrophic bacteria and phagotrophic protists are adept at locating and exploiting diffusing microscale resource patches within very short time frames. We have also shown that up to moderate shear rates, marine bacteria are able to fight the flow and swim through their environment at their own accord. However, beyond a threshold high shear level, bacteria are aligned in the shear flow and are less capable of swimming without disturbance from the flow. Microfluidics represents a novel and inexpensive approach for studying aquatic microbial ecology, and due to its suitability for accurately creating realistic flow fields and substrate gradients at the microscale, is ideally applicable to examinations of microbial behaviour at the smallest scales of interaction. We therefore suggest that microfluidics represents a valuable tool for obtaining a better understanding of the ecology of microorganisms in the ocean.     

Growth and function of fungal mycelia in heterogeneous environments

As decomposer organisms, pathogens, plant symbionts and nutrient cyclers, fungi are of fundamental importance in the terrestrial environment. Moreover, in addition to their well-known applications in industry, many species also have great potential in environmental biotechnology. The study of this important class of organisms is difficult through experimental means alone due to the heterogeneity of their natural growth habitat and the microscopic scale of growth. In this work we present a mathematical model for colony expansion that is derived through consideration of the growth characteristics on the microscale. The model equations are of mixed hyperbolic-parabolic type and are treated with a numerical scheme that preserves positivity and conserves mass. The numerical solutions are compared against experimental results in a variety of environments. Thus the effect of different translocation mechanisms on fungal growth and function are identified. The derivation and analysis of an approximation to the full model yields further results concerning basic properties of mycelial growth. Finally, the acidification of the growth habitat is considered and the model thus provides important predictions on the functional consequences of the redistribution of internally-located material.     

Crown illumination limits the population growth rate of a neotropical understorey palm (Geonoma macrostachys,Arecaceae)

The importance of light as a limiting factor for growth and reproductionin tropical understorey plants is well known, but the population-levelconsequences of light limitation remain little explored. Here, I usedemographicmodelling to examine if the effect of canopy gaps on individual-levelperformance in a tropical understorey palm translates into an effect on thepopulation growth rate. The demographic effects of heterogeneity in crownillumination (index of hemispherical canopy openness), forest-phase, and othermicroenvironmental parameters were quantified using data on 2592 individuals ofall sizes in permanent plots followed over a 1.5 year period. Supplementaryexperiments investigating the effects of canopy conditions on seedlingrecruitment were also conducted. Among the microenvironmental parameters onlycrown illumination and forest-phase had strong and consistent demographiceffects. Growth and fecundity generally increased with increasing crownillumination. Under open forest-phase conditions growth tended to increase andsurvival to decrease (due to increased physical damage). Seedlings transplantedinto gap centres were damaged by solarization. The population-level effect ofheterogeneity in crown illumination and forest-phase was investigated usingtransition matrix models. The overall population growth rate was 0.999, and notsignificantly different from 1. Illumination-specific models showed thatG. macrostachys would be unable to persist at permanentlylow illumination, but would increase in density under higher illumination.Forest-phase-specific models gave similar, but weaker results. Thus, inG. macrostachys effects of canopy openness onindividual-level performance strongly limit the population growth rate. Thepresent study thereby shows that fine-scale spatiotemporal variation in canopyopenness in the tropical rain forest understorey can play a central role in thepopulation ecology of shade-tolerant understorey plants.     

Population-level ecological effect assessment: estimating the effect of toxic chemicals on density-dependent populations

We examined the relationship between individual-level and population-level effects of toxic chemicals, employing the equilibrium population size as an index of population-level effects. We first analyzed two-stage matrix models considering four life-history types and four density-dependent models, and then we analyzed ecotoxicological and life-history data of the fathead minnow (Pimephales promelas) and brook trout (Salvelinus fontinalis) as real examples. Our elasticity analysis showed that toxic impacts on density-dependent populations depended largely on the differences in density-dependence and in life histories of the organisms. In particular, the importance of adult survivability was considerably increased in iteroparous organisms with density-dependent juvenile survivability or fertility. Our results also suggested that population-level effects, as indicated by the percentage reduction in equilibrium population size, were often greater than the percentage reductions in vital rates of individuals. Our analysis indicates that assessing population-level risk and developing a risk-reduction strategy without considering density-dependence can be risky.     

How far details are important in ecosystem modelling: the case of multi-limiting nutrients in phytoplankton-zooplankton interactions

We try to answer the question of to what extent details in nutrient uptake and phytoplankton physiology matter for population and community dynamics. To this end, we study how two nutrients interact in limiting phytoplankton growth. A popular formulation uses a product-rule for nutrient uptake, which we compare with that on the basis of synthesizing units. We first fit different nutrient uptake models to a dataset and conclude that the quantitative differences between the models are small. Then we study the sensitivity of phytoplankton growth and zooplankton-phytoplankton interactions (ZPi) models to uptake formulations. Two population models are compared; they are based on different assumptions on the relation between nutrient uptake and phytoplankton growth. We find that the population and community models are sensitive to uptake formulations. According to the uptake formulation used in the ZPi models, qualitative differences can be observed. Indeed, although two models based on functions with similar shapes have close equilibria, these can differ in stability properties. Since stability involves the derivatives of formulas, even if two formulas provide close values, large numerical differences in the stability criterion may occur after derivation. We conclude that mechanistic details can be of importance for community modelling.     

Individual-based modeling of phytoplankton: evaluating approaches for applying the cell quota model

Present phytoplankton models typically use a population-level (lumped) modeling (PLM) approach that assumes average properties of a population within a control volume. For modern biogeochemical models that formulate growth as a nonlinear function of the internal nutrient (e.g. Droop kinetics), this averaging assumption can introduce a significant error. Individual-based (agent-based) modeling (IBM) does not make the assumption of average properties and therefore constitutes a promising alternative for biogeochemical modeling. This paper explores the hypothesis that the cell quota (Droop) model, which predicts the population-average specific growth or cell division rate, based on the population-average nutrient cell quota, can be applied to individual algal cells and produce the same population-level results. Three models that translate the growth rate calculated using the cell quota model into discrete cell division events are evaluated, including a stochastic model based on the probability of cell division, a deterministic model based on the maturation velocity and fraction of the cell cycle completed (maturity fraction), and a deterministic model based on biomass (carbon) growth and cell size. The division models are integrated into an IBM framework (iAlgae), which combines a lumped system representation of a nutrient with an individual representation of algae. The IBM models are evaluated against a conventional PLM (because that is the traditional approach) and data from a number of steady and unsteady continuous (chemostat) and batch culture laboratory experiments. The stochastic IBM model fails the steady chemostat culture test, because it produces excessive numerical randomness. The deterministic cell cycle IBM model fails the batch culture test, because it has an abrupt drop in cell quota at division, which allows the cell quota to fall below the subsistence quota. The deterministic cell size IBM model reproduces the data and PLM results for all experiments and the model parameters (e.g. maximum specific growth rate, subsistence quota) are the same as those for the PLM. In addition, the model-predicted cell age, size (carbon) and volume distributions are consistent with those derived analytically and compare well to observations. The paper discusses and illustrates scenarios where intra-population variability in natural systems leads to differences between the IBM and PLM models.     

Scaling up phenotypic plasticity with hierarchical population models

Individuals respond to different environments by developing different phenotypes, which is generally seen as a mechanism through which individuals can buffer adverse environmental conditions and increase their fitness. To understand the consequences of phenotypic plasticity it is necessary to study how changing a particular trait of an individual affects either its survival, growth, reproduction or a combination of these demographic vital rates (i.e. fitness components). Integrating vital rate changes due to phenotypic plasticity into models of population dynamics allows detailed study of how phenotypic changes scale up to higher levels of integration and forms an excellent tool to distinguish those plastic trait changes that really matter at the population level. A modeling approach also facilitates studying systems that are even more complex: traits and vital rates often co-vary or trade-off with other traits that may show plastic responses over environmental gradients. Here we review recent developments in the literature on population models that attempt to include phenotypic plasticity with a range of evolutionary assumptions and modeling techniques. We present in detail a model framework in which environmental impacts on population dynamics can be followed analytically through direct and indirect pathways that importantly incorporate phenotypic plasticity, trait-trait and trait-vital rate relationships. We illustrate this framework with two case studies: the population-level consequences of phenotypic responses to nutrient enrichment of plant species occurring in nutrient-poor habitats and of responses to changes in flooding regimes due to climate change. We conclude with exciting prospects for further development of this framework: selection analyses, modeling advances and the inclusion of spatial dynamics by considering dispersal traits as well.     

Demographic heterogeneity impacts density-dependent population dynamics

Among-individual variation in vital parameters such as birth and death rates that is unrelated to age, stage, sex, or environmental fluctuations is referred to as demographic heterogeneity. This kind of heterogeneity is prevalent in ecological populations, but is almost always left out of models. Demographic heterogeneity has been shown to affect demographic stochasticity in small populations and to increase growth rates for density-independent populations. The latter is due to ??cohort selection,?? where the most frail individuals die out first, lowering the cohort??s average mortality as it ages. The importance of cohort selection to population dynamics has only recently been recognized. We use a continuous-time model with density dependence, based on the logistic equation, to study the effects of demographic heterogeneity in mortality and reproduction. Reproductive heterogeneity is introduced in three ways: parent fertility, offspring viability, and parent?Coffspring correlation. We find that both the low-density growth rate and the equilibrium population size increase as the magnitude of mortality heterogeneity increases or as parent?Coffspring phenotypic correlation increases. Population dynamics are affected by complex interactions among the different types of heterogeneity, and trade-off scenarios are examined which can sometimes reverse the effect of increased heterogeneity. We show that there are a number of different homogeneous approximations to heterogeneous models, but all fail to capture important parts of the dynamics of the full model.     

Estimating the impact of oyster restoration scenarios on transient fish production

Oyster reef restoration projects are increasing in number both to enhance oyster density and to retain valuable ecosystem services provided by oyster reefs. Although some oyster restoration projects have demonstrated success by increasing density and biomass of transient fish, it still remains a challenge to quantify the effects of oyster restoration on transient fish communities. We developed a bioenergetics model to assess the impact of selected oyster reef restoration scenarios on associated transient fish species. We used the model to analyze the impact of changes in (1) oyster population carrying capacity; (2) oyster population growth rate; and (3) diet preference of transient fish on oyster reef development and associated transient fish species. Our model results indicate that resident fish biomass is directly affected by oyster restoration and oyster biomass, and oyster restoration can have cascading impacts on transient fish biomass. Furthermore, the results highlight the importance of a favorable oyster population growth rate during early restoration years, as it can lead to rapid increases in mean oyster biomass and biomass of transient fish species. The model also revealed that a transient fish's diet solely dependent on oyster reef‐derived prey could limit the biomass of transient fish species, emphasizing the importance of habitat connectivity in estuarine areas to enhance transient fish species biomass. Simple bioenergetics models can be developed to understand the dynamics of a system and make qualitative predictions of management and restoration scenarios.     

Herbivory and population dynamics of invasive and native <Emphasis Type="Italic">Lespedeza</Emphasis>

Some exotic plants are able to invade habitats and attain higher fitness than native species, even when the native species are closely related. One explanation for successful plant invasion is that exotic invasive plant species receive less herbivory or other enemy damage than native species, and this allows them to achieve rapid population growth. Despite many studies comparing herbivory and fitness of native and invasive congeners, none have quantified population growth rates. Here, we examined the contribution of herbivory to the population dynamics of the invasive species, Lespedeza cuneata, and its native congener, L. virginica, using an herbivory reduction experiment. We found that invasive L. cuneata experienced less herbivory than L. virginica. Further, in ambient conditions, the population growth rate of L. cuneata (λ = 20.4) was dramatically larger than L. virginica (λ = 1.7). Reducing herbivory significantly increased fitness of only the largest L. virginica plants, and this resulted in a small but significant increase in its population growth rate. Elasticity analysis showed that the growth rate of these species is most sensitive to changes in the seed production of small plants, a vital rate that is relatively unaffected by herbivory. In all, these species show dramatic differences in their population growth rates, and only 2% of that difference can be explained by their differences in herbivory incidence. Our results demonstrate that to understand the importance of consumers in explaining the relative success of invasive and native species, studies must determine how consumer effects on fitness components translate into population-level consequences. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Trophic interactions and population growth rates: describing patterns and identifying mechanisms

While the concept of population growth rate has been of central importance in the development of the theory of population dynamics, few empirical studies consider the intrinsic growth rate in detail, let alone how it may vary within and between populations of the same species. In an attempt to link theory with data we take two approaches. First, we address the question ''what growth rate patterns does theory predict we should see in time-series?'' The models make a number of predictions, which in general are supported by a comparative study between time-series of harvesting data from 352 red grouse populations. Variations in growth rate between grouse populations were associated with factors that reflected the quality and availability of the main food plant of the grouse. However, while these results support predictions from theory, they provide no clear insight into the mechanisms influencing reductions in population growth rate and regulation. In the second part of the paper, we consider the results of experiments, first at the individual level and then at the population level, to identify the important mechanisms influencing changes in individual productivity and population growth rate. The parasitic nematode Trichostrongylus tenuis is found to have an important influence on productivity, and when incorporated into models with their patterns of distribution between individuals has a destabilizing effect and generates negative growth rates. The hypothesis that negative growth rates at the population level were caused by parasites was demonstrated by a replicated population level experiment. With a sound and tested model framework we then explore the interaction with other natural enemies and show that in general they tend to stabilize variations in growth rate. Interestingly, the models show selective predators that remove heavily infected individuals can release the grouse from parasite-induced regulation and allow equilibrium populations to rise. By contrast, a tick-borne virus that killed chicks simply leads to a reduction in the equilibrium. When humans take grouse they do not appear to stabilize populations and this may be because many of the infective stages are available for infection before harvesting commences. In our opinion, an understanding of growth rates and population dynamics is best achieved through a mechanistic approach that includes a sound experimental approach with the development of models. Models can be tested further to explore how the community of predators and others interact with their prey.     

Environmental heterogeneity and not vicariant biogeographic barriers generate community‐wide population structure in desert‐adapted snakes

Genetic structure can be influenced by local adaptation to environmental heterogeneity and biogeographic barriers, resulting in discrete population clusters. Geographic distance among populations, however, can result in continuous clines of genetic divergence that appear as structured populations. Here, we evaluate the relevant importance of these three factors over a landscape characterized by environmental heterogeneity and the presence of a hypothesized biogeographic barrier in producing population genetic structure within 13 codistributed snake species using a genomic data set. We demonstrate that geographic distance and environmental heterogeneity across western North America contribute to population genomic divergence. Surprisingly, landscape features long thought to contribute to biogeographic barriers play little role in divergence community wide. Our results suggest that isolation by environment is the most important contributor to genomic divergence. Furthermore, we show that models of population clustering that incorporate spatial information consistently outperform nonspatial models, demonstrating the importance of considering geographic distances in population clustering. We argue that environmental and geographic distances as drivers of community‐wide divergence should be explored before assuming the role of biogeographic barriers.     

Spatial Complementarity and the Coexistence of Species

Coexistence of apparently similar species remains an enduring paradox in ecology. Spatial structure has been predicted to enable coexistence even when population-level models predict competitive exclusion if it causes each species to limit its own population more than that of its competitor. Nevertheless, existing hypotheses conflict with regard to whether clustering favours or precludes coexistence. The spatial segregation hypothesis predicts that in clustered populations the frequency of intra-specific interactions will be increased, causing each species to be self-limiting. Alternatively, individuals of the same species might compete over greater distances, known as heteromyopia, breaking down clusters and opening space for a second species to invade. In this study we create an individual-based model in homogeneous two-dimensional space for two putative sessile species differing only in their demographic rates and the range and strength of their competitive interactions. We fully characterise the parameter space within which coexistence occurs beyond population-level predictions, thereby revealing a region of coexistence generated by a previously-unrecognised process which we term the triadic mechanism. Here coexistence occurs due to the ability of a second generation of offspring of the rarer species to escape competition from their ancestors. We diagnose the conditions under which each of three spatial coexistence mechanisms operates and their characteristic spatial signatures. Deriving insights from a novel metric — ecological pressure — we demonstrate that coexistence is not solely determined by features of the numerically-dominant species. This results in a common framework for predicting, given any pair of species and knowledge of the relevant parameters, whether they will coexist, the mechanism by which they will do so, and the resultant spatial pattern of the community. Spatial coexistence arises from complementary combinations of traits in each species rather than solely through self-limitation.