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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↗

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↗

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↗

Relative fitness of carriers of the mitochondrial DNA mutation 3243A > G.

Deleterious point mutations in mitochondrial DNA (mtDNA) have been found in many human populations and always at a low frequency suggesting that they are under strong negative selection. It is assumed that this selection is caused by reduced genetic fitness of mutation carriers, but the fitness of carriers of any mtDNA mutation has not been determined. We estimated the reproductive disadvantage caused by the mitochondrial DNA mutation 3243A > G in a population-based group of female carriers (n = 32). The person-years method, Kaplan-Meier survival analysis and population statistics were used to estimate net reproduction rates of the mutation carriers and the general population. We found that women with 3243A > G reproduced at the same rate as women in the general population, suggesting that on average host-level selection against women harbouring the 3243A > G mutation is not strong.

Adolescent↗

Sublethal iridovirus disease of the mosquito Aedes aegypti is due to viral replication not cytotoxicity.

Invertebrate iridescent viruses (Iridoviridae) possess a highly cytotoxic protein. In mosquitoes (Diptera: Culicidae), invertebrate iridescent virus 6 (IIV-6) usually causes covert (inapparent) infection that reduces fitness. To determine whether sublethal effects of IIV-6 are principally due to cytotoxicity of the viral inoculum (which inhibits macromolecular synthesis in the host), or caused by replication of the virus larvae of the mosquito Aedes aegypti (L) were exposed to untreated IIV-6 virus that had previously been deactivated by heat or ultraviolet light. Control larvae were not exposed to virus. Larval development time was shortest in control larvae and extended in larvae exposed to untreated virus. Covertly infected mosquitoes laid significantly fewer eggs, produced between 20 and 35% fewer progeny and had reduced longevity compared to other treatments. Wing length was shortest in mosquitoes exposed to heat-deactivated virus. Multivariate analysis of the same data identified fecundity and progeny production as the most influential variables in defining differences among treatments. Overall, viral infection resulted in a 34% decrease in the net reproductive rate (R0) of covertly infected mosquitoes, vs. only 5-17% decrease of R0 following treatments with deactivated virus, compared to controls. Sublethal effects of IIV-6 in Ae. aegypti appear to be mainly due to virus replication, rather than cytotoxic effects of the viral inoculum.

Aedes↗

Experimental removal of sexual selection reverses intersexual antagonistic coevolution and removes a reproductive load.

Although sexual selection can provide benefits to both sexes, it also can be costly because of expanded opportunities for intersexual conflict. We evaluated the role of sexual selection in a naturally promiscuous species, Drosophila melanogaster. In two replicate populations, sexual selection was removed through enforced monogamous mating with random mate assignment or retained in promiscuous controls. Monogamous mating constrains the reproductive success of mates to be identical, thereby converting prior conflicts between mates into opportunities for mutualism. Random mate assignment removes the opportunity for females to choose beneficial qualities in their mate. The mating treatments were maintained for 47 generations, and evolution was allowed to proceed naturally within the parameters of the design. In the monogamous populations, males evolved to be less harmful to their mates, and females evolved to be less resistant to male-induced harm. The monogamous populations also evolved a greater net reproductive rate than their promiscuous controls. These results indicate a potentially widespread cost of sexual selection caused by conflicts inherent to promiscuity.

Animals↗

Interaction in the laboratory between Helisoma duryi, a possible competitor snail, and Biomphalaria pfeifferi, snail intermediate host of Schistosoma mansoni.

The planorbid snail, Helisoma duryi, has been proposed as a possible biocontrol agent against the intermediate host snails of schistosomiasis. In an attempt to evaluate the possible effect of interference between H. duryi and Biomphalaria pfeifferi, life-tables were compiled for these two snail species maintained both in the presence of each other and separately. The calculated population parameters indicated that H. duryi had a higher innate capacity of increase, net reproduction rate and finite rate of increase as well as a longer lifespan than the target species. However, the biological potential of B. pfeifferi was not influenced by the presence of H. duryi, and the latter appears to be unable to act as competitor against B. pfeifferi under similar prevailing conditions. It is possible that the situation might change under conditions of crowding and starvation.

Animals↗

Effects of snowdrop lectin on Mexican rice borer (Lepidoptera: Pyralidae) life history parameters.

The effects of the snowdrop lectin, Galanthus nivalis agglutinin (GNA), delivered through an artificial diet, on growth, development, and life history parameters of the Mexican rice borer, Eoreuma loftini (Dyar), were evaluated in the laboratory. Incorporation of GNA at three treatment levels, 0.5, 1.0, and 2.0% of total dietary protein, in the larval diet significantly decreased larval survivorship and percentage of adults emerging relative to a control diet lacking GNA, whereas differences were not observed among the three treatment levels. Both larvae and pupae in the control were 8-25% larger than those in the GNA treatments, but differences were not observed between larvae in the GNA treatments. Furthermore, presence of GNA did not affect larval and pupal developmental periods, longevities, and fecundities compared with the control. Mexican rice borer life history parameters, such as net reproductive rate and intrinsic rate of increase, were substantially reduced by the presence of GNA in the diet, but differences were not evident among the three GNA treatment levels.

Animals↗

Intraspecific variation in the reproductive capacity of Anopheles stephensi (Diptera: Culicidae).

Intraspecific variation in the reproductive capacity of Anopheles stephensi Liston females was studied under constant laboratory conditions. Of 421 engorged females examined individually throughout their lifetimes, 260 laid a total of 479 egg batches with a maximum of nine ovipositions per female. The number of eggs per oviposition varied from 5 to 247 (average 96.8). The number of ovipositions per female were correlated positively with the average number of eggs per batch and exhibited a negative binomial distribution among females, indicating that a small portion of the population exhibited a particularly high fecundity. Among the ovipositing females, the total fecundity and fertility ranged, respectively, from 5 to 1,084 eggs and from 0 to 1,036 larvae per female. The estimated maximal number of female progeny produced by a female in her lifetime was 317, and the estimates of net reproductive rate (Ro) and capacity for increase (rc) were 25.7 and 0.17, respectively. The number of eggs in the first oviposition was predictive of the total fecundity of a female. The wide range of individual variation in the reproductive capacity of An. stephensi emphasized the requirement for a large sample size for reliable estimation.

Animals↗