Stochastic differential equation for two-phase growth model

Most mathematical models to describe natural phenomena in ecology are models with single-phase. The models are created as such to represent the phenomena as realistic as possible such as logistic models with different types. However, several phenomena in population growth such as embryos, cells and human are better approximated by two-phase models because their growth can be divided into two phases, even more, each phase requires different growth models. Most two-phase models are presented in the form of deterministic models, since two-phase models using stochastic approach have not been extensively studied. In previous study, Zheng’s two-phase growth model had been implemented in continuous time Markov chain (CTMC). It assumes that the population growth follows Yule process before the critical size, and the Prendiville process after that. In this research, Zheng’s two-phase growth model has been modified into two new models. Generally, probability distribution of birth and death processes (BDPs) of CTMC is intractable; and even if its first–passage time distribution can be obtained, the conditional distribution for the second-phase is complicated to be determined. Thus, two-phase growth models are often difficult to build. To overcome this problem, stochastic differential equation (SDE) for two-phase growth model is proposed in this study. The SDE for BDPs is derived from CTMC for each phase, via Fokker-Planck equations. The SDE for twophase population growth model developed in this study is intended to be an alternative to the two-phase models of CTMC population model, since the significance of the SDE model is simpler to construct, and it gives closer approximation to real data

Nonlinear dynamics of plankton ecosystem with impulsive control and environmental fluctuations

It is well known that the density of plankton populations always increases and decreases or keeps invariant for a long time, and the variation of plankton density is an important factor influencing the real aquatic environments, why do these situations occur? It is an interesting topic which has become the common interest for many researchers. As the basis of the food webs in oceans, lakes, and reservoirs, plankton plays a significant role in the material circulation and energy flow for real aquatic ecosystems that have a great effect on the economic and social values. Planktonic blooms can occur in some environments, however, and the direct or indirect adverse effects of planktonic blooms on real aquatic ecosystems, such as water quality, water landscape, aquaculture development, are sometimes catastrophic, and thus planktonic blooms have become a challenging and intractable problem worldwide in recent years. Therefore, to understand these effects so that some necessary measures can be taken, it is important and meaningful to investigate the dynamic growth mechanism of plankton and reveal the dynamics mechanisms of formation and disappearance of planktonic blooms. To this end, based on the background of the ecological environments in the subtropical lakes and reservoirs, this dissertation research takes mainly the planktonic algae as the research objective to model the mechanisms of plankton growth and evolution. In this dissertation, some theories related to population dynamics, impulsive control dynamics, stochastic dynamics, as well as the methods of dynamic modeling, dynamic analysis and experimental simulation, are applied to reveal the effects of some key biological factors on the dynamics mechanisms of the spatial-temporal distribution of plankton and the termination of planktonic blooms, and to predict the dynamics evolutionary processes of plankton growth. The main results are as follows: Firstly, to discuss the prevention and control strategies on planktonic blooms, an impulsive reaction-diffusion hybrid system was developed. On the one hand, the dynamic analysis showed that impulsive control can significantly influence the dynamics of the system, including the ultimate boundedness, extinction, permanence, and the existence and uniqueness of positive periodic solution of the system. On the other hand, some experimental simulations were preformed to reveal that impulsive control can lead to the extinction and permanence of population directly. More precisely, the prey and intermediate predator populations can coexist at any time and location of their inhabited domain, while the top predator population undergoes extinction when the impulsive control parameter exceeds some a critical value, which can provide some key arguments to control population survival by means of some reaction-diffusion impulsive hybrid systems in the real life. Additionally, a heterogeneous environment can affect the spatial distribution of plankton and change the temporal-spatial oscillation of plankton distribution. All results are expected to be helpful in the study of dynamic complex of ecosystems. Secondly, a stochastic phytoplankton-zooplankton system with toxic phytoplankton was proposed and the effects of environmental stochasticity and toxin-producing phytoplankton (TPP) on the dynamics mechanisms of the termination of planktonic blooms were discussed. The research illustrated that white noise can aggravate the stochastic oscillation of plankton density and a high-level intensity of white noise can accelerate the extinction of plankton and may be advantageous for the disappearance of harmful phytoplankton, which imply that the white noise can help control the biomass of plankton and provide a guide for the termination of planktonic blooms. Additionally, some experimental simulations were carried out to reveal that the increasing toxin liberation rate released by TPP can increase the survival chance of phytoplankton population and reduce the biomass of zooplankton population, but the combined effects of those two toxin liberation rates on the changes in plankton are stronger than that of controlling any one of the two TPP. All results suggest that both white noise and TPP can play an important role in controlling planktonic blooms. Thirdly, we established a stochastic phytoplankton-toxic producing phytoplankton-zooplankton system under regime switching and investigated how the white noise, regime switching and TPP affect the dynamics mechanisms of planktonic blooms. The dynamical analysis indicated that both white noise and toxins released by TPP are disadvantageous to the development of plankton and may increase the risk of plankton extinction. Also, a series of experimental simulations were carried out to verify the correctness of the dynamical analysis and further reveal the effects of the white noise, regime switching and TPP on the dynamics mechanisms of the termination of planktonic blooms. On the one hand, the numerical study revealed that the system can switch from one state to another due to regime shift, and further indicated that the regime switching can balance the different survival states of plankton density and decrease the risk of plankton extinction when the density of white noise are particularly weak. On the other hand, an increase in the toxin liberation rate can increase the survival chance of phytoplankton but reduce the biomass of zooplankton, which implies that the presence of toxic phytoplankton may have a positive effect on the termination of planktonic blooms. These results may provide some insightful understanding on the dynamics of phytoplankton-zooplankton systems in randomly disturbed aquatic environments. Finally, a stochastic non-autonomous phytoplankton-zooplankton system involving TPP and impulsive perturbations was studied, where the white noise, impulsive perturbations and TPP are incorporated into the system to simulate the natural aquatic ecological phenomena. The dynamical analysis revealed some key threshold conditions that ensure the existence and uniqueness of a global positive solution, plankton extinction and persistence in the mean. In particular, we determined if there is a positive periodic solution for the system when the toxin liberation rate reaches a critical value. Some experimental simulations also revealed that both white noise and impulsive control parameter can directly influence the plankton extinction and persistence in the mean. Significantly, enhancing the toxin liberation rate released by TPP increases the possibility of phytoplankton survival but reduces the zooplankton biomass. All these results can improve our understanding of the dynamics of complex of aquatic ecosystems in a fluctuating environment

Atmospheric CO2 drawdown, community dynamics and selection of surface microbiomes in marine cold-water ecosystems

The European Arctic is characterized by large surface areas of coastal seas and long coastlines where important ecosystem processes are regulated by marine microbiomes that contribute to global carbon cycling via primary productivity and atmospheric CO2 drawdown. In addition to biogeochemical cycling, these complex microbial ecosystems also support major marine food webs and lend themselves to marine bioprospecting for novel biotechnologies. However, they are not well understood and remain unpredictable. For example, northern coastal Norway is periodically affected by unwanted ecosystem functions such as sporadic harmful algae blooms that are detrimental to local aquaculture industry. These cold adapted marine microbiomes perform ecological processes that are often driven by phytoplankton and their associated heterotrophic communities which undergo strong seasonal variation within complex and variable oceanographical and biogeochemical conditions. Climate change driven temperature increases with resulting direct and undirect changes on environmental conditions have been reported to alter microbial community structures of surface microbiomes. Hence, these important microbial ecosystems are in transition, and it is difficult to predict the trajectory of how specific ecosystem functions may be changing. This thesis is centered around cold-water communities of phytoplankton and bacterioplankton with the aim to enhance our contemporary understanding on surface microbial ecosystems and their function with respect to carbon cycling, community dynamics and community selection. Paper I and Paper II took place in northern Norwegian fjords and costal systems where spatial variation and magnitude of atmospheric CO2 uptake were investigated and the main physical and biological factors driving surface partial pressure of CO2 with respect to atmospheric CO2 were assessed in four fjords and a coastal bay through seasonal changes. The results indicate that northern Norwegian fjords free of sea-ice act as a sink for atmospheric CO2, although the magnitude of air-to-sea CO2 flux showed fjord-specific variation, and the biological fixation of CO2 is a strong driver of CO2 undersaturation. In addition, the temporal and spatial dynamics of early summer microeukaryotes with co-blooming bacteria were examined during a destructive haptophyte Chrysochromulina leadbeateri-associated harmful algae bloom. The coastal habitats harbor highly localized phytoplankton microbial communities which succession dynamics of blooming populations (including C. leadbeateri) undergo strong temporal variability. Paper III took place across a long transect from Atlantic water influenced Barents Sea to less influenced Nansen Basin in the high Arctic with the aim to understand more about the influence of ecological community processes on the distribution of phytoplankton and microbial taxa. Inferences based on phylogenetic turnover, generated through null modeling randomization of phylogenetic relatedness, indicates that the dominant selective force is homogeneous across the studied transect despite differences regarding temperature, sea-ice conditions, and origin of a water mass. Our findings highlight that both large scale and local studies are important to form the needed comprehensive understanding of these microbial ecosystems as the regional taxonomic pool is determined by fundamental ecological processes but community structure influencing ecosystem function is instead subjected to more localized variation of abiotic and biotic factors

STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH APPLICATIONS IN ECOLOGY AND EPIDEMICS

Mathematical modeling with delay differential equations (DDEs) is widely used for analysis and predictions in various areas of life sciences, such as population dynamics, epidemiology, immunology, physiology, and neural networks. The memory or time-delays, in these models, are related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period, and so on. In ordinary differential equations (ODEs), the unknown state and its derivatives are evaluated at the same time instant. In DDEs, however, the evolution of the system at a certain time instant depends on the past history/memory. Introduction of such time-delays in a differential model significantly improves the dynamics of the model and enriches the complexity of the system. Moreover, natural phenomena counter an environmental noise and usually do not follow deterministic laws strictly but oscillate randomly about some average values, so that the population density never attains a fixed value with the advancement of time. Accordingly, stochastic delay differential equations (SDDEs) models play a prominent role in many application areas including biology, epidemiology and population dynamics, mostly because they can offer a more sophisticated insight through physical phenomena than their deterministic counterparts do. The SDDEs can be regarded as a generalization of stochastic differential equations (SDEs) and DDEs.This dissertation, consists of eight Chapters, is concerned with qualitative and quantitative features of deterministic and stochastic delay differential equations with applications in ecology and epidemics. The local and global stabilities of the steady states and Hopf bifurcations with respect of interesting parameters of such models are investigated. The impact of incorporating time-delays and random noise in such class of differential equations for different types of predator-prey systems and infectious diseases is studied. Numerical simulations, using suitable and reliable numerical schemes, are provided to show the effectiveness of the obtained theoretical results.Chapter 1 provides a brief overview about the topic and shows significance of the study. Chapter 2, is devoted to investigate the qualitative behaviours (through local and global stability of the steady states) of DDEs with predator-prey systems in case of hunting cooperation on predators. Chapter 3 deals with the dynamics of DDEs, of multiple time-delays, of two-prey one-predator system, where the growth of both preys populations subject to Allee effects, with a direct competition between the two-prey species having a common predator. A Lyapunov functional is deducted to investigate the global stability of positive interior equilibrium. Chapter 4, studies the dynamics of stochastic DDEs for predator-prey system with hunting cooperation in predators. Existence and uniqueness of global positive solution and stochastically ultimate boundedness are investigated. Some sufficient conditions for persistence and extinction, using Lyapunov functional, are obtained. Chapter 5 is devoted to investigate Stochastic DDEs of three-species predator prey system with cooperation among prey species. Sufficient conditions of existence and uniqueness of an ergodic stationary distribution of the positive solution to the model are established, by constructing a suitable Lyapunov functional. Chapter 6 deals with stochastic epidemic SIRC model with time-delay for spread of COVID-19 among population. The basic reproduction number ℛs0 for the stochastic model which is smaller than ℛ0 of the corresponding deterministic model is deduced. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov functional, and conditions for the extinction of the disease are obtained. In Chapter 7, some numerical schemes for SDDEs are discussed. Convergence and consistency of such schemes are investigated. Chapter 8 summaries the main finding and future directions of research. The main findings, theoretically and numerically, show that time-delays and random noise have a significant impact in the dynamics of ecological and biological systems. They also have an important role in ecological balance and environmental stability of living organisms. A small scale of white noise can promote the survival of population; While large noises can lead to extinction of the population, this would not happen in the deterministic systems without noises. Also, white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can also occur due to the time-delay in the transmission terms

Fluorescence Methods for Investigation of Living Cells and Microorganisms

Fluorescence methods play a leading role in the investigation of biological objects. They are the only non-destructive methods for investigating living cells and microorganisms in vivo. Using intrinsic and artificial fluorescence methods provides deep insight into mechanisms underlying physiological and biochemical processes. This book covers a wide range of modern methods involved in experimental biology. It illustrates the use of fluorescence microscopy and spectroscopy, confocal laser scanning microscopy, flow cytometry, delayed fluorescence, pulse-amplitude-modulation fluorometry, and fluorescent dye staining protocols. This book provides an overview of practical and theoretical aspects of fluorescence methods and their successful application in the investigation of static and dynamic processes in living cells and microorganisms

Book of Abstracts

ICES Annual Science Conference, 19 – 23 September 2011, Gdańsk Music and Congress Center, Gdańsk, Poland. IMR contributors: Benjamin Planque, Torild Johansen, Tuula Skarstein, Jon‐Ivar Westgaard, Halvor Knutsen, Kristin Helle, Michael Pennington, Marek Ostrowski, Nils Olav Handegard, Mette Skern‐Mauritzen, Edda Johannesen, Ulf Lindstrøm, Harald Gjøsæter, Ken Drinkwater, Trond Kristiansen, Geir Ottersen, Esben Moland Olse

Feasibility Study for an Aquatic Ecosystem Earth Observing System Version 1.2.

International audienceMany Earth observing sensors have been designed, built and launched with primary objectives of either terrestrial or ocean remote sensing applications. Often the data from these sensors are also used for freshwater, estuarine and coastal water quality observations, bathymetry and benthic mapping. However, such land and ocean specific sensors are not designed for these complex aquatic environments and consequently are not likely to perform as well as a dedicated sensor would. As a CEOS action, CSIRO and DLR have taken the lead on a feasibility assessment to determine the benefits and technological difficulties of designing an Earth observing satellite mission focused on the biogeochemistry of inland, estuarine, deltaic and near coastal waters as well as mapping macrophytes, macro-algae, sea grasses and coral reefs. These environments need higher spatial resolution than current and planned ocean colour sensors offer and need higher spectral resolution than current and planned land Earth observing sensors offer (with the exception of several R&D type imaging spectrometry satellite missions). The results indicate that a dedicated sensor of (non-oceanic) aquatic ecosystems could be a multispectral sensor with ~26 bands in the 380-780 nm wavelength range for retrieving the aquatic ecosystem variables as well as another 15 spectral bands between 360-380 nm and 780-1400 nm for removing atmospheric and air-water interface effects. These requirements are very close to defining an imaging spectrometer with spectral bands between 360 and 1000 nm (suitable for Si based detectors), possibly augmented by a SWIR imaging spectrometer. In that case the spectral bands would ideally have 5 nm spacing and Full Width Half Maximum (FWHM), although it may be necessary to go to 8 nm wide spectral bands (between 380 to 780nm where the fine spectral features occur -mainly due to photosynthetic or accessory pigments) to obtain enough signal to noise. The spatial resolution of such a global mapping mission would be between ~17 and ~33 m enabling imaging of the vast majority of water bodies (lakes, reservoirs, lagoons, estuaries etc.) larger than 0.2 ha and ~25% of river reaches globally (at ~17 m resolution) whilst maintaining sufficient radiometric resolution

Loodusliku muutlikkuse mõju madalate järvede ökoseisundi hindamisele

A thesis for applying for the degree of Doctor of Philosophy in Applied BiologyThe dissertation contributes to the improvement of large lake monitoring, demonstrating that besides following the class boundaries of ecological status established by law, reliable status estimates of such lakes require profound expert knowledge on ecosystem functioning, and considering the share of natural and human induced factors influencing the ecosystem. WFD defines the status of water bodies by the extent of anthropogenic deviation from the reference conditions, i.e. conditions that should occur at sites of any particular type in the absence of human impact. Ecological status of Estonian large, shallow lakes Peipsi and Võrtsjärv is greatly influenced by direct human activities as well as climate change. For example, the trend of water brownification influencing the whole matter circulation of lakes, results from natural hydrological processes, but also from decreasing atmospheric sulphur deposition – both determining the mobility of humic substances. It is a complicated task to find simple, well-functioning indicators to assess ecological status of water bodies which are influenced by natural factors, such as large water level fluctuations and strong seasonality, more than by human impact. For example, for Lake Võrtsjärv, all common water quality indicators show worse ecological status in periods of low water level despite unchanged human impact. It should also be considered that the influence of changed environmental conditions may become evident with a time lag – after one or even several years. In Lake Võrtsjärv, changes in water surface temperature and water level explain approximately one half of the total changes in values of ecological status indicators. The reliability of status estimates can be significantly increased by statistically correcting the values of status indicators for factors causing natural variability. Analysis of spatial variability of status indicators in Lake Võrtsjärv showed that the permanent sampling station at the deepest site of the lake is representative for more than 90% of the lake area. To improve cost-effectiveness of the state monitoring programme, this sampling site remains the only open water monitoring site at the lake since 2017.Töö annab panuse suurte madalate järvede seire paremaks korraldamiseks, näidates, et usaldusväärse seisundihinnangu andmiseks on lisaks seadusega paika pandud veekvaliteedi klassipiiride järgimisele vaja ka põhjalikke teadmisi ökosüsteemi kui terviku talitlusest ja seda mõjutavatest teguritest. Vastavalt Euroopa Liidu veepoliitika raamdirektiivile tuleb looduslike veekogude seisundit ja selle muutusi hinnata lähtuvalt inimmõju ulatusest. Eesti suurte ja madalate järvede, Peipsi ja Võrtsjärve, seisundit mõjutavad tugevalt nii nende valglal toimuv otsene inimtegevus kui ka kliima ja selle muutused. Näiteks peituvad kogu järvede aineringet mõjutava vee „pruunistumise“ trendi taga nii looduslikud hüdroloogilised põhjused kui ka atmosfäärse väävlireostuse vähenemine, mis mõlemad mõjutavad huumusainete liikuvust. Selliste veeökosüsteemide seisundi hindamiseks, kus inimtegevuse mõjude kõrval on ülekaalus looduslikud tegurid nagu suured veetaseme kõikumised ja tugev sesoonsus, on raske leida lihtsaid, hästitoimivaid indikaatoreid. Näiteks Võrtsjärves näitavad kõik tavapärased veekvaliteedi mõõdikud madalvee perioodidel halvemat olukorda isegi muutumatu inimmõju tingimustes ja tihti on inimtekkeliste ja looduslike muutuste vahel raske vahet teha. Tuleb ka arvestada, et muutunud keskkonnatingimuste mõju võib avalduda hilinemisega – alles järgmisel aastal või isegi aastate pärast. Võrtsjärves selgitavad vee pinnatemperatuuri ja veetaseme muutused ligikaudu poole ökoseisundi näitajate kogumuutlikkusest. Seisundihinnangu usaldusväärsust saab oluliselt tõsta, kui seisundinäitajate väärusi statistiliste meetodite abil korrigeerida looduslikku muutlikkust põhjustavate tegurite suhtes. Võrtsjärve seisundinäitajate ruumilise muutlikkuse analüüs näitas, et järve sügavaimas kohas asuv seirekoht iseloomustab hästi järve kogu avaveelist osa ehk rohkem kui 90% tema pindalast. Kulude kokkuhoiu eesmärgil ongi see alates 2017. aastast riiklikus seireprogrammis ainuke avavee seirekoht.Publication of this thesis is supported by the Estonian University of Life Sciences