A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal

AbstractAccording to classic theory, species’ population dynamics and distributions are less influenced by species interactions under harsh climatic conditions compared to under more benign climatic conditions. In alpine and boreal ecosystems in Fennoscandia, the cyclic dynamics of rodents strongly affect many other species, including ground-nesting birds such as ptarmigan. According to the ‘alternative prey hypothesis’ (APH), the densities of ground-nesting birds and rodents are positively associated due to predator-prey dynamics and prey-switching. However, it remains unclear how the strength of these predator-mediated interactions change along a climatic harshness gradient in comparison with the effects of climatic variation. We built a hierarchical Bayesian model to estimate the sensitivity of ptarmigan populations to interannual variation in climate and rodent occurrence across Norway during 2007–2017. Ptarmigan abundance was positively linked with rodent occurrence, consistent with the APH. Moreover, we found that rodent dynamics had stronger effects on ptarmigan in colder regions. Our study highlights how species interactions play an important role for the population dynamics of species at higher latitudes and suggests that they can become even more important in the most climatically harsh regions.

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Coarse, Medium or Fine? A Quantum Mechanics Approach to Single Species Population Dynamics

10.1101/2020.07.22.215061 ◽

2020 ◽

Author(s):

Olcay Akman ◽

Leon Arriola ◽

Aditi Ghosh ◽

Ryan Schroeder

Keyword(s):

Population Dynamics ◽

Quantum Mechanics ◽

Single Species ◽

Stable Equilibrium Point ◽

Ode Model ◽

Deterministic Models ◽

Species Population ◽

Quantum Approach ◽

Single Species Population ◽

Quantum Framework

AbstractStandard heuristic mathematical models of population dynamics are often constructed using ordinary differential equations (ODEs). These deterministic models yield pre-dictable results which allow researchers to make informed recommendations on public policy. A common immigration, natural death, and fission ODE model is derived from a quantum mechanics view. This macroscopic ODE predicts that there is only one stable equilibrium point . We therefore presume that as t → ∞, the expected value should be . The quantum framework presented here yields the same standard ODE model, however with very unexpected quantum results, namely . The obvious questions are: why isn’t , why are the probabilities ≈ 0.37, and where is the missing probability of 0.26? The answer lies in quantum tunneling of probabilities. The goal of this paper is to study these tunneling effects that give specific predictions of the uncertainty in the population at the macroscopic level. These quantum effects open the possibility of searching for “black–swan” events. In other words, using the more sophisticated quantum approach, we may be able to make quantitative statements about rare events that have significant ramifications to the dynamical system.

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Mathematical Modeling and Stability Analysis of Population Dynamics

Dynamical Systems, Bifurcation Analysis and Applications - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-981-32-9832-3_1 ◽

2019 ◽

pp. 3-13 ◽

Cited By ~ 1

Author(s):

Auni Aslah Mat Daud

Keyword(s):

Mathematical Modeling ◽

Population Dynamics ◽

Stability Analysis

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Predicting coral community recovery using multi-species population dynamics models

Ecology Letters ◽

10.1111/ele.13153 ◽

2018 ◽

Vol 21 (12) ◽

pp. 1790-1799 ◽

Cited By ~ 18

Author(s):

Mohsen Kayal ◽

Hunter S. Lenihan ◽

Andrew J. Brooks ◽

Sally J. Holbrook ◽

Russell J. Schmitt ◽

...

Keyword(s):

Population Dynamics ◽

Coral Community ◽

Community Recovery ◽

Species Population ◽

Population Dynamics Models ◽

Dynamics Models

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II.2 Density Dependence and Single-Species Population Dynamics

The Princeton Guide to Ecology ◽

10.1515/9781400833023.166 ◽

2009 ◽

pp. 166-171 ◽

Cited By ~ 3

Keyword(s):

Population Dynamics ◽

Density Dependence ◽

Single Species ◽

Species Population ◽

Single Species Population

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Evaluating the effect of predation mortality on forage species population dynamics in the Northeast US continental shelf ecosystem using multispecies virtual population analysis

ICES Journal of Marine Science ◽

10.1093/icesjms/fsn185 ◽

2008 ◽

Vol 65 (9) ◽

pp. 1689-1700 ◽

Cited By ~ 23

Author(s):

Megan C. Tyrrell ◽

Jason S. Link ◽

Hassan Moustahfid ◽

William J. Overholtz

Keyword(s):

Population Dynamics ◽

Continental Shelf ◽

Population Analysis ◽

Northwest Atlantic ◽

Virtual Population Analysis ◽

Virtual Population ◽

Predation Mortality ◽

Forage Species ◽

Species Population ◽

Northeast Us

AbstractTyrrell, M. C., Link, J. S., Moustahfid, H., and Overholtz, W. J. 2008. Evaluating the effect of predation mortality on forage species population dynamics in the Northeast US continental shelf ecosystem using multispecies virtual population analysis. – ICES Journal of Marine Science, 65: 1689–1700. An expanded version of multispecies virtual population analysis (MSVPA) is used to analyse the effects of predation by 14 key predators on Atlantic herring and Atlantic mackerel in the Northwest Atlantic ecosystem for the period 1982–2002. For herring, MSVPA produced greater abundance estimates than single-species assessments, especially for the youngest age classes. The average rate of predation mortality for herring aged 0 and 1 was also higher than the standard total natural mortality rate (0.2) for the 21-year time frame (0.84–3.2). The same was true for mackerel in this MSVPA (0.37–1.6). Consumptive removals of herring and mackerel generally increased over time. From 1999 to 2001, the biomass removed by predators exceeded each species' commercial landings. The sum of consumption and landings notably exceeded the multispecies maximum sustainable yield for herring for the years 1995–2002 and for mackerel for the period 1999–2002. We highlight the importance of accounting for predation on forage species in the context of changes to the fish community that have taken place in the Northwest Atlantic over the past few decades.

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