A model for blue-green algae and gorillas

1977 ◽  
Vol 14 (4) ◽  
pp. 675-688 ◽  
Author(s):  
Byron J. T. Morgan ◽  
B. Leventhal
Keyword(s):  
Exact Solutions ◽  
Green Algae ◽  
Death Rate ◽  
Death Process ◽  
Birth And Death Process ◽  
Mean Values ◽  
Blue Green Algae ◽  
Supercritical Case ◽  
The Mean ◽  
Runge Kutta

The linear birth-and-death process is elaborated to allow the elements of the process to live as members of linear clusters which have the possibility of breaking up. For the supercritical case, expressions, based on an approximation, are derived for the mean numbers of clusters of the various sizes as time → ∞. These expressions compare very well with exact solutions obtained by the method of Runge-Kutta. Exact solutions for the mean values for all time are given for when the death rate is zero.

A model for blue-green algae and gorillas

1977 ◽  
Vol 14 (04) ◽  
pp. 675-688 ◽  
Author(s):  
Byron J. T. Morgan ◽  
B. Leventhal
Keyword(s):  
Exact Solutions ◽  
Green Algae ◽  
Death Rate ◽  
Death Process ◽  
Birth And Death Process ◽  
Mean Values ◽  
Blue Green Algae ◽  
Supercritical Case ◽  
The Mean ◽  
Runge Kutta

The linear birth-and-death process is elaborated to allow the elements of the process to live as members of linear clusters which have the possibility of breaking up. For the supercritical case, expressions, based on an approximation, are derived for the mean numbers of clusters of the various sizes as time → ∞. These expressions compare very well with exact solutions obtained by the method of Runge-Kutta. Exact solutions for the mean values for all time are given for when the death rate is zero.

On the parity of individuals in birth and death processes

1982 ◽  
Vol 14 (03) ◽  
pp. 484-501
Author(s):  
S. K. Srinivasan ◽  
C. R. Ranganathan
Keyword(s):  
General Model ◽  
Death Process ◽  
Birth And Death Process ◽  
Birth Rates ◽  
Birth And Death Processes ◽  
Age Dependent ◽  
The Mean ◽  
Number Of Individuals ◽  
Number Of Births

This paper deals with the parity of individuals in an age-dependent birth and death process. A more general model with parity and age-dependent birth rates is also considered. The mean number of individuals with parity 0, 1, 2, ·· ·is obtained for the two models. The first moments of the total number of births in the population up to time t and the sum of the parities of the individuals existing at time t are obtained. A brief discussion on the parity of individuals in a population including ‘twins' is also given.

A linear birth-and-death predator–prey process

1995 ◽  
Vol 32 (01) ◽  
pp. 274-277
Author(s):  
John Coffey
Keyword(s):  
Death Rate ◽  
Birth Rate ◽  
Prey Population ◽  
Death Process ◽  
Predator Population ◽  
Birth And Death Process ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ 1 X and death rate μ 1 X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ 2 Y and the death rate is . It is proven that and iff

The asymptotic behaviour of a divergent linear birth and death process

1978 ◽  
Vol 15 (1) ◽  
pp. 187-191 ◽  
Author(s):  
John Haigh
Keyword(s):  
Asymptotic Behaviour ◽  
Death Rate ◽  
High Probability ◽  
Birth Rate ◽  
Mean Value ◽  
Death Process ◽  
Applied Probability ◽  
Birth And Death Process ◽  
Initial Size

A recent paper in Advances in Applied Probability (Siegel (1976)) considered the duration of the time Tmn for a linear birth and death process to grow from a (large) initial size m to a larger size n. The main aim was to show that, when the birth rate exceeds the death rate, Tmn is close to its mean value, log n/m, with high probability. This paper establishes this result using much simpler techniques.

scholarly journals On selecting the most reliable components

1998 ◽  
Vol 2 (2) ◽  
pp. 133-145 ◽  
Author(s):  
Dylan Shi
Keyword(s):  
Markov Process ◽  
Death Process ◽  
Series System ◽  
Birth And Death Process ◽  
Retrograde Motion ◽  
The Past ◽  
Optimal Policies ◽  
Average Proportion ◽  
The Mean ◽  
Mean Time

Consider a series system consisting of n components of k types. Whenever a unit fails, it is replaced immediately by a new one to keep the system working. Under the assumption that all the life lengths of the components are independent and exponentially distributed and that the replacement policies depend only on the present state of the system at each failure, the system may be represented by a birth and death process. The existence of the optimum replacement policies are discussed and the ε-optimal policies axe derived. If the past experience of the system can also be utilized, the process is not a Markov process. The optimum Bayesian policies are derived and the properties of the resulting process axe studied. Also, the stochastic processes are simulated and the probability of absorption, the mean time to absorption and the average proportion of the retrograde motion are approximated.

Interparticle dependence in a linear death process subjected to a random environment

1990 ◽  
Vol 27 (3) ◽  
pp. 491-498 ◽  
Author(s):  
Claude Lefèvre ◽  
György Michaletzky
Keyword(s):  
Random Environment ◽  
Death Rate ◽  
Monotone Function ◽  
Death Process ◽  
Birth And Death Process ◽  
Survival Times ◽  
Current State ◽  
Non Linear

Recently, Ball and Donnelly (1987) investigated the nature of the interparticle dependence in a death process with non-linear rates. In this note, after some remarks on their result, a similar problem is examined for a linear death process where the death rate per particle is a monotone function of the current state of a random environment. It is proved that if the exterior process involved is a homogeneous birth-and-death process valued in ℕ, then the survival times of any subset of particles are positively upper orthant dependent. A simple example shows that this property is not valid for general exterior processes.

Interparticle dependence in a linear death process subjected to a random environment

1990 ◽  
Vol 27 (03) ◽  
pp. 491-498 ◽  
Author(s):  
Claude Lefèvre ◽  
György Michaletzky
Keyword(s):  
Random Environment ◽  
Death Rate ◽  
Monotone Function ◽  
Death Process ◽  
Birth And Death Process ◽  
Survival Times ◽  
Current State ◽  
Non Linear

Recently, Ball and Donnelly (1987) investigated the nature of the interparticle dependence in a death process with non-linear rates. In this note, after some remarks on their result, a similar problem is examined for a linear death process where the death rate per particle is a monotone function of the current state of a random environment. It is proved that if the exterior process involved is a homogeneous birth-and-death process valued in ℕ, then the survival times of any subset of particles are positively upper orthant dependent. A simple example shows that this property is not valid for general exterior processes.

scholarly journals Modeling Neutral Evolution Using an Infinite-Allele Markov Branching Process

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaowei Wu ◽  
Marek Kimmel
Keyword(s):  
Frequency Spectrum ◽  
Branching Process ◽  
Asymptotic Expression ◽  
Interval Estimation ◽  
Neutral Evolution ◽  
Death Process ◽  
Birth And Death Process ◽  
Markov Branching Process ◽  
The Mean ◽  
Time Point

We consider an infinite-allele Markov branching process (IAMBP). Our main focus is the frequency spectrum of this process, that is, the proportion of alleles having a given number of copies at a specified time point. We derive the variance of the frequency spectrum, which is useful for interval estimation and hypothesis testing for process parameters. In addition, for a class of special IAMBP with birth and death offspring distribution, we show that the mean of its limiting frequency spectrum has an explicit form in terms of the hypergeometric function. We also derive an asymptotic expression for convergence rate to the limit. Simulations are used to illustrate the results for the birth and death process.

scholarly journals Studies in the dynamics of disinfection. XI. The effect of lethal temperatures on standard cultures ofBact. coli. IV. An investigation of that portion of the population which survives prolonged exposure atpH 7·0

1947 ◽  
Vol 45 (3) ◽  
pp. 342-353 ◽  
Author(s):  
R. C. Jordan ◽  
S. E. Jacobs ◽  
H. E. F. Davies
Keyword(s):  
Heat Resistance ◽  
Death Rate ◽  
Prolonged Exposure ◽  
Death Rates ◽  
Mean Values ◽  
The Third ◽  
Lethal Temperatures ◽  
Viable Cells ◽  
The Mean ◽  
Experimental Findings

1. An attempt has been made to discover the origin and nature of the small proportion of the cells in standard cultures ofBact. coliwhich is able to withstand, apparently indefinitely, exposure to temperatures of 49, 51 and 53° C.2. The method adopted was to allow these survivors to generate fresh cultures in the same flask merely by reducing the temperature to 35° C. and to subject the resulting cultures in turn to heat treatment. Only one process of regeneration and subsequent disinfection was carried out at 49 and 53° C., but at 51° C. the process was repeated four times. The disinfection curve was determined on each occasion and the permanent population allowed to become established.3. Changes in the heat resistance of the cultures were judged by (a) the disinfection times (99·99 % mortality), (b) the maximum death-rates, (c) the levels of the surviving populations and (d) the variations in death-rate with time during each disinfection.4. Marked fluctuation in numbers of viable cells was observed during each of the phases of permanent surviving population. The exact levels of survivors were therefore uncertain, but after exposure to 49° C. the mean values were not higher than when 53° C. was used, nor was there an increase in the mean numbers of survivors in the successively regenerated cultures.5. The survivors did not grow when inoculated into either nutrient agar plates or tubes of broth held at the respective high temperatures, although they remained alive and developed readily on being transferred to 35° C.6. The maximum death-rate decreased and the disinfection time increased markedly after one regeneration of the cultures. The increase in the latter was not wholly due to the decrease in the former, as the death-rates throughout the disinfection of the regenerated culture were lower.7. After the second regeneration (at 51° C.) the maximum death-rate declined and the disinfection time rose still higher, but the process was reversed after the third and fourth regenerations.8. The shape of the graph of log survivors against time altered markedly after the second regeneration at 51° C. The initial death-rate was higher but fell sharply to a minimum before rising again to the final maximum.9. The experimental findings are discussed. An increase in the general heat resistance of these cultures may have occurred as a result of one regeneration, but the technique employed permitted the gradual alteration of the environmental conditions, and this appears to have exerted complex effects on the cultures so that the results of further regenerations are inconclusive.

The asymptotic behaviour of a divergent linear birth and death process

1978 ◽  
Vol 15 (01) ◽  
pp. 187-191 ◽  
Author(s):  
John Haigh
Keyword(s):  
Asymptotic Behaviour ◽  
Death Rate ◽  
High Probability ◽  
Birth Rate ◽  
Mean Value ◽  
Death Process ◽  
Applied Probability ◽  
Birth And Death Process ◽  
Initial Size

A recent paper in Advances in Applied Probability (Siegel (1976)) considered the duration of the time Tmn for a linear birth and death process to grow from a (large) initial size m to a larger size n. The main aim was to show that, when the birth rate exceeds the death rate, Tmn is close to its mean value, log n/m, with high probability. This paper establishes this result using much simpler techniques.

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