Spatio-temporal behaviour of the deep chlorophyll maximum in Mediterranean Sea: Development of a stochastic model for picophytoplankton dynamics

Transition prediction in the Ising-model

Dynamical systems can be subject to critical transitions where a system’s state abruptly shifts from one stable equilibrium to another. To a certain extent such transitions can be predicted with a set of methods known as early warning signals. These methods are often developed and tested on systems simulated with equation-based approaches that focus on the aggregate dynamics of a system. Many ecological phenomena however seem to necessitate the consideration of a system’s micro-level interactions since only there the actual reasons for sudden state transitions become apparent. Agent-based approaches that simulate systems from the bottom up by explicitly focusing on these micro-level interactions have only rarely been used in such investigations. This study compares the performance of a bifurcation estimation method for predicting state transitions when applied to data from an equation-based and an agent-based version of the Ising-model. The results show that the method can be applied to agent-based models and, despite its greater stochasticity, can provide useful predictions about state changes in complex systems.

Impact of time delays and environmental noise on the extinction of a population dynamics model

ABSTRACT

In this paper, we examine a population model with carrying capacity, time delay, and sources of additive and multiplicative environmental noise. We find that time delay, noise sources and their correlation induce regime shifts and transitions between the population survival state and the extinction state. To explore the transition mechanism between these two states, we analyzed the shift time to extinction, or the delayed extinction time, of populations. The main finding is that the extinction transition time as a function of the noise intensity shows a maximum, indicating the existence of an appropriate noise intensity leading to a maximal delayed extinction. This nonmonotonic behavior, with a maximum, is a signature of the noise-enhanced stability phenomenon, observed in many physical and complex metastable systems. In particular, this maximum increases (or decreases) as the cross-correlation intensity or the delay time in the death process increases. Furthermore, the signal-to-noise ratio as a function of noise intensity shows a maximum, which is a signature of the stochastic resonance phenomenon in the population dynamics model investigated in the presence of time delay and environmental noise.

An integrative model of cancer cell differentiation with immunotherapy. Phys Biol 2021;18. [PMID: 34633296 DOI: 10.1088/1478-3975/ac2e72] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

In order to improve cancer treatments, cancer cell differentiation and immunotherapy are the subjects of several studies in different branches of interdisciplinary sciences. In this work, we develop a new population model that integrates other complementary ones, thus emphasizing the relationship between cancer cells at different differentiation stages and the main immune system cells. For this new system, specific ranges were found where transdifferentiation of differentiated cancer cells can occur. In addition, a specific therapy against cancer stem cells was analysed by simulating cytotoxic cell vaccines. In reference to the latter, the different combinations of parameters that optimize it were studied.

Temporal fluctuation scaling in nonstationary time series using the path integral formalism

We model the time evolution of the mean and the variance of nonstationary time series using the path integral formalism with the purpose to obtain the temporal fluctuation scaling presents in complex systems. To this end, we first show how the probability of change between two times of a stochastic variable can be written in terms of a Feynman kernel, where the cumulant generating function of statistical moments is identified as the Hamiltonian of the system. Thus, by including the effects of a stochastic drift and a temporal logarithmic term in the cumulant generating function, we find analytical expressions describing the temporal evolutions of the mean and the variance in terms of cumulants. Starting from these expressions, we obtain the temporal fluctuation scaling written as a general analytical relation between the variance and the mean, in such a way that this relation satisfies a power law, with the exponent being a function on time. Additionally, we study several financial time series associated with changes of prices for some stock indexes and currencies. For this financial time series, we find that the temporal evolution of the mean and the variance, the temporal fluctuation scaling, and the temporal evolution of the exponent which are obtained from this path integral approach are in agreement with those obtained using the empirical data.

Coexistence in a competition-diffusion-advection system with equal amount of total resources

We consider a Lotka-Volterra competition-diffusion-advection system with the total resources for two competitors fixed at the same level. We reveal the combined effect of competition abilities and spatial variations on the coexistence of two competing species. It is obtained that when the ratio of advection rate α to diffusion rate d₁ is appropriately large, the two competing species will always coexist if the inter-specific competition coefficients (b,c) in (0,1]×(0,1] and when the ratio is appropriately small, the two species will coexist if the inter-specific competition coefficients c is appropriately small and b is in (0,1].

Persistence and extinction of species in a disease-induced ecological system under environmental stochasticity

Population extinction is a serious issue both from the theoretical and practical points of view. We explore here how environmental noise influences persistence and extinction of interacting species in presence of a pathogen even when the populations remain stable in its deterministic counterpart. Multiplicative white noise is introduced in a deterministic predator-prey-parasite system by randomly perturbing three biologically important parameters. It is revealed that the extinction criterion of species may be satisfied in multiple ways, indicating various routes to extinction, and disease eradication may be possible with the right environmental noise. Predator population cannot survive, even when its focal prey strongly persists if its growth rate is lower than some critical value, measured by half of the corresponding noise intensity. It is shown that the average extinction time of population decreases with increasing noise intensity and the probability distribution of the extinction time follows the log-normal density curve. A case study on red grouse (prey) and fox (predator) interaction in presence of the parasites trichostrongylus tenuis of grouse is presented to demonstrate that the model well fits the field data.

Stability analysis and Hopf bifurcation of a fractional order mathematical model with time delay for nutrient-phytoplankton-zooplankton

In recent years, some researchers paid their attention to the interaction between toxic phytoplankton and zooplankton. Their studies showed that the mechanism of food selection in zooplankton is still immature and when different algae of the same species (toxic and nontoxic) coexist, some zooplankton may not be able to distinguish between toxic and nontoxic algae, and even show a slight preference for toxic strains. Thus, in this article, a fractional order mathematical model with time delay is constructed to describe the interaction of nutrient-phytoplankton-toxic phytoplankton-zooplankton. The main purpose of this paper is to study the influence of fractional order and time delay on the ecosystem. The sufficient conditions for the existence and local stability of each equilibrium are obtained by using fractional order stability theory. By choosing time delay as the bifurcation parameter, we find that Hopf bifurcation occurs when the time delay passes through a sequence of critical values. After that, some numerical simulations are performed to support the analytic results. At last we make some conclusion and point out some possible future work.

Fine metagenomic profile of the Mediterranean stratified and mixed water columns revealed by assembly and recruitment

BACKGROUND

The photic zone of aquatic habitats is subjected to strong physicochemical gradients. To analyze the fine-scale variations in the marine microbiome, we collected seven samples from a single offshore location in the Mediterranean at 15 m depth intervals during a period of strong stratification, as well as two more samples during the winter when the photic water column was mixed. We were able to recover 94 new metagenome-assembled genomes (MAGs) from these metagenomes and examine the distribution of key marine microbes within the photic zone using metagenomic recruitment.

RESULTS

Our results showed significant differences in the microbial composition of different layers within the stratified photic water column. The majority of microorganisms were confined to discreet horizontal layers of no more than 30 m (stenobathic). Only a few such as members of the SAR11 clade appeared at all depths (eurybathic). During the winter mixing period, only some groups of bloomers such as Pseudomonas were favored. Although most microbes appeared in both seasons, some groups like the SAR116 clade and some Bacteroidetes and Verrucomicrobia seemed to disappear during the mixing period. Furthermore, we found that some microbes previously considered seasonal (e.g., Archaea or Actinobacteria) were living in deeper layers within the photic zone during the stratification period. A strong depth-related specialization was detected, not only at the taxonomic level but also at the functional level, even within the different clades, for the manipulation and uptake of specific polysaccharides. Rhodopsin sequences (green or blue) also showed narrow depth distributions that correlated with the taxonomy of the microbe in which they were found but not with depth.

CONCLUSIONS

Although limited to a single location in the Mediterranean, this study has profound implications for our understanding of how marine microbial communities vary with depth within the photic zone when stratified. Our results highlight the importance of collecting samples at different depths in the water column when comparing seasonal variations and have important ramifications for global marine studies that most often take samples from only one single depth. Furthermore, our perspective and approaches (metagenomic assembly and recruitment) are broadly applicable to other metagenomic studies.

Time-delay-induced dynamical behaviors for an ecological vegetation growth system driven by cross-correlated multiplicative and additive noises

In this paper, the modified potential function, the stationary probability distribution function (SPDF), the mean growth time and the mean degeneration time for a vegetation growth system with time delay are investigated, where the vegetation system is assumed to be disturbed by cross-correlated multiplicative and additive noises. The results reveal some fact that the multiplicative and additive noises can both reduce the stability and speed up the decline of the vegetation system, while the strength of the noise correlation and time delay can both enhance the stability of the vegetation and slow down the depression process of the ecological system. On the other hand, with regard to the impacts of noises and time delay on the mean development and degeneration processes of the ecological system, it is discovered that 1) in the development process of the vegetation population, the increase of the noise correlation strength and time delay will restrain the regime shift from the barren state to the boom one, while the increase of the additive noise can lead to the fast regime shift from the barren state to the boom one. 2) Conversely, in the depression process of the ecological system, the increase of the strength of the correlation noise and time delay will prevent the regime shift from the boom state to the barren one. Comparatively, the increase of the additive and multiplicative noises can accelerate the regime shift from the boom state to the barren state.

Spatio-temporal dynamics of a planktonic system and chlorophyll distribution in a 2D spatial domain: matching model and data

Field data on chlorophyll distribution are investigated in a two-dimensional spatial domain of the Mediterranean Sea by using for phytoplankton abundances an advection-diffusion-reaction model, which includes real values for physical and biological variables. The study exploits indeed hydrological and nutrients data acquired in situ, and includes intraspecific competition for limiting factors, i.e. light intensity and phosphate concentration. As a result, the model allows to analyze how both the velocity field of marine currents and the two components of turbulent diffusivity affect the spatial distributions of phytoplankton abundances in the Modified Atlantic Water, the upper layer of the water column of the Mediterranean Sea. Specifically, the spatio-temporal dynamics of four phytoplankton populations, responsible for about 80% of the total chlorophyll a, are reproduced. Results for phytoplankton abundances obtained by the model are converted in chlorophyll a concentrations and compared with field data collected in twelve marine sites along the Cape Passero (Sicily)- Misurata (Libya) transect. Statistical checks indicate a good agreement between theoretical and experimental distributions of chlorophyll concentration. The study can be extended to predict the spatio-temporal behaviour of the primary production, and to prevent the consequent decline of some fish species in the Mediterranean Sea.

How diffusivity, thermocline and incident light intensity modulate the dynamics of deep chlorophyll maximum in Tyrrhenian Sea

During the last few years theoretical works have shed new light and proposed new hypotheses on the mechanisms which regulate the spatio-temporal behaviour of phytoplankton communities in marine pelagic ecosystems. Despite this, relevant physical and biological issues, such as effects of the time-dependent mixing in the upper layer, competition between groups, and dynamics of non-stationary deep chlorophyll maxima, are still open questions. In this work, we analyze the spatio-temporal behaviour of five phytoplankton populations in a real marine ecosystem by using a one-dimensional reaction-diffusion-taxis model. The study is performed, taking into account the seasonal variations of environmental variables, such as light intensity, thickness of upper mixed layer and profiles of vertical turbulent diffusivity, obtained starting from experimental findings. Theoretical distributions of phytoplankton cell concentration was converted in chlorophyll concentration, and compared with the experimental profiles measured in a site of the Tyrrhenian Sea at four different times (seasons) of the year, during four different oceanographic cruises. As a result we find a good agreement between theoretical and experimental distributions of chlorophyll concentration. In particular, theoretical results reveal that the seasonal changes of environmental variables play a key role in the phytoplankton distribution and determine the properties of the deep chlorophyll maximum. This study could be extended to other marine ecosystems to predict future changes in the phytoplankton biomass due to global warming, in view of devising strategies to prevent the decline of the primary production and the consequent decrease of fish species.

Delay-driven irregular spatiotemporal patterns in a plankton system

An inhomogeneous distribution of species density over physical space is a widely observed scenario in plankton systems. Understanding the mechanisms resulting in these spatial patterns is a central topic in plankton ecology. In this paper we explore the impact of time delay on spatiotemporal patterns in a prey-predator plankton system. We find that time delay can trigger the emergence of irregular spatial patterns via a Hopf bifurcation. Moreover, a phase transition from a regular spiral pattern to an irregular one was observed and the latter gradually replaced the former and persisted indefinitely. The characteristic length of the emergent spatial pattern is consistent with the scale of plankton patterns observed in field studies.

Dynamics of two picophytoplankton groups in mediterranean sea: analysis of the deep chlorophyll maximum by a stochastic advection-reaction-diffusion model

A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for the cell concentrations of the two picophytoplankton groups. The results are converted into chlorophyll a and divinil chlorophyll a concentrations and compared with experimental data collected in two different sites of the Sicily Channel (southern Mediterranean Sea). The comparison shows that real distributions are well reproduced by theoretical profiles. Specifically, position, shape and magnitude of the theoretical deep chlorophyll maximum exhibit a good agreement with the experimental values.