Further remarks on Darwinian selection and “altruism”

In a recent note, Maynard Smith (Theor. Pop. Biol., in press) has claimed that there are certain difficulties in applying the method developed by us (Theor. Pop. Biol.14, 268–280) which incorporates the evolution of altruism into the population genetic theory of frequency-dependent selection. Of the four examples presented by Maynard Smith, the case of alarm calls was shown to have a natural expression in our multiplicative framework, and to produce conclusions different from those expected under the usual additive assumptions. We show here that the examples of the sterile worker, and of parental care are both simply expressible in terms of our conditional probability approach. The fourth example, the case of incest taboos, will be discussed elsewhere. Using Maynard Smith's examples important differences between the results for the additive and multiplicative fitness constructions are revealed. It is concluded that the heuristic approach using “inclusive fitness” offers no substantive advantages over exact population genetic modelling.     

Delayed germination of seeds: Cohen's model revisited

D. Cohen's (1966, J. Theor. Biol., 12, 110–129) model of delayed germination of seeds in a variable environment is extended to incorporate density dependence. It is shown that this has a considerable impact on the optimal germination rate, and the results are interpreted in terms of bet-hedging behavior. The effect of spatial dispersal is briefly considered.     

Demographic Models for Subdivided Populations: The Renewal Equation Approach

Le Bras (Theor. Popul. Biol.2, 100–121, 1971) and Rogers (Demography11, 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 gullLarus ridibunduspopulation.     

On necessary and sufficient conditions for group selection efficacy

The statement “group selection predominates over individual selection” is formulated within a class of patch-structured models. Conditions involving both “selfish” and “altruistic” predator characteristics are then shown to be necessary and sufficient for group selection predominance in this class of models. Maynard Smith's criterion M < 1 (Group selection, Quart. Rev. Biol., June 1976, pp. 277–283) is shown to be sufficient but not necessary for group selection predominance.     

Evolutionary stability of plant communities and the maintenance of multiple dispersal types

S.A. Levin, D. Cohen, and A. Hastings (1984, Theor. Popul. Biol. 19, 169–200) and D. Cohen and S.A. Levin (1991, Theor. Popul. Biol. 39, 63–99) by analytic solution of the problem of invasion of a single dispersal type by any other, have provided a theory for evolutionarily stable strategies for seed dispersal in a random environment. Here the results of Cohen and Levin are extended to describe evolutionarily stable combinations of dispersal types. Such combinations of two types are coalitions that cannot be invaded by any other, although in isolation either of the types in the combination is invasible by others. These combinations appear when there is a negative correlation between the seed production of sites in successive years, or when environments are spatially heterogeneous, or presumably under other circumstances. In this work, we examine only the case of negative correlations. For this situation the configuration of evolutionarily stable strategies (ESS) and evolutionarily stable combinations (ESC) depends upon the ratio of (precompetitive) survival rates of dispersersing and nondispersing seeds, which is denoted by α. For low values of α, the purely nondispersing type is an ESS. At a somewhat higher value of α, the purely dispersing type can invade the nondispersing type, and the two types form an ESC, i.e., a combination that cannot be invaded by any other type. For still larger values of α, the purely nondispersing type is excluded by the ESC. Finally, for the largest values of α, pure dispersal is the ESS. In cases where a single dispersal type cannot exclude all others, the stationary distribution of types has a large spread. It can be adequately approximated by equations for conditional means of the proportions of various types at a site of a given quality, but these means must be conditioned upon the prior history at each site. For some purposes we have found that the history of as many as 8–10 generations is required for a good approximation. This phenomenon appears to preclude simple analytic approximations for the ESC.     

The evolution of life histories under pleiotropic constraints and r-selection

A way of generating simple derivatives from H. Caswell's (1978, Theor. Pop. Biol.14, 215–230) population growth rate sensitivity measure is described that allows the analysis of pleiotropism involving modifications of an arbitrary number of life history parameters. Some cases are investigated that show that the precise nature of the pleiotropic constraints is critical in determining whether or not a new life history trait will be favored, thereby making it difficult to identify a single optimal life history. Caswell's measure is then generalized to cases in which the stable age distribution does not hold, a situation more applicable to many r-selected species.     

A note on the sampling theory for infinite alleles and infinite sites models

This note considers sampling theory for a selectively neutral locus where it is supposed that the data provide nucleotide sequences for the genes sampled. It thus anticipates that technical advances will soon provide data of this form in volume approaching that currently obtained from electrophoresis. The assumption made on the nature of the data will require us to use, in the terminology ofKimura (Theor. Pop. Biol.2, 174–208 (1971)), the “infinite sites” model of Karlin and McGregor (Proc. Fifth Berkeley Symp. Math. Statist. Prob.4, 415–438 (1967)) rather that the “infinite alleles” model of Kimura and Crow (Genetics49, 174–738 (1964)). We emphasize that these two models refer not to two different real-world circumstances, but rather to two different assumptions concerning our capacity to investigate the real world. We compare our results where appropriate with corresponding sampling theory of Ewens (Theor. Pop. Biol.3, 87–112 (1972)) for the “infinite alleles” model. Note finally that some of our results depend on an assumption of independence of behavior at individual sites; a parallel paper byWatterson (submitted for publication (1974)) assumes no recombination between sites. Real-world behavior will lie between these two assumptions, closer to the situation assumed by Watterson than in this note. Our analysis provides upper bounds for increased efficiency in using complete nucleotide sequences.     

On the hypothesis that polymorphic enzyme alleles are selectively neutral. I. The evenness of allele frequency distribution

Using the theory developed by Ewens (1972, Theor. Pop. Biol.3, 87–112), some properties of the ratio of the observed to effective number of alleles are investigated. In particular the expected value of this ratio, as a function of the observed number of alleles, is seen to increase markedly under the neutral hypothesis. However, the corresponding values from field data for some drosophila species decrease as a function of the observed number of alleles.     

Some multiallele partial assortative mating systems for a polygamous species

The consequences of preferential mating in the presence of partial assortative and sexual selection mechanisms are ascertained for a two-allele one-locus trait involving two phenotype classes C₁ = {all homozygotes} and C₂ = {heterozygotes}. Relevant biological cases may include Burley (1977, Proc. Nat. Acad. Sci. USA 74, 3476–3479), Wilbur et al. (1978, Evolution 32, 264–270), and Singh and Zouros (1978, Evolution 32, 342–353). When the preference rate for the heterozygote exceeds that for homozygotes, it is established that the unique stable state is the central Hardy-Weinberg equilibrium. The rate of approach is faster with sexual selection than for the corresponding model of assortative mating. When the preference rates favor the homozygotes then in this symmetric model of sexual selection two asymmetric Hardy-Weinberg polymorphisms can evolve, and which succeeds depends on initial conditions. The models are also analyzed with natural selection acting on phenotypes superimposed on assortative mating. In this case we can have up to three coexisting stable states involving both fixation alternatives and a central polymorphism. The corresponding model with sexual selection maintains either the central equilibrium as in assortative mating or two asymmetric polymorphic equilibria.     

Permuted tRNA genes of Cyanidioschyzon merolae, the origin of the tRNA molecule and the root of the Eukarya domain

An evolutionary analysis is conducted on the permuted tRNA genes of Cyanidioschyzon merolae, in which the 5′ half of the tRNA molecule is codified at the 3′ end of the gene and its 3′ half is codified at the 5′ end. This analysis has shown that permuted genes cannot be considered as derived traits but seem to possess characteristics that suggest they are ancestral traits, i.e. they originated when tRNA molecule genes originated for the first time. In particular, if the hypothesis that permuted genes are a derived trait were true, then we should not have been able to observe that the most frequent class of permuted genes is that of the anticodon loop type, for the simple reason that this class would derive by random permutation from a class of non-permuted tRNA genes, which instead is the rarest. This would not explain the high frequency with which permuted tRNA genes with perfectly separate 5′ and 3′ halves were observed. Clearly the mechanism that produced this class of permuted genes would envisage the existence, in an advanced stage of evolution, of minigenes codifying for the 5′ and 3′ halves of tRNAs which were assembled in a permuted way at the origin of the tRNA molecule, thus producing a high frequency of permuted genes of the class here referred. Therefore, this evidence supports the hypothesis that the genes of the tRNA molecule were assembled by minigenes codifying for hairpin-like RNA molecules, as suggested by one model for the origin of tRNA [Di Giulio, M., 1992. On the origin of the transfer RNA molecule. J. Theor. Biol. 159, 199–214; Di Giulio, M., 1999. The non-monophyletic origin of tRNA molecule. J. Theor. Biol. 197, 403–414]. Moreover, the late assembly of the permuted genes of C. merolae, as well as their ancestrality, strengthens the hypothesis of the polyphyletic origins of these genes. Finally, on the basis of the uniqueness and the ancestrality of these permuted genes, I suggest that the root of the Eukarya domain is in the super-ensemble of the Plantae and that the Rhodophyta to which C. merolae belongs are the first line of divergence.     

Production of trout,Salmo trutta,in a Danish stream

Synopsis The numbers of trout,Salmo trutta, in Granslev », Denmark, were estimated by the removal method on 18 dates from March 1974 to March 1976. Populations density varied from 0.39 to 0.74 trout m^–2 in 1974–1975 and from 0.36 to 0.59 m^–2 in 1975–1976 and at all times four or five year classes were present. The age structure of the population was unstable and the variable natural survival, immigration into and emigration from the study site could not be separated. An annual growth cycle with the most rapid growth for all year classes taking place from May to early August was found. Statistically significant differences between different years occurred in the growth of the 0,I and II age groups, but no evidence of density-dependent growth was found. The biomass ranged from 35.4 to 9.5 g m^–2. The total mean annual biomass was 22.8 and 14.7 g m^–2 in the two years and the II group made the greatest contribution, 44 and 48%, respectively. During 1975–1976 the mean annual biomass of each year class only was about two-thirds of that in 1974–1975. Annual production in the two years was 25.7 (range 24.7–28.5) and 12.6 g m^–2 (range 11.7–15.0) and the II group accounted for about 46 and 38% of the production. In addition eel,Anguilla anguilla, produced about 0.5 g m^–2 yr^–2. The unstable age structure of the trout population was compared with trout populations from other streams. The importance of immigration as a recruitment process in middle and lower reaches of streams and of migrations as a mechanism to optimise utilization of the total stream habitat, as well as temperature as a factor controlling the growth rate are discussed.     

Models of the evolution of altruism

There are two ways of calculating the spread of a gene for altruism. One, originally proposed by Hamilton, is to allow for the effects of the gene on the survival and reproduction of collateral relatives of the individual carrying it (i.e., “inclusive fitness”); this leads to the condition k > 1/r for the spread of the gene, where k is a benefit/cost ratio. The other is to count only the direct offspring of a carrier, but to allow for the altruistic acts performed toward the carrier by its relatives (“neighbour modulated fitness” or “personal fitness”). A recent personal fitness model (L. L. Cavalli Sforza and M. W. Feldman, 1978, Theor. Pop. Biol.14, 268–280) analyses parent-offspring and sib-sib altruism and concludes that k > 1/r is applicable only when fitness components are combined additively. The present paper analyses some simple models in which the phenotypic effects are carefully specified. It is concluded that it is sometimes, but not always, appropriate to combine fitness components additively. The relative roles of inclusive and personal fitness models are compared. The former have the virtue of being easier to think about in causal terms; and the latter of incorporating the evolution of altruism into the corpus of population genetics as an example of frequency-dependent selection.     

Multilocus model of sympatric speciation II. Two characters

The method used in the previous paper (Kondrashov, 1983Theor. Pop. Biol.27, 000-000) is applied to population polymorphic at two quantitative characters. Sympatric speciation is found to be possible in the case when difference in two characters is necessary for reproductive isolation. The influence of various factors on the process of sympatric speciation is studied and selection forces necessary for its completion are found. Speciation occurs more readily under the action both of disruptive selection in separate characters and of selection against individuals with “unbalanced” phenotypes. This type of selection is also most realistic when various phenotypes make use of different niches. The results obtained allow the supposition that the possibility of sympatric speciation is not reduced to a few cases when reproductive isolation between the forming species develops due to minor genetic differences. It is also shown that if one of the characters is not directly involved in the processes concerning speciation then the forming species do not differ in the character. Relative frequencies of the intermediate phenotypes are found for the terminal stage of speciation.     

On the interaction between stabilizing social factors and destabilizing trophic factors in small rodent populations

Mathematical models are developed in order to analyze whether or not social factors, such as, for example, the “social fence” (J. B. Hestbeck, 1982, Oikos 39, 157–163) will stabilize population density: the dynamic interaction between social factors and (dynamic) trophic factors is analyzed. It is concluded that social factors such as the “social fence” tend to stabilize population density; hence, if density cycles (as, e.g., seen in many microtine rodents) are observed in nature, it seems reasonable to conclude that density cycles are driven by, for example, trophic interactions and not by social factors. It is suggested that the “social fence” may explain why so many populations including several microtine populations have fairly stable densities despite the ever-existing destabilizing trophic interactions. Contrary to what is implied by J. B. Hestbeck (1983, “A Mathematical Model of Population Regulation in Cyclic Mammals,” Lecture notes in biomathematics, Vol. 52, Springer-Verlag, Berlin/New York), the analysis presented in this paper demonstrates that seasonal environmental changes are not essential for the generation of regular density cycles. Seasonal changes may, however, be necessary for generating a microtine-like density cycle. Empirical information on microtine rodents relating to the “social fence hypothesis” is discussed.     

Evolutionary game dynamics in diploid populations

Selection that influences behaviour can be studied using game theory if individual behavioural success depends on the frequencies of various behavioural types in the population. The evolutionarily stable strategy of J. Maynard Smith and G. R. Price (1973. Nature (London) 246, 15–18) is an equilibrium concept like the solution of a game. The dynamic model of Taylor and Jonker, studied in detail by Zeeman, goes beyond game theory using fitness to cause evolution, perhaps towards an equilibrium. A diploid version of their haploid model is considered and it is found that diploid evolution can be quite different. For example “catastrophic” bifurcations can occur between stable internal polymorphisms when the game matrix entries are changed slowly. A slight drop in food supply may cause extinction. Totally unfit altruistic genotypes can be maintained if they help the rest of the population. The relation of haploid game models to constant selection in diploids is also discussed.     

Bias in estimating the Malthusian parameter for Leslie matrices

For Leslie matrices of order 3 × 3 or larger, conditions for concavity or convexity of the Malthusian parameter in each of the entries in the matrix are given. Both cases are possible so it follows that the expected population growth rate computed from a Leslie matrix whose entries are random variables can be either smaller or larger than the growth rate computed from the expected value of the matrix. Boyce [(1977) Theor. Pop. Biol.12] showed that in the 2 × 2 case this bias is always positive; we give a numerical example illustrating the magnitude of the bias in this case, and compare it with the sampling error of the parameter for the same example.     

m-Alkyl, α,α,α-trifluoroacetophenones: A new class of potent transition state analog inhibitors of acetylcholinesterase

A series of m-alkyl α,α,α-trifluoroacetophenones (1–5) was synthesized and evaluated as inhibitors of acetylcholinesterase from Torpedo california. All ketones (1–5) were found to be potent inhibitors of the enzyme; m-t-butyl α,α,α-trifluoroacetophenone (4) was the most potent inhibitor with a K_i value of 3.7 pM.     

Bayesian birds: A simple example of Oaten's stochastic model of optimal foraging

Allan Oaten (1977, Theor. Pop. Biol.12, 263–285) has argued that stochastic models of optimal foraging may produce results qualitatively different from those of the analogous deterministic models. Oaten's model is very general and difficult to understand intuitively. In this paper a simple, tractable model is considered in which the predator searches each patch systematically (without going over the same area twice) until he exhausts the patch or decides the patch is not very good. It is assumed that each patch contains a fixed number of bits, each of which may contain a prey. The number of prey per patch is assumed to have a binomial distribution with n equal to the number of bits and p being a random variable having a beta distribution. After searching each bit the predator decides whether to leave the patch or not according to how many prey it has found. In this paper the best strategy is determined and the long-term rate of feeding is compared with that of the naive animal that searches each patch completely. The advantage of being a Bayesian is determined for a variety of environmental conditions.     

Synthesis and cytotoxic activity of gamma-aryl substituted alpha-alkylidene-gamma-lactones and alpha-alkylidene-gamma-lactams

A series of 5-aryl-3-alkylidenedihydrofuran-2(3H)-ones 6a–g″ and 11a,b as well as 5-aryl-3-methylidenepyrrolidin-2-ones 10a–c and 12 were synthesized starting from 4-aryl-2-diethoxyphosphoryl-4-oxobutanoates 3a–g. Reaction sequence includes reduction or reductive amination of the carbonyl group, lactonization or lactamization step and finally the Horner–Wadsworth–Emmons olefination of aldehydes using thus obtained 5-aryl-3-diethoxyphosphoryl-3,4-dihydrofuran-2(5H)-ones 5a–g″ or 5-aryl-3-diethoxyphosphorylpyrrolidin-2-ones 9a–c. Furanones 6 and 11, as well as pyrrolidinones 10 and 12, were evaluated in vitro against mouse leukemia cell line L-1210 and two human leukemia cell lines HL-60 and NALM-6. Several of the obtained furanones proved to be very potent against all three cell lines with IC₅₀ values lower than 6 μM. Structure–activity relationships of these compounds, as well as 5-alkyl or 5-arylmethyl-3-methylidenedihydrofuran-2(3H)-ones 13a–e, previously obtained in our laboratory, are discussed.