Periodic solutions of integro-differential equations which arise in population dynamics

The problem of the existence and stability of periodic solutions of infinite-lag integra-differential equations is considered. Specifically, the integrals involved are of the convolution type with the dependent variable being integrated over the range (- ∞,t), as occur in models of population growth. It is shown that Hopf bifurcation of periodic solutions from a steady state can occur, when a pair of eigenvalues crosses the imaginary axis. Also considered is the existence of traveling wave solutions of a model population equation allowing spatial diffusion in addition to the usual temporal variation. Lastly, the stability of the periodic solutions resulting from Hopf bifurcation is determined with aid of a Floquet theory.

The first chapter is devoted to linear integro-differential equations with constant coefficients utilizing the method of semi-groups of operators. The second chapter analyzes the Hopf bifurcation providing an existence theorem. Also, the two-timing perturbation procedure is applied to construct the periodic solutions. The third chapter uses two-timing to obtain traveling wave solutions of the diffusive model, as well as providing an existence theorem. The fourth chapter develops a Floquet theory for linear integro-differential equations with periodic coefficients again using the semi-group approach. The fifth chapter gives sufficient conditions for the stability or instability of a periodic solution in terms of the linearization of the equations. These results are then applied to the Hopf bifurcation problem and to a certain population equation modeling periodically fluctuating environments to deduce the stability of the corresponding periodic solutions.

On the population dynamics of Eudiaptomus gracilis Sars and Heterocope borealis Fischer in the Bodensee-Obersee. Part B. Eudiaptomus gracilis Sars. [Translation from: Trudy Instituta Biologii Vnutrennykh Vodnany 12(15) 170-174, 1966.]

Experimental research was conducted to study the development of eggs of Eudiaptomus gracilis Sars. The egg production was studied as well as the population dynamics. Factors like losses in the lake and through the effluent Rhine at Konstanz were considered.

Population dynamics of Windermere perch

This paper looks briefly at some of the more recent analyses and interpretations of the changes that have occurred in the population dynamics of Windermere perch and at the present level of understanding. The long-term study has shown how flexible the population is and how it has behaved in different ways over successive periods of time since 1939. Through one of these periods it was possible to account for nearly all the variance in recruitment by a relatively simple explanatory model. The reduction in numbers on the outbreak of disease in 1976 started a natural experiment which will form a baseline for future studies.

Aspects of the biology and population dynamics of freshwater mussels in Lake Kariba and Lake McIlwaine

The essential aim of this study was to provide a broad foundation of biological knowledge upon which a programme of mussel utilization and management could be built. Results of the study are presented in three main sections. Part 1 describes the stock of Lake Kariba and Lake McIlwaine; part 2 describes various aspects of the breeding biology of the three species; and part 3 presents the results of morphological, biochemical and age analyses - aspects which are used for initial standing crop and production calculations. The final discussion concludes the thesis with a general examination in ecological terms of the factors which have influenced the development and nature of the mussel faunas of the two lakes under consideration.

Population dynamics and exploitation of Metapenaeus affinis in Kuwaiti waters

Length-frequency data of Metapenaeus affinis collected from the trawl catches of R/V Bahith in Kuwaiti waters from 1985 to 1989 were combined with estimates of monthly total catch by the commercial and small-scale fleets operating in Kuwait, and analyzed using the Compleat ELEFAN software package. A major recruitment pulse of M. affinis occurs in spring and a minor one in autumn. Optimum relative yield per recruit (Y'/R) is obtained with the length-at-first capture (L sub(c)) of 24.4 cm CL for females and < 17.6 m CL for males. Virtual population analysis results indicated that the biomasses have decreased during the last three-year period for which data were available.

Sensitivity of Lake Sturgeon population dynamics and genetics to demographic parameters [Powerpoint Slide]

Lake sturgeon Acipenser fulvescens restoration is a priority throughout the Great Lakes basin, where sturgeon have been reduced to less than 1% of historic levels due to habitat degradation, overharvest, and fragmentation of spawning populations. The population parameters most important to long-term lake sturgeon persistence are unknown.

Biology and population dynamics of cowcod (Sebastes levis) in the southern California Bight

Cowcod (Sebastes levis) is a large (100-cm-FL), long-lived (maximum observed age 55 yr) demersal rockfish taken in multispecies commercial and recreational fisheries off southern and central California. It lives at 20–500 m depth: adults (>44 cm TL) inhabit rocky areas at 90–300 m and juveniles inhabit fine sand and clay at 40–100 m. Both sexes have similar growth and maturity. Both sexes recruit to the fishery before reaching full maturity. Based on age and growth data, the natural mortality rate is about M =0.055/yr, but the estimate is uncertain. Biomass, recruitment, and mortality during 1951–98 were estimated in a delay-difference model with catch data and abundance indices. The same model gave less precise estimates for 1916–50 based on catch data and assumptions about virgin biomass and recruitment such as used in stock reduction analysis. Abundance indices, based on rare event data, included a habitat-area–weighted index of recreational catch per unit of fishing effort (CPUE index values were 0.003–0.07 fish per angler hour), a standardized index of proportion of positive tows in CalCOFI ichthyoplankton survey data (binomial errors, 0–13% positive tows/yr), and proportion of positive tows for juveniles in bottom trawl surveys (binomial errors, 0–30% positive tows/yr). Cowcod are overfished in the southern California Bight; biomass during the 1998 season was about 7% of the virgin level and recent catches have been near 20 metric tons (t)/yr. Projections based on recent recruitment levels indicate that biomass will decline at catch levels > 5 t/yr. Trend data indicate that recruitment will be poor in the near future. Recreational fishing effort in deep water has increased and has become more effective for catching cowcod. Areas with relatively high catch rates for cowcod are fewer and are farther offshore. Cowcod die after capture and cannot be released alive. Two areas recently closed to bottom fishing will help rebuild the cowcod stock.

Life history and population dynamics of the finetooth shark (Carcharhinus isodon) in the northeastern Gulf of Mexico

The life history and population dynamics of the finetooth shark (Carcharhinus isodon) in the north-eastern Gulf of Mexico were studied by determining age, growth, size-at-maturity, natural mortality, productivity, and elasticity of vital rates of the population. The von Bertalanffy growth model was estimated as Lt=1559 mm TL (1–e–0.24 (t+2.07)) for females and Lt = 1337 mm TL (1–e–0.41 (t+1.39)) for males. For comparison, the Fabens growth equation was also fitted separately to observed size-at-age data, and the fits to the data were found to be similar. The oldest aged specimens were 8.0 and 8.1 yr, and theoretical longevity estimates were 14.4 and 8.5 yr for females and males, respectively. Median length at maturity was 1187 and 1230 mm TL, equivalent to 3.9 and 4.3 yr for males and females, respectively. Two scenarios, based on the results of the two equations used to describe growth, were considered for population modeling and the results were similar. Annual rates of survivorship estimated through five methods ranged from 0.850/yr to 0.607/yr for scenario 1 and from 0.840/yr to 0.590/yr for scenario 2. Productivities were 0.041/yr for scenario 1 and 0.038/yr for scenario 2 when the population level that produces maximum sustain-able yield is assumed to occur at an instantaneous total mortality rate (Z) equaling 1.5 M, and were 0.071/yr and 0.067/yr, when Z=2 M for scenario 1 and 2, respectively. Mean generation time was 6.96 yr and 6.34 yr for scenarios 1 and 2, respectively. Elasticities calculated through simulation of Leslie matrices averaged 12.6% (12.1% for scenario 2) for fertility, 47.7% (46.2% for scenario 2) for juvenile survival, and 39.7% (41.6% for scenario 2) for adult survival. In all, the finetooth shark exhibits life-history and population characteristics intermediate to those of sharks in the small coastal complex and those from some large coastal species, such as the blacktip shark (Carcharhinus limbatus).