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  • Branch autonomy  (1)
  • Delay differential equations  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 23 (1986), S. 247-262 
    ISSN: 1432-1416
    Keywords: Age-structured population models ; Distributed maturation rates ; Delay differential equations ; Leslie matrix
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the use of age structured population models for agricultural applications such as the modeling of crop-pest interactions it is often essential that the model take into account the distribution in maturation rates present in some or all of the populations. The traditional method for incorporating distributed maturation rates into crop and pest models has been the so-called “distributed delay” method. In this paper we review the application of the distributed delay formalism to the McKendrick equation of an age structured population. We discuss the mathematical properties of the system of ordinary differential equations arising out of the distributed delay formalism. We then discuss an alternative method involving modification of the Leslie matrix.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-2285
    Keywords: Branch autonomy ; Light-canopy relationships ; N cycling ; N isotopes ; Juglans regia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Intracanopy variation in net leaf nitrogen (N) resorption and N cycling through leaves in mature walnut (Juglans regia L. cv Hartley) trees were monitored in 3 different years. Differential irradiance among the spurs sampled was inferred from differences among leaves in dry weight per unit area (LW/LA) which varied from 4.0 mg · cm−2 to 7.0 mg · cm−2 in shaded (S) and exposed (E) canopy positions, respectively. Our results, using 15N-depleted (NH4)2SO4 validated the concept that N influx and efflux through fully expanded leaves occurred concurrently during the period of embryo growth. Additionally, it also suggested that N influx into leaves was substantially greater in exposed as compared with shaded canopy positions. Because of its well documented phloem immobility, leaf Ca accumulation was used to better estimate the relative influx of N into exposed and shaded leaves. N cycling varied locally within the tree canopy, i. e. Ca (and presumably N) influx was 100% greater in exposed than shaded tree canopy positions, but influx was not influenced significantly by the proximity of developing fruit. In contrast, both the amount and percentage N efflux was significantly greater during embryo growth in fruit-bearing than defruited spurs. Net leaf N resorption averaged 2–4 times greater (25–30%) in fruit-bearing spurs than the 5–10% decrease in the leaf N content in defruited spurs. Since about 90% of leaf N content reportedly occurs as protein, fruit N demand apparently influenced protein turnover and catalysis in associated spur leaves. The amount of leaf N resorption was greater in exposed than shaded positions in the tree canopy in 2 of the 3 years of data collection. Our data show that like leaf N content, N influx, N efflux and net leaf N resorption vary throughout mature walnut tree canopies under the combined local influences of fruiting and irradiance.
    Type of Medium: Electronic Resource
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