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  • 1
    Electronic Resource
    Electronic Resource
    How many victims will a pitfall make? (1979)
    Springer
    Acta biotheoretica 28 (1979), S. 98-122 
    Details
    ISSN: 1572-8358
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract A model for the trapping of animals with a circular pitfall is formulated. The model's assumptions are: (1) The animals move independently according to the same Brownian motions. (2) The boundary of the pitfall acts as an absorbing or elastic barrier. (3) Initially a fixed number of animals is independently homogeneously distributed over a finite study area (a), or the initial positions follow a homogeneous planar Poisson process (b). The model depends on three free parameters: (i) the motility of the animals, (ii) their reaction to the pitfall, (iii) the initial density. It appears that the catches in disjoint time intervals are multinomially (a) or independently Poisson (b) distributed. The parameters of these distributions are obtained by solving certain partial differential equations. Estimation and testing problems are considered, and the data of some laboratory and field experiments are analyzed. It appears that it is possible to estimate both the animals' motility and density from a pitfall experiment. However, the accuracy is very low. To solve this problem at least partially, experiments for the separate estimation of parameters other than the density are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046807
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  • 2
    Electronic Resource
    Electronic Resource
    Reviews (1975)
    Springer
    Acta biotheoretica 24 (1975), S. 77-81 
    Details
    ISSN: 1572-8358
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01556742
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  • 3
    Electronic Resource
    Electronic Resource
    Review (1973)
    Springer
    Acta biotheoretica 22 (1973), S. 207-210 
    Details
    ISSN: 1572-8358
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01813228
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  • 4
    Electronic Resource
    Electronic Resource
    Review (1972)
    Springer
    Acta biotheoretica 21 (1972), S. 306-307 
    Details
    ISSN: 1572-8358
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557184
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  • 5
    Electronic Resource
    Electronic Resource
    The epidemic in a closed population with all susceptibles equally vulnerable; some results for large susceptible populations and small initial infections (1978)
    Springer
    Acta biotheoretica 27 (1978), S. 75-123 
    Details
    ISSN: 1572-8358
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Kendall's (1956) approach to the ‘general’ epidemic is generalized by dropping the assumptions of constant infectivity and random recovery or death of ill individuals. A great deal of attention is paid to the biological background and the heuristics of the model formulation. Some new results are: (l) the derivation of Kermack's and McKendrick's integral equation from what seems to be the most general set of assumptions in section 2.2, (2) the use of Kermack's and McKendrick's final value equation to arrive at a finite time version of the threshold theorem for the general case, comparable to that for the case of only one Markovian state of illness in section 2.5, (3) the analysis of the behaviour of the solutions of the integral equation when the starting infection approaches zero in section 2.7, (4) the derivation of the probability structure of a general branching process, after conditioning on extinction in section 3.6, (5) the statement of the generalized versions of Kendall's ideas in the form of precise limit conjectures in section 4, (6) the derivation of a closed expression for the limit epidemic resulting from (3) in appendix 4.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00048405
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  • 6
    Electronic Resource
    Electronic Resource
    What are the advantages of dispersing; a paper by Kuno explained and extended (1983)
    Springer
    Oecologia 57 (1983), S. 166-169 
    Details
    ISSN: 1432-1939
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary Contrary to Kuno's (1981) contention, dispersing does not help and individual to get a larger average progeny in an unpredictable and heterogeneous but nonlimiting environment: average progeny is exactly equal for (partially) dispersing and nondispersing populations. However, the geometric time averages of pro-capita reproduction as well as geometric averages over replicates of final progeny size after a fixed number of years differ, just as Kuno asserts. Moreover, if populations of the two types are grown in mixed culture it is the disperser who will win in the long run. This even applies if dispersal means the incurring of some additional mortality. Models with partial dispersal are much more complicated to deal with than models with either a complete redistribution each generation or no dispersal at all, contrary to the assertion of e.g. Venable and Lawlor (1980). Partial dispersers will win from nondispersers, but the optimal amount of dispersal unfortunately seems to depend sensitively on the details of the model specification, except that it has to be small if the number of independent patches is large.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00379576
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  • 7
    Electronic Resource
    Electronic Resource
    Reflections and calculations on a prey-predator-patch problem (1989)
    Springer
    Acta applicandae mathematicae 14 (1989), S. 23-35 
    Details
    ISSN: 1572-9036
    Keywords: 92A15 ; physiologically structured population models ; predator-prey-plant interaction ; patch structure, model simplification ; time scale arguments ; qualitative analysis ; multiple stable steady states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: This paper is concerned with models for the interaction of plants, herbivores and their predators. We concentrate on situations in which local colonies of herbivores either over-exploit their host plant or are driven to extinction by predators. Starting from a complicated structured model, in which the local prey and predator density within patches is taken into account, we use time scale arguments to derive a three dimensional system of ordinary differential equations. The simplified system is analysed and the existence of multiple stable steady states is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046671
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  • 8
    Electronic Resource
    Electronic Resource
    The saturating contact rate in marriage- and epidemic models (1993)
    Springer
    Journal of mathematical biology 31 (1993), S. 529-539 
    Details
    ISSN: 1432-1416
    Keywords: Contact rate ; Time-scale arguments ; Mass-action kinetics ; Epidemic models ; Marriage models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this note we show how to derive, by a mechanistic argument, an expression for the saturating contact rate of individual contacts in a population that mixes randomly. The main assumption is that the individual interaction times are typically short as compared to the time-scale of changes in, for example, individual-type, but that the interactions yet make up a considerable fraction of the time-budget of an individual. In special cases an explicit formula for the contact rate is obtained. The result is applied to mathematical epidemiology and marriage models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00173891
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  • 9
    Electronic Resource
    Electronic Resource
    Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. Part I: The full model and some of its limits (1985)
    Springer
    Journal of mathematical biology 22 (1985), S. 209-238 
    Details
    ISSN: 1432-1416
    Keywords: Functional response ; Structured population models ; Markov processes approximating stochastic processes ; van Kampen expansion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper we give an analytical reformulation of Holling's (1966) simulation model for invertebrate predatory behaviour. To this end we represent a population of predators as a frequency distribution over a space of (physiological) states. The functional response of a predator is calculated from the (stable) equilibrium distribution of its state as a function of prey density. Starting from the general model various other models are obtained by limit processes, some of them new and some of them old. The more interesting of which will be studied in further papers in this series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275716
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  • 10
    Electronic Resource
    Electronic Resource
    Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. Part II: Negligible handling time (1985)
    Springer
    Journal of mathematical biology 22 (1985), S. 239-257 
    Details
    ISSN: 1432-1416
    Keywords: Stochastic models ; Invertebrate predation ; Functional response
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper we analyse a stochastic model for invertebrate predation taking account of the predator's satiation. This model approximates Holling's “hungry mantid” model when handling time is negligible (see Part I). For this model we derive equations from which we can calculate the functional response and the variance of the total catch. Moreover we study a number of approximations which can be used to calculate these quantities in practical cases in a relatively simple manner.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275717
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