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Demographic Models for Subdivided Populations: The Renewal Equation Approach

Le Bras (Theor. Popul. Biol. 2, 100-121, 1971) and Rogers (Demography 11, 473-481, 1974), in two neglected papers, have generalized to the multisite case the Euler-Lotka renewal equation and demographic characteristics such as age structure and reproductive value. The purpose of this paper is twofold: first, to restate the multisite renewal equation in the matrix context; second, to derive results on age structure, net reproduction rate, generation time, and sensitivities, as generalizations of the one site case. The potential of this approach for population biology is illustrated using a model of a black-headed gull Larus ridibundus population.

Journal Article↗

Population Dynamics of Evolutionary Change: Demographic Parameters as Indicators of Fitness

I evaluated demographic parameters as indicators of fitness by calculating the net reproductive rate (R0), exponential rate of change (r), lifetime reproductive success (LRS), and Malthusian parameter (m) for nine genotypes and four phenotypes (two alleles at each of two independent loci) of an age-structured population. The given starting conditions included age-specific survival rates of males and females and age-specific fecundity of females for each genotype (to simplify the problem I presumed no differences in survivorship or fecundity of genotypes with the same phenotype) and the same age structure for each genotype. The prevailing genotype had the greatest m, but it did not have the greatest r, R0 , or LRS, or even the greatest survivorship of either juveniles or adults, or the greatest fecundity. This result indicates that m is the only correct measure of fitness (i.e., as a predictor of which genotype should prevail from among a group of genotypes) and that comparisons of r, R0 , LRS, juvenile or adult survival rates, or fecundity may be misleading indicators of which genotype should prevail (i.e., be most "fit") over time (i.e., be selected for).

Journal Article↗

On the process of stabilization in the renewal model: approximations for the time to convergence.

The transient behaviour of the renewal model leading to the stable age distribution is studied for weakly skewed net maternity functions (found in human as well as in some animal populations). The study, which is partly based on heuristic arguments, first provides approximate expressions for the damping constant and the circular frequency (in terms of the moments of the net maternity function) belonging to the principal oscillatory component of the birth trajectory. The time to stability (defined as the time interval after which the principal oscillatory component has become less than a certain fraction of the stable solution) is then determined in two cases: For the genesis model and for a stable population in which the net reproduction rate is reduced to one. The results are applied to a problem which arises in the mass rearing of pest insects.

Animals↗

The combined effects of hardness, pH, and dissolved organic carbon on the chronic toxicity of Zn to D. magna: development of a surface response model.

The effect of changes in pH, hardness, and dissolved organic carbon (DOC) and the possible interactions among these parameters on the chronic toxicity of zinc to D. magna were investigated. Based on a Central Composite Design, models were developed that can explain the observed variation in EC(10) and EC(50) as a function of these toxicity modifying factors. All three parameters significantly altered the observed effect concentrations based on net reproductive rate. The largest differences in 21-day EC(10)s and EC(50)s caused by these factors were 10.1 and 4.9, respectively. An increase in pH and/or DOC decreased zinc toxicity. The significant interaction between pH and DOC on observed chronic Zn toxicity is in accordance with earlier reported increased sorption efficiency of Zn to humic substances at higher pH levels. Lowest Zn toxicity was observed in tests performed with moderately hard test media (between 200 and 300 mg/L as CaCO(3)). Lower or higher hardness of the test medium resulted in lower effect concentrations. Based on physico-chemical characteristics of the test media, developed models can be used to explain the variation between reported NOECs for Zn and may improve current environmental risk assessment procedures of metals.

Animals↗

Effects of azadirachtin on the two-spotted spider mite, Tetranychus urticae (Acari: Tetranychidae).

Effects of sublethal azadirachtin exposure to the biological performance of Tetranychius urticae Koch was studied under laboratory conditions. Bioassay was used to asses the effect of different concentrations of azadirachtin on longevity, fecundity, fertility, and offspring development. Azadirachtin (64 and 128 ppm) affected fecundity and mortality but had no effect on fertility and offspring development. A subsequent life-table study with 80 ppm of azadirachtin found that the compound caused a reduction of 50% in survival to adult stage. The peak of reproduction was reached at 5 days causing a decrease in the mean fecundity to almost eight times than of untreated females. The net reproductive rate (R0), the intrinsic rate of increase (r(m)), and the finite rate of increase (lambda) of treated females were lower. Treatment showed a negative value of r(m), resulting in a declining population. These results suggest that azadirachtin could be incorporated in Integrated Pest Management (IPM) programmes of T. urticae.

Animals↗

Detection of 'candidatus Cardinium' bacteria from the haploid host Brevipalpus californicus (Acari: Tenuipalpidae) and effect on the host.

Brevipalpus californicus (Banks) was infected with 'Candidatus Cardinium' bacteria (Cardinium). Tetracycline-treated females produced many male progeny even though untreated females produced only female progeny. B. californicus appears to be feminized by Cardinium. The values for net reproduction rate (R0), generation time (T) and intrinsic rate of natural increase (r(m)) calculated for B. californicus were 7.48/day, 31.45 days and 0.064/day, respectively. The comparison of infected females with uninfected males and other closely related species, indicated that Cardinium does not have a negative effect on the fitness of B. californicus.

Animals↗

Life history of Kampimodromus aberrans as a predator of Phytoptus avellanae (Acari: Phytoseiidae, Phytoptidae).

The biology of Kampimodromus aberrans (Oudemans), a predator of the big bud mite, Phytoptus avellanae Nalepa, was studied under laboratory conditions. All experiments were conducted on hazelnut leaf discs in an incubator at 25 +/- 1 degrees C, with 16:8 h L:D, at an average daily relative air humidity of 76%. Observations were made twice daily for the immature stages and daily for the adults to determine developmental time, survival and fecundity. The mean developmental time for females was 6.90 days and for males was 7.10 days, and mean adult longevity for females was 11.67 days. The mean total and daily egg production were 12.67 and 1.85 eggs, respectively. The net reproduction rate (R0) was 7.09 females/female, intrinsic rate of increase (rm) was 0.153 female/female/day and mean generation time (T0) was 12.80 days. The mortality rate of immature stages was 0.66% and the sex ratio was 0.51 female.

Animals↗

Assessment of sublethal effects of clofentezine on life-table parameters in Hawthorn spider mite (Tetranychus viennensis).

A leaf disc bioassay was employed in the laboratory to assess the population responses of Tetranychus viennensis Zacher to clofentezine at three concentrations (LC(10), LC(25) and LC(50)) in three successive generations. Life-table parameters were calculated in each acaricide exposure regime and compared by jackknife procedures. Clofentezine treatments in the juvenile stages significantly delayed development of the mites, and this delay increased with increasing dose but decreased as the mites developed. Exposure to clofentezine reduced the net reproduction rate (R(0)) in a concentration-dependent manner. The LC(50) treatment had strong effects on the hatchability of eggs produced by surviving females. Hatch rate dropped from 0.83 in the untreated control to 0.51 in the third generation. When exposed to constant concentrations of clofentezine in three successive generations, the intrinsic rate of increase and R(0) of the mites decreased significantly, but they increased significantly when exposed to decreasing concentrations. Unexposed offspring of the exposed mother also displayed increases in R(0) and the jackknife procedures indicated no significant differences in R(0) between LC(10) and LC(25) offspring and their mothers vs. the control, while R(0) in unexposed LC(50) offspring was significantly higher than their mother's, but lower than that in the control. These changing patterns of r(m) reveal that acaricide effects at the population level strongly depend on the life-history characteristics of T. viennensis and the chemical mode of action.

Aging↗

Malthusian parameter on the Finnish population in the 20th century.

We were interested in studying a demographic indicator, the Malthusian parameter which had not been investigated earlier in the case of the Finnish population. We computed the Malthusian parameter with a known renewal equation, which is, as usual, approximated on discrete data by using normal distribution, on the Finnish population in the 20th century. The data was collected from the abundant official statistical sources which are known to be accurate and reliable in Finland. In addition to this parameter we computed the gross and net reproduction rates, the total fertility index, and the mean and variance age of females at child-bearing. The Malthusian parameter seems to be a rather good means of characterizing the development of the population. If the parameter is positive for long enough, the population tends to grow. If it is negative, as has been the case in Finland since 1969, the population starts to diminish sooner or later. On the other hand, it cannot take all factors into account. For instance, because of still increasing lifetime and also because of a relatively large quantity of females at the reproductive age the population is not yet decreasing in Finland. In any case, the Malthusian parameter forecasts the future trend of the decreasing population.

Adolescent↗

A laboratory study on the possible use of Helisoma duryi in the biological control of Bulinus africanus, intermediate host of Schistosoma haematobium.

In order to evaluate the possible use of Helisoma duryi as biological competitor of Bulinus africanus, life-tables were compiled for these two snail species maintained either in the presence of each other, or separately. Population parameters were calculated from these life-tables and it was found that H. duryi had a higher innate capacity of increase, net reproduction rate and growth rate as well as a longer lifespan and reproductive period than Bu. africanus. Furthermore, the biological potential of Bu. africanus was found to be adversely affected in the presence of H. duryi. It was concluded that the latter might be capable of replacing Bu. africanus in certain freshwater habitats and that field trials ought to be undertaken in South Africa.

Animals↗

Effects of different food (Chlorella) concentrations on the chronic toxicity of cadmium to survivorship, growth and reproduction of Echinisca triserialis (Crustacea: Cladocera).

Extraneous factors have been shown to greatly modify pollutant stress. The present study was conducted with the objective of determining whether differences in food levels could modify chronic toxicity of cadmium to the various life-history parameters of the cladoceran Echinisca triserialis. Laboratory experiments were conducted on a sublethal range of cadmium (0, 2.5, 5.0, 10 and 20 microg litre(-1)) on life-history parameters such as survivorship, longevity, life expectancy, age at first reproduction, total fecundity, neonate size, net reproductive rate (R0), generation time (T), intrinsic rate of natural increase (r) and growth of Echinisca triserialis in relation to different food (Chlorella) levels of 0.5 (low), 1.5 (medium) and 4.5 (high) x 10(6) cells ml(-1). Cadmium levels of 10 microg litre(-1) and above, and low food levels, had a profound effect in decreasing the magnitude of all parameters studied. EC50 levels computed for life-history parameters, such as longevity, life expectancy at birth, total fecundity, R0 and T, were in the range of 2 to 21 microg litre(-1) cadmium, and this is indicative of extreme adverse effects on the population dynamics of E. triserialis when exposed to low food levels. At high food levels the EC50 was not achieved for cadmium in the toxicant range studied. The significance of these results is discussed in relation to field conditions.

Journal Article↗

Chronic effect of NaCl salinity on a freshwater strain of Daphnia magna Straus (Crustacea: Cladocera): a demographic study.

Daphnia magna is mainly recognized as a freshwater cladoceran, but there are some strains that grow in brackish waters. The tolerance to salinity of a freshwater strain was assessed at NaCl concentrations of 0, 2, 4, 6, and 7 g L(-1). The green microalga Ankistrodesmus falcatus was fed at optimal concentration (4 x 10(5)cells mL(-1)). Reproduction and survival were recorded in two experimental series: in the first one, 20 female neonates were individually studied for each treatment. In the second, cohorts of 10 female neonates were distributed in each of five replicates per treatment. In both cases, experiments were conducted over a full life-cycle. The determined 48-h LC(50) for NaCl was 5.48 g L(-1), but we recorded reproduction at up to 7 g NaCl L(-1). The average clutch size, total progeny, number of clutches, and longevity were significantly reduced by the NaCl concentration (P<0.01); total progeny ranged from 467 to 25 neonates as edge values for NaCl concentrations of 0-7 g L(-1). Inter-brood time was significantly higher for females grown at 7 g NaCl L(-1) (3.9 days). The Life Table analysis demonstrates that average lifespan, life expectancy at birth, net reproductive rate and intrinsic rate of growth were also significantly reduced according to NaCl concentration. Based on the results for the two highest NaCl concentrations (6 and 7 g L(-1)), we conclude that the used D. magna strain was acclimated to develop satisfactorily under concentrations of up to 6 g NaCl L(-1); however, the established salinity conditions reduced significantly reproduction and survival in this strain.

Animals↗

Can chromosomal instability initiate tumorigenesis?

Cancers result from the accumulation of inherited and somatic mutations in oncogenes and tumor suppressor genes. These genes encode proteins that function in growth regulatory and differentiation pathways. Mutations in those genes increase the net reproductive rate of cells. Chromosomal instability (CIN) is a feature of most human cancers. Mutations in CIN genes increase the rate at which whole chromosomes or large parts of chromosomes are lost or gained during cell division. CIN causes an imbalance in chromosome number (aneuploidy) and an enhanced rate of loss of heterozygosity, which is an important mechanism of inactivating tumor suppressor genes. A crucial question of cancer biology is whether CIN is an early event and thus a driving force of tumorigenesis. Here we discuss mathematical models of situations where inactivation of one or two tumor suppressor genes is required for tumorigenesis. If two tumor suppressor genes have to be inactivated in rate-limiting steps, then CIN is likely to emerge before the inactivation of the first tumor suppressor gene.

Animals↗

Evolutionarily stable age at first reproduction in a density-dependent model.

We develop a new model of life history evolution to investigate the evolution of age at first reproduction. Density dependence is taken into account. For a given "species", age of maturity, offspring survival, immature survival, adult survival, fecundity, immature age-classes entering in competition with adults and immature competitive ability are traits adjustable by natural selection, and constitute a particular strategy. On the contrary, the type of intraspecific competition (scramble or contest), strength of competition and inherent net reproductive rate Ro(inh) are fixed (specific) characteristics. As a consequence of fixing Ro(inh), the evolution of any trait will affect trade-offs between others. Evolutionarily stable strategies are determined numerically by using the mathematical concept of Lyapunov exponents. Altogether, we consider 960 different hypothetical "species" (i.e. different combinations of fixed traits). Corresponding ESSs are analyzed with respect to their age at first reproduction, adult survival and immature competitive ability components. They appear to be gathered in three groups. One is intuitive and characterized by a reduction of immature competitive ability and a correlation of age of maturity with adult survival; populations reach mainly equilibria. The two other groups respectively include "species" with low age of maturity but high adult survival, and "species" close to semelparity with delayed maturity; immature competitive ability may not be minimized, and populations possibly exhibit complex dynamics. In conclusion, the hypothesis that the evolution of a demographic parameter modifies trade-offs between others turns out to have important consequences. We argue that life history theory cannot ignore the source and mode-of-operation of density dependence and must regard potential short-term instability as essential.

Animals↗

Viral sex, levels of selection, and the origin of life.

Several issues in Chao's related paper J. theor. Biol. (1991, 153, 229-246) are revisited. It is argued that mixes of segments from different viral coinfection groups cannot be regarded as sex, unless one is willing to accept that these groups are replicators and individuals. But, because selection in coinfection groups is dynamically analogous to that in trait groups in structured demes, one should also regard these latter groups as replicators. This approach is unacceptable since the groups in question have irregular ploidies, an unfixed number of parents, and no rules analogous to those of meiosis. It is emphasized, however, that the effective presence of neighbour-modulated fitness can ensure dynamical coexistence of covirus segments, even if the equal net reproduction rate within groups is not warranted. It seems that during the origin of coviruses from complete viruses, a higher-level evolutionary unit has become disintegrated, whereas during the origin of life a higher-level unit, the protocell, has emerged from lower-level ones, i.e. unlinked, replicating genes. These two gene-level systems are not homologous, but analogous. Although it is true that the resistance to parasites and the need to avoid a mutational collapse of the genome are likely to have called for some compartmentation in precellular stages of evolution, no clear demonstration, that the proposed mechanisms (the compartmentalized hypercycle and the stochastic corrector model) do in fact solve the error threshold problem, exists. Neither has a plausible mode of protocellular sex been suggested.

Origin of Life↗

Biological populations obeying difference equations: the effects of stochastic perturbation.

We consider the effects of stochastic perturbation in various components of a finite difference model arising in population biology. In particular, we examine how fluctuation in the net reproductive rate can effect the population dynamics of the system. Computer simulation and some elementary analyses bear out the result that, in the mean, the stochastic dynamics will behave like the deterministic dynamics. This study also answers a currently unanswered conjecture published by the first author in 1977.

Animals↗

Using rotifer population demographic parameters to assess impacts of the degradation products from trinitrotoluene phytoremediation.

The objective of this study was to evaluate the chronic lethal and sublethal aquatic toxicity effects associated with the phytoremediation of water contaminated with 2,4,6-trinitrotoluene (TNT) by the wetland plant species Myriophyllum aquaticum (parrot feather). Rotifers (Brachionus calyciflorus) feeding on an algal species (Nannochloropsis spp.) were used as the aquatic test organisms. Continuous flow laboratory microcosms were used to quantify effects on rotifer populations from TNT and the primary degradation product aminodinitrotoluene (ADNT) during and after phytoremediation. Rotifer demographic parameters from life tables, including survivorship, fecundity, reproductive values, net reproductive rate, generation time, intrinsic growth rate, and life expectancy, were used as measures of treatment effects. High-performance liquid chromatography analyses were performed to determine nitroaromatic concentrations. Results from this study have revealed significant differences in rotifer demographic parameters between microcosms with elevated initial TNT concentrations. Significant differences in demographic parameters also existed between the microcosms that did and did not receive phytoremediation treatment and the control microcosms. Study results have indicated that TNT phytoremediation via artificial wetlands not only may clean up hazardous waste at munitions sites but also may encourage the growth of aquatic populations such as rotifers.

Algorithms↗

Temperature tolerance of the diamondback moth, Plutella xylostella (Lepidoptera: Yponomeutidae) in tropical and temperate regions of Asia.

Temperature tolerance was investigated in nine populations of Plutella xylostella Linnaeus from tropical and temperate regions of Asia. At all rearing temperatures between 15 and 35 degrees C, no clear differences were observed in female egg production or larval development between tropical and temperate populations. Thus, tropical populations did not show a high-temperature tolerance superior to that of the temperate populations. In all populations, the net reproductive rate (number of new females born per female) largely depended on the number of eggs laid per female, and egg production significantly decreased with increasing temperature (P < 0.001). Larval developmental rate also showed a significant positive correlation with temperature (P < 0.001). Per cent hatch of eggs and larval survival did not show a significant correlation with temperature: hatching was constant between 15 and 32.5 degrees C, but considerably lower at 35 degrees C. Larval survival was similar between 15 and 30 degrees C, appreciably lower at 32.5 degrees C and declined to 0% at 35 degrees C. Based on these results, environmental conditions under which P. xylostella can maintain a high population density throughout the year in tropical and subtropical regions are discussed.

Animals↗