scholarly journals Atto-Foxes and Other Minutiae

2021 ◽  
Vol 83 (10) ◽  
Author(s):  
A. C. Fowler
Keyword(s):  
Continuous Model ◽  
Simple Explanation ◽  
Predator Prey ◽  
Large Numbers ◽  
Continuous Models ◽  
Number Dynamics ◽  
Stochastic Logistic Model ◽  
Age Structured ◽  
Age Structured Model ◽  
Type 3

AbstractThis paper addresses the problem of extinction in continuous models of population dynamics associated with small numbers of individuals. We begin with an extended discussion of extinction in the particular case of a stochastic logistic model, and how it relates to the corresponding continuous model. Two examples of ‘small number dynamics’ are then considered. The first is what Mollison calls the ‘atto-fox’ problem (in a model of fox rabies), referring to the problematic theoretical occurrence of a predicted rabid fox density of $$10^{-18}$$ 10 - 18 (atto-) per square kilometre. The second is how the production of large numbers of eggs by an individual can reliably lead to the eventual survival of a handful of adults, as it would seem that extinction then becomes a likely possibility. We describe the occurrence of the atto-fox problem in other contexts, such as the microbial ‘yocto-cell’ problem, and we suggest that the modelling resolution is to allow for the existence of a reservoir for the extinctively challenged individuals. This is functionally similar to the concept of a ‘refuge’ in predator–prey systems and represents a state for the individuals in which they are immune from destruction. For what I call the ‘frogspawn’ problem, where only a few individuals survive to adulthood from a large number of eggs, we provide a simple explanation based on a Holling type 3 response and elaborate it by means of a suitable nonlinear age-structured model.

scholarly journals An age-structured continuum model for myxobacteria

2018 ◽  
Vol 28 (09) ◽  
pp. 1737-1770 ◽  
Author(s):  
Pierre Degond ◽  
Angelika Manhart ◽  
Hui Yu
Keyword(s):  
Molecular Mechanisms ◽  
Ad Hoc ◽  
Order Approximation ◽  
Continuous Model ◽  
Two Dimensions ◽  
Macroscopic Model ◽  
Particle Model ◽  
Diffusion Term ◽  
Age Structured ◽  
Age Structured Model

Myxobacteria are social bacteria, that can glide in two dimensions and form counter-propagating, interacting waves. Here, we present a novel age-structured, continuous macroscopic model for the movement of myxobacteria. The derivation is based on microscopic interaction rules that can be formulated as a particle-based model and set within the Self-Organized Hydrodynamics (SOH) framework. The strength of this combined approach is that microscopic knowledge or data can be incorporated easily into the particle model, whilst the continuous model allows for easy numerical analysis of the different effects. However, we found that the derived macroscopic model lacks a diffusion term in the density equations, which is necessary to control the number of waves, indicating that a higher order approximation during the derivation is crucial. Upon ad hoc addition of the diffusion term, we found very good agreement between the age-structured model and the biology. In particular, we analyzed the influence of a refractory (insensitivity) period following a reversal of movement. Our analysis reveals that the refractory period is not necessary for wave formation, but essential to wave synchronization, indicating separate molecular mechanisms.

A multispecies statistical age-structured model to assess predator–prey balance: application to an intensively managed Lake Michigan pelagic fish community

2014 ◽  
Vol 71 (4) ◽  
pp. 627-644 ◽  
Author(s):  
Iyob Tsehaye ◽  
Michael L. Jones ◽  
James R. Bence ◽  
Travis O. Brenden ◽  
Charles P. Madenjian ◽  
...  
Keyword(s):  
Fish Community ◽  
Lake Michigan ◽  
Response Analysis ◽  
Functional Responses ◽  
Structured Model ◽  
Predator Prey ◽  
Modeling Approach ◽  
Trade Offs ◽  
Age Structured ◽  
Age Structured Model

Using a Bayesian modeling approach, we developed a multispecies statistical age-structured model to assess trade-offs between predatory demands and prey productivities, with the aim to inform management of top predators. Focusing on the Lake Michigan fish community, we assessed these trade-offs in terms of predation mortalities and productivities of alewife (Alosa pseudoharengus) and rainbow smelt (Osmerus mordax) and functional responses of salmonines. Our predation mortality estimates suggested that salmonine consumption has been a major driver of prey dynamics, with sharp declines in alewife abundance in the 1960s–1980s and the 2000s coinciding with increased predation rates. Our functional response analysis indicated that feedback mechanisms are unlikely to help maintain a predator–prey balance, with Chinook salmon (Oncorhynchus tshawytscha) and lake trout (Salvelinus namaycush) consumption declining only at the lowest prey densities, while the other salmonines consumed prey at a maximum rate across all observed prey densities. This study demonstrates that a multispecies modeling approach combining stock assessment methods with explicit consideration of predator–prey interactions can provide a basis for tactical decision-making from a broader ecosystem perspective.

scholarly journals The emergence of rabbit haemorrhagic disease virus: will a non-pathogenic strain protect the UK?

2001 ◽  
Vol 356 (1411) ◽  
pp. 1087-1095 ◽  
Author(s):  
P.J. White ◽  
R.A. Norman ◽  
R.C. Trout ◽  
E.A. Gould ◽  
P.J. Hudson
Keyword(s):  
Disease Virus ◽  
Pathogenic Strain ◽  
Rabbit Haemorrhagic Disease Virus ◽  
Rabbit Haemorrhagic Disease ◽  
Seroprevalence Data ◽  
Age Structured ◽  
Reproductive Rates ◽  
The Uk ◽  
Haemorrhagic Disease ◽  
Age Structured Model

Rabbit haemorrhagic disease virus emerged in China in 1984, and has killed hundreds of millions of wild rabbits in Australia and Europe. In the UK there appears to be an endemic non–pathogenic strain, with high levels of seroprevalence being recorded, in the absence of associated mortality. Using a seasonal, age–structured model we examine the hypothesis that differences in rabbit population demography differentially affect the basic reproductive rates ( R 0 ) of the pathogenic and non–pathogenic strains, leading to each dominating in some populations and not others. The strain with the higher R 0 excluded the other, with the dynamics depending upon the ratio of the two R 0 values. When the non–pathogenic strain dominated, the pathogenic strain caused only transient mortality, although this could be significant when the two R 0 values were similar. When the pathogenic strain dominated, repeated epidemics led to host eradication. Seroprevalence data suggest that the non–pathogenic strain may be protecting some, but not all UK populations, with half being ‘at risk’ from invasion by the pathogenic strain and a fifth prone to significant transient mortality. We identify key questions for empirical research to test this prediction.

POTENTIAL YIELD OF A ROCK SHRIMP STOCK, SICYONIA PENICILLATA IN THE NORTHERN GULF OF CALIFORNIA

Crustaceana ◽  
1999 ◽  
Vol 72 (6) ◽  
pp. 581-590 ◽  
Author(s):  
Juana Lopez-Martinez ◽  
Edgar Alcantara-Razo ◽  
Sergio Hernandez-Vazquez ◽  
Ernesto Chavez
Keyword(s):  
Gulf Of California ◽  
Age Groups ◽  
Potential Yield ◽  
Natural Oscillations ◽  
Recruitment Pattern ◽  
Stock Recruitment ◽  
Age Structured ◽  
Stochastic Recruitment ◽  
Age Structured Model ◽  
Compensatory Effect

AbstractA stock of rock shrimp Sicyonia penicillata was assessed in a fishery recently opened at Bahoa Kino, Sonora, Mexico. An age-structured model with stochastic recruitment was developed, which considers growth rate, natural mortality, and fishing mortality by age. Age groups were followed year by year with a stock-recruitment Ricker function where the seasonal recruitment pattern was defined as well. Simulations might be interpreted as showing a stable population with four year cycles, reflecting a density-dependent process. In 1996, fishing intensity had an apparent compensatory effect on the stock, decreasing the amplitude of natural oscillations and maintaining the stock at a biomass level similar to the size observed in a condition of no exploitation. The stock was found currently underexploited. As a result of the seasonal accessibility and the age of first-catch fishing (adult shrimp), the stock might be capable to withstand high fishing pressure without being overexploited. Se evaluo una poblacion de camaron de roca Sicyonia penicillata, de una pesqueroa recientemente abierta en Bahoa Kino, Sonora, Mexico. Se desarrollo un modelo basado en la estructura por edades que considera reclutamiento estocastico, tasa de crecimiento, mortalidad natural y mortalidad por pesca por grupo de edad. Estos grupos de edad fueron determinados ano tras ano mediante la funcion de reclutamiento de Ricker, en los que tambien se definio el patron estacional de reclutamiento. Las simulaciones muestran una poblacion estable con ciclos de cuatro anos, que indican un proceso de densodependencia. En 1996, la intensidad de pesca tuvo un efecto compensatorio sobre la poblacion, reduciendo la amplitud de las oscilaciones naturales y manteniendo al stock en un nivel de biomasa similar al observado en la condicion sin explotacion. Se encontro que el recurso esta subexplotado. Como resultado de la accesibilidad estacional y de que la edad de primera captura corresponde a camaron adulto, el recurso soporta alta presion de pesca sin dar evidencias de sobreexplotacion.

scholarly journals The development and validation of an age-structured model for the evaluation of disease control strategies for intestinal helminths

Parasitology ◽  
1994 ◽  
Vol 109 (3) ◽  
pp. 389-396 ◽  
Author(s):  
M. S. Chan ◽  
H. L. Guyatt ◽  
D. A. P. Bundy ◽  
G. F. Medley
Keyword(s):  
Helminth Infection ◽  
Control Strategies ◽  
Intestinal Helminth ◽  
Intestinal Helminths ◽  
Parasite Control ◽  
Age Related ◽  
Control Programmes ◽  
Age Structured ◽  
Development And Validation ◽  
Age Structured Model

SummaryEpidemiological modelling can be a useful tool for the evaluation of parasite control strategies. An age-structured epidemiological model of intestinal helminth dynamics is developed. This model includes the explicit representation of changing worm distributions between hosts as a result of treatment, and estimates the morbidity due to heavy infections. The model is used to evaluate the effectiveness of different programmes of age-targeted community chemotherapy in reducing the amount of morbidity due to helminth infection. The magnitude of age-related heterogeneities is found to be very important in determining the results of age-targeted treatment programmes. The model was verified using field data from control programmes for Ascaris lumbricoides and Trichuris trichiura, and was found to provide accurate predictions of prevalence and mean intensities of infection during and following different control regimes.

An Age-Structured Model of Fish Population Enhancement

2002 ◽  
pp. 376-394
Author(s):  
Richard Langton ◽  
James Lindholm ◽  
James Wilson ◽  
Sally Sherman
Keyword(s):  
Fish Population ◽  
Structured Model ◽  
Age Structured ◽  
Age Structured Model
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