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Register a new userFluctuations and Dispersal Rates in Population Dyanmics
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Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V. Hutson, K. Mischaikow, et al., J. Math. Bio. 37, 61 (1998)) of two species which differ only in their dispersal rates the slow species always dominates. We demonstrate that fluctuations can change this conclusion and can lead to dominance by the fast species or to coexistence, depending on parameters. We discuss two different effects of fluctuations, and show that our results are consistent with more complex treatments that find that selected dispersal rates are not monotonic with the cost of migration.
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In his seminal work in the 1970s Robert May suggested that there was an upper limit to the number of species that could be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed complexity of many natural ecosystems. The so-called stability-diversity debate ensued, and the discussion about the factors making an ecosystem stable or unstable continues to this day. We show in this work that dispersal can be a destabilising influence. To do this, we combine ideas from Alan Turings work on pattern formation with Mays random-matrix approach. We demonstrate how a stable equilibrium in a complex ecosystem with two trophic levels can become unstable with the introduction of dispersal in space. Conversely, we show that Turing instabilities can occur more easily in complex ecosystems with many species than in the case of only a few species. Our work shows that adding more details to the model of May gives rise to more ways in which an equilibrium can become unstable. Making Mays simple model more realistic is therefore unlikely to remove the upper bound on complexity.
This study analyzed the morbidity and mortality rates of the COVID-19 pandemic in different prefectures of Japan. Under the constraint that daily maximum confirmed deaths and daily maximum cases should exceed 4 and 10, respectively, 14 prefectures were included, and cofactors affecting the morbidity and mortality rates were evaluated. In particular, the number of confirmed deaths was assessed excluding the cases of nosocomial infections and nursing home patients. A mild correlation was observed between morbidity rate and population density (R2=0.394). In addition, the percentage of the elderly per population was also found to be non-negligible. Among weather parameters, the maximum temperature and absolute humidity averaged over the duration were found to be in modest correlation with the morbidity and mortality rates, excluding the cases of nosocomial infections. The lower morbidity and mortality are observed for higher temperature and absolute humidity. Multivariate analysis considering these factors showed that determination coefficients for the spread, decay, and combined stages were 0.708, 0.785, and 0.615, respectively. These findings could be useful for intervention planning during future pandemics, including a potential second COVID-19 outbreak.
Dispersal-induced growth (DIG) occurs when two populations with time-varying growth rates, each of which, when isolated, would become extinct, are able to persist and grow exponentially when dispersal among the two populations is present. This work provides a mathematical exploration of this surprising phenomenon, in the context of a deterministic model with periodic variation of growth rates, and characterizes the factors which are important in generating the DIG effect and the corresponding conditions on the parameters involved.
Traditional approaches to ecosystem modelling have relied on spatially homogeneous approximations to interaction, growth and death. More recently, spatial interaction and dispersal have also been considered. While these leads to certain changes in community dynamics, their effect is sometimes fairly minimal, and demographic scenarios in which this difference is important have not been systematically investigated. We take a simple mean-field model which simulates birth, growth and death processes, and rewrite it with spatially distributed discrete individuals. Each individuals growth and mortality is determined by a competition measure which captures the effects of neighbours in a way which retains the conceptual simplicity of a generic, analytically-solvable model. Although the model is generic, we here parameterise it using data from Caledonian Scots Pine stands. The dynamics of simulated populations, starting from a plantation lattice configuration, mirror those of well-established qualitative descriptions of natural forest stand behaviour; an analogy which assists in understanding the transition from artificial to old-growth structure. When parameterised for Scots Pine populations, the signature of spatial processes is evident, but they do not have a large effect on first-order statistics such as density and biomass. The sensitivity of this result to variation in each individual rate parameter is investigated; distinct differences between spatial and mean-field models are seen only upon alteration of the interaction strength parameters, and in low density populations. Under the Scots Pine parameterisation, dispersal also has an effect of spatial structure, but not first-order properties. Only in more intense competitive scenarios does altering the relative scales of dispersal and interaction lead to a clear signal in first order behaviour.
We introduce a model of traveling agents ({it e.g.} frugivorous animals) who feed on randomly located vegetation patches and disperse their seeds, thus modifying the spatial distribution of resources in the long term. It is assumed that the survival probability of a seed increases with the distance to the parent patch and decreases with the size of the colonized patch. In turn, the foraging agents use a deterministic strategy with memory, that makes them visit the largest possible patches accessible within minimal travelling distances. The combination of these interactions produce complex spatio-temporal patterns. If the patches have a small initial size, the vegetation total mass (biomass) increases with time and reaches a maximum corresponding to a self-organized critical state with power-law distributed patch sizes and Levy-like movement patterns for the foragers. However, this state collapses as the biomass sharply decreases to reach a noisy stationary regime characterized by corrections to scaling. In systems with low plant competition, the efficiency of the foraging rules leads to the formation of heterogeneous vegetation patterns with $1/f^{alpha}$ frequency spectra, and contributes, rather counter-intuitively, to lower the biomass levels.
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