The paradox of the plankton highlights the apparent contradiction between Gauses law of competitive exclusion and the observed diversity of phytoplankton. It is well known that phytoplankton dynamics depend heavily on two main resources: light and nutrients. Here we treat light as a continuum of resources rather than a single resource by considering the visible light spectrum. We propose a spatially explicit reaction-diffusion-advection model to explore under what circumstance coexistence is possible from mathematical and biological perspectives. Furthermore, we provide biological context as to when coexistence is expected based on the degree of niche differentiation within the light spectrum and overall turbidity of the water.
Empirical observations in marine ecosystems have suggested a balance of biological and advection time scales as a possible explanation of species coexistence. To characterise this scenario, we measure the time to fixation in neutrally evolving populations in chaotic flows. Contrary to intuition the variation of time scales does not interpolate straightforwardly between the no-flow and well-mixed limits; instead we find that fixation is the slowest at intermediate Damkohler numbers, indicating long-lasting coexistence of species. Our analysis shows that this slowdown is due to spatial organisation on an increasingly modularised network. We also find that diffusion can either slow down or speed up fixation, depending on the relative time scales of flow and evolution.
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model describing the competition of two species and incorporating all the above ingredients. We find that the presence of habitat preference --- generating spatial niches --- strongly stabilizes the coexistence of the two species. Eliminating habitat preference --- neutral dynamics --- the model generates patterns, such as distribution of population sizes, practically identical to those obtained in the presence of habitat preference, provided an higher immigration rate is considered. Notwithstanding the similarity in the population distribution, we show that invasibility properties depend on habitat preference in a non-trivial way. In particular, the neutral model results results more invasible or less invasible depending on whether the comparison is made at equal immigration rate or at equal distribution of population size, respectively. We discuss the relevance of these results for the interpretation of invasibility experiments and the species occupancy of preferred habitats.
In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in Wuhan, China and later spread to every corner of the globe. Whilst the number of infection-induced deaths in Ghana, West Africa are minimal when compared with the rest of the world, the impact on the local health service is still significant. Compartmental models are a useful framework for investigating transmission of diseases in societies. To understand how the infection will spread and how to limit the outbreak. We have developed a modified SEIR compartmental model with nine compartments (CoVCom9) to describe the dynamics of SARS-CoV-2 transmission in Ghana. We have carried out a detailed mathematical analysis of the CoVCom9, including the derivation of the basic reproduction number, $mathcal{R}_{0}$. In particular, we have shown that the disease-free equilibrium is globally asymptotically stable when $mathcal{R}_{0}<1$ via a candidate Lyapunov function. Using the SARS-CoV-2 reported data for confirmed-positive cases and deaths from March 13 to August 10, 2020, we have parametrised the CoVCom9 model. The results of this fit show good agreement with data. We used Latin hypercube sampling-rank correlation coefficient (LHS-PRCC) to investigate the uncertainty and sensitivity of $mathcal{R}_{0}$ since the results derived are significant in controlling the spread of SARS-CoV-2. We estimate that over this five month period, the basic reproduction number is given by $mathcal{R}_{0} = 3.110$, with the 95% confidence interval being $2.042 leq mathcal{R}_0 leq 3.240$, and the mean value being $mathcal{R}_{0}=2.623$. Of the 32 parameters in the model, we find that just six have a significant influence on $mathcal{R}_{0}$, these include the rate of testing, where an increasing testing rate contributes to the reduction of $mathcal{R}_{0}$.
Thermoregulation in honey bee colonies during winter is thought to be self-organised. We added mortality of individual honey bees to an existing model of thermoregulation to account for elevated losses of bees that are reported worldwide. The aim of analysis is to obtain a better fundamental understanding of the consequences of individual mortality during winter. This model resembles the well-known Keller-Segel model. In contrast to the often studied Keller-Segel models, our model includes a chemotactic coefficient of which the sign can change as honey bees have a preferred temperature: when the local temperature is too low, they move towards higher temperatures, whereas the opposite is true for too high temperatures. Our study shows that we can distinguish two states of the colony: one in which the colony size is above a certain critical number of bees in which the bees can keep the core temperature of the colony above the threshold temperature, and one in which the core temperature drops below the critical threshold and the mortality of the bees increases dramatically, leading to a sudden death of the colony. This model behaviour may explain the globally observed honey bee colony losses during winter.
Cyclic dominance is frequently believed to be a mechanism that maintains diversity of competing species. But this delicate balance could also be fragile if some of the members is weakened because an extinction of a species will involve the annihilation of its predator hence leaving only a single species alive. To check this expectation we here introduce a fourth species which chases exclusively a single member of the basic model composed by three cyclically dominant species. Interestingly, the coexistence is not necessarily broken and we have detected three consecutive phase transitions as we vary only the invasion strength of the fourth pestilent species. The resulting phases are analyzed by different techniques including the study of the Hamming distance density profiles. Some of our observations strengthen previous findings about cyclically dominant system, but they also offer new revelations and counter-intuitive phenomenon, like supporting pestilent species may result in its extinction, hence enriching our understanding about these very simple but still surprisingly complex systems.
Christopher M. Heggerud
,King-Yeung Lam
,Hao Wang
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(2021)
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"Niche differentiation in the light spectrum promotes coexistence of phytoplankton species: a spatial modelling approach"
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Christopher Heggerud M
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