Modeling the role of constant and time varying recycling delay on an ecological food chain

summary:We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the daily variation in nutrient recycling and deduce the stability criteria of the variable delay model. A comparison of the variable delay model with the constant delay one is performed to unearth the biological relevance of oscillating delay in some real world ecological situations. Numerical simulations are done in support of analytical results

On a three-tier ecological food chain model with deterministic and random harvesting: A mathematical study

In the present study, we consider a nutrient-autotroph-herbivore ecosystem model where the herbivore species is assumed to have a commercial value. We use a Holling type-II harvest function to model density dependent herbivore harvesting. Stability criteria of the resulting model is investigated both from analytical and numerical viewpoints. The investigation revealed the existence of a number of threshold values of the harvest rate that have a remarkable influence on the system dynamics. Next we incorporate a noise term in the parameter representing harvest rate to model the phenomenon of poaching as random harvesting. The stochastic model is analyzed for exponential mean square stability and the resulting criteria in terms of harvest related parameters obtained. These parameter thresholds could be utilized to develop effective harvesting strategies and wildlife management policies which take into account the overall survival of the ecological populations

Positividad y acotamiento de soluciones de un modelo epidemiologico estacional estocástico para el virus respiratorio sincitial

In this paper we investigate the positivity and boundedness of the solution of a stochastic seasonal epidemic model for the respira tory syncytial virus (RSV). The stochasticity in the model is due to fluctuating physical and social environments and is introduced by perturbing the transmission parameter of the seasonal disease. We show the existence and uniqueness of the positive solution of the stochastic seasonal epidemic model which is required in the modeling of populations since all populations must be positive from a biological point of view. In addition, the positivity and boundedness of solutions is important to other nonlinear models that arise in sciences and engineering. Numerical simulations of the stochastic model are performed using the Milstein numerical scheme and are included to support our analytic results.En este trabajo se investiga la positividad y acotamineto de la solución de un modelo epidemiologico estacional estocástico para el virus respiratorio sincitial (RSV). La estocasticidad en el modelo se debe a entornos físicos y sociales fluctuantes y se introduce perturbando el parámetro de transmisión de la enfermedad. Se demuestra la existencia y unicidad de la solución positiva del modelo epidemiologico estacional estocástico, lo cual se requiere en el modelado de las poblaciones ya que todas las poblaciones deben ser positivos desde el punto de vista biológico. Adicionalmente, la positividad y la acotación de las soluciones es importante para otros modelos no lineales que se presentan en las ciencias y la ingeniería. Las simulaciones numéricas del modelo estocástico se realizan utilizando el esquema numérico de Milstein y se incluyen para apoyar los resultados analíticos

Parsing the Particulars of Pollination: Ecological and Anthropogenic Drivers of Plant and Pollinator Dynamics

My research focuses on wild pollinating insects and the external influences on their population dynamics in both natural and human altered settings. Pollination from wild insects (e.g. wild bees, flies, butterflies, etc.) is critically important for both agricultural systems and the maintenance of wild/native plant biodiversity. Unfortunately, similarly to honey bees, numerous wild pollinating insects are experiencing global declines in abundance and diversity. Causes for the declines are varied and far reaching with mounting evidence showing these declines manifest in both, natural and human altered environments. Accordingly, the declines in pollinator health will have similarly widespread consequences, posing a precipitous threat to biodiversity, food production, and economic stability. The breadth and severity of the global pollinator decline highlights the need to develop a thorough understanding of how wild pollinators interface with their environments in both natural and human altered settings. Specifically, my research aims to help elucidate the drivers of natural plant and pollinator dynamics as well as the causes of wild pollinator decline utilizing comprehensive interwoven empirical and theory-based approaches. The first half of this thesis investigates the effects of urban development on wild bee communities using urban gardens as study sites in southeastern Michigan. My colleagues and I developed a large-scale multi-faceted research project sampling thousands of bees and numerous environmental variables across our sites. Results described in chapter two reveal that the negative effects of urban development on ground nesting bumble bees are driven entirely by declines in females while males show no response to urbanization. It also details a surprisingly abundant bumble bee population in the city of Detroit MI. Chapter three expands focus to the entire sampled set of bees and shows that the differential effect of urban development on females and males is apparent in all sampled ground nesting bees groupings. However, wild bees which nest in above-ground cavities have positive correlations with urban development. Chapter four uses US census data to investigate how socioeconomic conditions in urban settings can influence the location and floral quality of our study sites, urban gardens. The second half examines wild plant and pollinator dynamics in natural settings using theoretical models informed by empirical data and observations. Chapter five investigates the direct and indirect effects of insect herbivores on pollination in a community context. When attacked by herbivores, plants mount chemical defenses which deter herbivores but also deter pollinators and consequently reduce individual plant reproduction. Using empirically vetted mathematical representations of these interactions, I show that while this defense strategy has significant costs to individual reproduction it has stabilizing effects on the population and community level. Chapter six focuses on an often overlooked pollinator, predatory syrphid flies. These flies are pollinators when adults but predators of insect herbivores when in their larval stage. While this can be beneficial, I demonstrate how this dynamic can lead to a negative feedback loop in communities isolated from background biodiversity. Chapter seven expands the consideration of ecologically distinct developmental stages to plants. Incorporating independent stages of plant development into a model framework is shown to fundamentally alter the effects certain demographic rates on both population and community dynamics. This work presents novel findings regarding pollinator interactions with their environment in both anthropogenic and natural settings, contributing to foundational ecological information which will hopefully aid in managing and conserving pollinator biodiversity.PHDEcology and Evolutionary BiologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145954/1/prglaum_1.pd

APPLICATION OF ECOSYSTEM ENERGETIC INDICATORS FOR THE VALUATION OF ECOSYSTEM SERVICES AND HEALTH

Ecosystems services are benefits that humans receive from ecosystem functions. Ecosystem health is a term that is commonly used in the literature to describe the state of an ecosystem. Ecologists and economists have stated that ecosystem health is important for the preservation and maintenance of ecosystem services essential to human society. Various methods and means have been proposed to assess ecosystem services and the economic values they provide to society, in relation to ecosystem health, by developing reliable holistic methods which assess health and services. Energy is a common denominator in all processes and measures of activity and if an ecosystem is distressed, it will not efficiently convert energy to work. In this study, energy indices were used to evaluate ecosystem health in relation to the ecosystem service of metals retention (iron and zinc) in wetlands. These indices included emergy (which evaluates the energy memory of the system), eco-exergy (a concept adapted to ecology to determine the efficiency of the work within the ecosystem) and ascendency (the diversity of the networks acting as an indicator of activity and organization within the system). Six wetlands, three volunteer and three treatment, which were all receiving metals contaminated water, were modeled using the STELLA dynamic simulation programming. A total system model was developed with hydrologic, ecosystem, and biogeochemical (iron and zinc retention) submodels. Field data from these systems were used to calibrate and validate each model. These models were evaluated for relationships between the indices, ecosystem service of metals retention, and to assess how the different systems (volunteer and treatment wetlands) vary between these indices. The results from this study suggest that there are relationships between ecosystem services and ecosystem health indices including iron retention and emergy, relative ascendency, specific exergy and the exergy/emergy ratio. In the case of zinc retention, there was a relationship with all indices excluding the exergy indices. Ascendency was a poor indicator of iron retention but it was also discovered that more zinc is retained in the higher ascendant systems. The systems with higher emergy had more metals retention suggesting that a system with greater emergy can provide a greater ecosystem service. This trend did not hold true with exergy and ascendency, meaning that as these indices increased, the service of metal retention decreased. Using exergy and ascendency indicators to determine a system’s potential to provide a service was less clear from the results. These six models, for both treatment and volunteer wetland systems, suggest that emergy is the only indicator that determines the potential ability of the system to provide a service

The stability of model ecosystems

Ecologists would like to understand how complexity persists in nature. In this thesis I have taken two fundamentally different routes to study ecosystem stability of model ecosystems: classical community ecology and classical population ecology. In community ecology models, we can study the mathematical mechanisms of stability in general, large model ecosystems. In population ecology models, fewer species are studied but greater detail of species interactions can be incorporated. Within these alternative contexts, this thesis contributes to two consuming issues concerning the stability of ecological systems: the ecosystem stability-complexity debate; and the causes of cyclic population dynamics. One of the major unresolved issues in community ecology is the relationship between ecosystem stability and complexity. In 1958 Charles Elton made the conjecture that the stability of an ecological system was coupled to its complexity and this could be a “wise principle of co-existence between man and nature” with which ecologists could argue the case for the conservation of nature for all species, including man. The earliest and simplest model systems were randomly constructed and exhibited a negative association between stability and complexity. This finding sparked the stability-complexity debate and initiated the search for organising principles that enhanced stability in real ecosystems. One of the universal laws of ecology is that ecosystems contain many rare and few common species. In this thesis, I present analytical arguments and numerical results to show that the stability of an ecosystem can increase with complexity when the abundance distribution is characterized by a skew towards many rare species. This work adds to the growing number of conditions under which the negative stability - complexity relationship can been inverted in theoretical studies. While there is growing evidence that the stability-complexity debate is progressing towards a resolution, community ecology has become increasingly subject to major criticism. A long-standing criticism is the reliance on local stability analysis. There is growing recognition that a global property called permanence is a more satisfactory definition of ecosystem stability because it tests only whether species can coexist. Here I identify and explain a positive correlation between the probability of local stability and permanence, which suggests local stability is a better measure of species coexistence than previously thought. While this offers some relief, remaining issues cause the stability-complexity debate to evade clear resolution and leave community ecology in a poor position to argue for the conservation of natural diversity for the benefit of all species. In classical population ecology, a major unresolved issue is the cause of non-equilibrium population dynamics. In this thesis, I use models to study the drivers of cyclic dynamics in Scottish populations of mountain hares (Lepus timidus), for the first time in this system. Field studies currently favour the hypothesis that parasitism by a nematode Trichostrongylus retortaeformis drives the hare cycles, and theory predicts that the interaction should induce cycling. Initially I used a simple, strategic host-parasite model parameterised using available empirical data to test the superficial concordance between theory and observation. I find that parasitism could not account for hare cycles. This verdict leaves three options: either the parameterisation was inadequate, there were missing important biological details or simply that parasites do not drive host cycles. Regarding the first option, reliable information for some hare-parasite model parameters was lacking. Using a rejection-sampling approach motivated by Bayesian methods, I identify the most likely parameter set to predict observed dynamics. The results imply that the current formulation of the hare-parasite model can only generate realistic dynamics when parasite effects are significantly larger than current empirical estimates, and I conclude it is likely that the model contains an inadequate level of detail. The simple strategic model was mathematically elegant and allowed mathematical concepts to be employed in analysis, but the model was biologically naïve. The second model is the antipode of the first, an individual based model (IBM) steeped in biological reality that can only be studied by simulation. Whilst most highly detailed tactical models are developed as a predictive tool, I instead structurally perturb the IBM to study the ecological processes that may drive population cycles in mountain hares. The model allows delayed responses to life history by linking maternal body size and parasite infection to the future survival and fecundity of offspring. By systematically removing model structure I show that these delayed life history effects are weakly destabilising and allow parameters to lie closer to empirical estimates to generate observed hare population cycles. In a third model I structurally modify the simple strategic host-parasite model to make it spatially explicit by including diffusion of mountain hares and corresponding advection of parasites (transportation with host). From initial simulations I show that the spatially extended host-parasite equations are able to generate periodic travelling waves (PTWs) of hare and parasite abundance. This is a newly documented behaviour in these widely used host-parasite equations. While PTWs are a new potential scenario under which cyclic hare dynamics could be explained, further mathematical development is required to determine whether adding space can generate realistic dynamics with parameters that lie closer to empirical estimates. In the general thesis discussion I deliberate on whether a hare-parasite model has been identified which can be considered the right balance between abstraction and relevant detail for this system

Zooplankton community responses to Ocean Acidification

Ocean acidification is affecting marine ecosystems directly through changes in pH, as well as indirectly, via trophic pathways. Thus, to evaluate impacts of ocean acidification on marine communities it is necessary to consider the potential pCO2 effects on population dynamics as well as community trophic interactions. Within the framework of the BIOACID II project (Biological Impacts of Ocean ACIDification), the overarching goal of this thesis was to study the effects of ocean acidification on zooplankton, focusing on copepods and jellyfish. The main results are described in four chapters (CHAPTER I to IV), each of which corresponds to a manuscript. The first part of this thesis evaluated pCO2 effects on natural mesozooplankton communities from a boreal fjord (CHAPTER I) and the subtropical Northeast Atlantic (CHAPTER II). Large-scale pelagic mesocosm units (a Kiel Off-Shore Mesocosms for Future Ocean Simulations : KOSMOS) were artificially enriched in CO2 to simulate future ocean conditions. In both experiments, we detected species-specific sensitivities to ocean acidification in copepods, as well as positive pCO2 effect on total mesozooplankton abundances under high-CO2 bloom conditions, caused by a bottom-up effect. During the Gullmar Fjord KOSMOS2013 experiment (CHAPTER I) species-specific sensitivities to CO2 were detected in copepods, as well as in hydromedusae. However, these effects on single species were not translated into the structure or the diversity of the community, likely due to the overwhelmingly dominance of Pseudocalanus acuspes, which resulted to be more abundant under acidic conditions, especially the younger (copepodite) life stage. In the Gran Canaria KOSMOS2014 study (CHAPTER II) a significant effect of pCO2 on phytoplankton succession was detected, ultimately affecting the development of the plankton community only after a simulated bloom event. The zooplankton community responded to the phytoplankton bloom in all mesocosms, although the response was delayed under high pCO2 conditions. The most abundant mesozooplankters were calanoid copepods, which did not respond to CO2 treatments during the pre-bloom phase of the experiment. However calanoids were more abundant under elevated pCO2 conditions than in low- pCO2 levels in the post-bloom phase. Bottom-up effects of CO2-driven increases in phyto- and microzooplankton standing stocks would explain the increase in copepod abundance during both experiments. These results suggest that, under realistic end-of-century scenarios, the above-mentioned ocean acidification effects detected on copepods could potentially affect biomass transfer to higher trophic levels. As in community experiments it is not possible to separate out the pCO2 direct and indirect effects, mesocosms studies were combined with laboratory experiments in the second part of this thesis work. The aim was to evaluate direct and indirect effects of global change conditions on the two main groups of interest for this thesis: copepods and jellyfish. Apart from direct acidification effects, the increasing carbon availability in the marine environment will likely change primary production and the quality of phytoplankton as food for higher trophic levels, showing higher C:nutrient ratios as CO2 availability increases. Hence, a change in biochemical composition when culturing algae (Rhodomonas salina) in elevated pCO2 levels caused a change in food quality, affecting zooplankton by decreased growth and development. Indirect negative pCO2 effects were observed on the dinoflagellate Oxyrrhis marina and nauplii and copepodite stages of the copepod Acartia tonsa. Direct pH effects on these consumers seem to be of lesser importance than the indirect effects caused by a CO2-associated decrease in algal quality when having only a food source (CHAPTER III), unlike the positive CO2-effect observed in copepods when feeding on natural plankton communities. Direct pH effects on zooplankton, however, must be placed in a global change context, considering that ocean acidification in future oceans will not act alone but in combination with other climate factors such as warming and deoxygenation. The direct effects of these three stressors in conjunction were thus studied on 1-day-old ephyrae of the moon jellyfish (Aurelia aurita) from a North Sea subpopulation off Helgoland Island (Germany). The results obtained during this experiment point that end-of-century pCO2 scenarios will not affect these ephyrae in a substantial way. However, A. aurita may not be robust to larger changes in ocean pH, warming and deoxygenation, especially if simultaneous increases in atmospheric pCO2 levels and seawater temperature occur (CHAPTER IV). A. aurita is an ecologically and economically relevant species due to its interactions with commercially important fish species, hence the tolerance or resilience of this jellyfish to climate change might be detrimental for future fisheries

Application of FTIR spectroscopy for monitoring water quality in a hypertrophic aquatic ecosystem (Lake Auensee, Leipzig)

FTIR spectroscopy as molecular fingerprint has been used to assess macromolecular and ele-mental stoichiometry as well as growth rates of phytoplankton cells. Chemometric models have been developed to extract quantitative information from FTIR spectra to reveal macro-molecular composition (of proteins, carbohydrates and lipids), C:N ratio, and growth potential. In this study, we tested these chemometric models based on lab-cultured algal species in mon-itoring changes of phytoplankton community structure in a hypertrophic lake (Lake Auensee, Leipzig, Germany), where a seasonal succession of spring green algal bloom followed by cya-nobacterial dominance in summer can be commonly observed. Our results demonstrated that green algae reacted to environmental changes such as nitrogen limitation (due to imbalanced nitrogen and phosphorus supply) with restricted growth by changing carbon allocation from protein synthesis to storage carbohydrates and/or lipids, and increased C:N ratio. By contrast, cyanobacteria proliferated under nitrogen limiting conditions. Furthermore, the FTIR-based growth potential of green alga matched well with the population biomass determined by the Chl-a concentration. However, the predicted growth potential based on FTIR spectroscopy cannot describe the realistic growth development of cyanobacteria in this lake. These results revealed that green algae and cyanobacteria have different strategies of C-allocation stoichi-ometry and growth patterns in response to environmental changes. These taxon-specific re-sponses may explain at a molecular level why green algae bloomed in the spring under condi-tions with sufficient nutrient, lower pH and lower water temperature; while cyanobacteria overgrew green algae and dominated in the summer under conditions with limited nutrient availability, higher pH and higher water temperature. In addition, the applicability of these chemometric models for predicting field cyanobacterial growth is of limited value. This may be attributed to other special adaptation properties of cyanobacterial species under stress growth conditions. We used flow cytometry to isolate functional algal groups from the water samples. Despite some drawbacks of the flow cytometry combined FTIR spectroscopy tech-nique, this method provides prospects of monitoring water quality and early warning of harmful algal blooms