How multiple mating by females affects sexual selection

Multiple mating by females is widely thought to encourage post-mating sexual selection and enhance female fitness. We show that whether polyandrous mating has these effects depends on two conditions. Condition 1 is the pattern of sperm utilization by females; specifically, whether, among females, male mating number, m (i.e. the number of times a male mates with one or more females) covaries with male offspring number, o. Polyandrous mating enhances sexual selection only when males who are successful at multiple mating also sire most or all of each of their mates'' offspring, i.e. only when Cov_♂(m,o), is positive. Condition 2 is the pattern of female reproductive life-history; specifically, whether female mating number, m, covaries with female offspring number, o. Only semelparity does not erode sexual selection, whereas iteroparity (i.e. when Cov_♀(m,o), is positive) always increases the variance in offspring numbers among females, which always decreases the intensity of sexual selection on males. To document the covariance between mating number and offspring number for each sex, it is necessary to assign progeny to all parents, as well as identify mating and non-mating individuals. To document significant fitness gains by females through iteroparity, it is necessary to determine the relative magnitudes of male as well as female contributions to the total variance in relative fitness. We show how such data can be collected, how often they are collected, and we explain the circumstances in which selection favouring multiple mating by females can be strong or weak.     

The volumes of some compartment systems with sampling and loss from one compartment

If the concentrationc ₁(t)=∑ _i=1 ⁿ A _i exp (−α _i t) for one compartment, one presumes a linear catenaryn-compartment system without sinks and loss only from the same compartment, then the volumesV _i , rate constantsk _ij , and concentrationsc _i (t) in each compartment can be determined in terms of theA _i 's,A _i ′s, α _i ′s, the dose injectedD _o and the partition coefficientsr _ij =k _ij /k _ji . If the concentration would become uniform at equilibrium, then the total volume of distribution may be determined without knowledge ofr _ij or restriction to catenary configuration.     

Allele frequencies in multidimensional Wright-Fisher models with a general symmetric mutation structure

The diffusion form of a multiple-allele Wright-Fisher model of allele frequencies of types A₁,…,A_K at a neutral locus where there are general symmetric mutation rates of M_ij (=M_ji) from A_i → A_j is studied. A convenient recurrence relationship for the moments of linear forms in the allele frequencies is found. A formula is derived for the expected homozygosity in the transient and stationary models, which is applied to general stepwise mutation models where mutation over more than one step is possible. The probability that two randomly chosen genes are j steps apart at time t in the stepwise mutation model is found to have a reasonably simple form if conditioning is on the initial allele frequencies arranged in order of magnitude. Of interest is a new geometric charge state model, mutation over several steps roughly corresponding to independent charge changes. The expected homozygosity and expected distance between two randomly chosen genes is tabulated in this model.     

Malthusian parameters,reproductive values and change under selection in self fertilizing age-structured populations

A population, reproducing wholly by selfing, is assumed to be observed at times . Individuals between x–1 and x units of age at time t are said to be in age class x at that time. The rate of increase in the long run of individuals of type A_iAj is denoted by m_ij+1=m_ji+1. For each genotype there is also a set of reproductive values, corresponding to all age classes and genotypes of individuals having descendants of that genotype. Then, if the number of individuals of each sort of ancestor is multiplied by its reproductive value and the products are summed, the result is the total value, which is V_ij(t) for genotype A_iAj. Then V_ij(t+1)–V_ij(t) is equal to m_ijV_ij(t), where m_ij is the Malthusian parameter for A_iAj. Furthermore, if the mean and variance at time t of the m_ijs, weighted by their corresponding reproductive values, are respectively (t) and _m²(t), then m¯(t+1)–m¯(t)=_m²(t)/(1+m¯(t)).     

A statistical model of the reproduction of aphids

1. The logistic function has been generally used to describe the reproductive process of a “population” of animal. However, this model can not give us any information about the reproductive process of “individuals” in the population. In this study a statistical model on the basis of the reproduction of individuals of barley aphid is presented to find the proportion of the mature individuals, the heterogeneity in reproductive ability of the aphids, etc.
2. The model is constructed as follows:
3. The probability that j insects are found on a plant at time t₀ is represented as Q(j).
4. The probability that h individuals of j have reproductive ability, say, mature individuals, in the period t₀ to t₁ is represented as B(h/j)=_jC_hw^h(1−w)^j−h, where w is the proportion of mature individuals.
5. In a population with a homogeneous reproductive ability, the probability that each parent lays i offspring in the period t₀ to t₁ is represented as P(i/m)=e^−mmⁱ/i!, where m is mean. And, in a population, m changes according to the gamma distribution. Hence the probability that a parent lays i offspring between t₀ and t₁ is represented as , where p and k are parameters of negative binomial distribution. The probability that h parents on a plant lays s offspring is represented as .
6. From the assumptions mentioned above, the probability that s offspring are to be found at time t₁ on a plant with the original j individuals at time t₀ is represented by
7. The experimental populations were demonstrated to fit well to the model.

     

A bisexual multitype branching process with applications in population genetics

A bisexual multiple branching process is studied. Consider a population with respect to three genotypes in both the female and male populations and let $$X(n) = \left\langle {X_1 (n), X_2 (n), X_3 (n)} \right\rangle and Y(n) = \left\langle {Y_1 (n), Y_2 (n), Y_3 (n)} \right\rangle$$ be random vectors giving the number of females and males (respectively) of each genotype in generationn. The mating of females and males is accommodated in the model withZ _ij (n) representing the number of females of theith genotype mated with a male of thejth genotype in generationn. The mating system is such that a female may be mated to only one male but a male may be mated with more than one female. By arranging the nine random variablesZ _ij (n),i, j=1, 2, 3, in a 1×9, vectorZ(n) it is shown that under certain conditions there is a positive constant ? such that when ?>1 the vectorsZ _n /ρⁿ,X _n /ρⁿ andY _n /ρⁿ converge almost surely asn→∞ to random vectors with fixed directions. The paper is divided into four sections. In section 1 the model is described in detail and its potential applications to population genetics are discussed. In section 2, the generating function of the transition probabilities of theZ-process are derived. Section3 is devoted to the study of the limiting behavior of the first and second moments of theZ-process, and in section4 the results of section3 are utilized to study the behavior of the random vectorsZ(n),X(n) andY(n) asn→∞.     

蝇蛹金小蜂的交配行为及雄蜂交配次数对雌蜂繁殖的影响

多数昆虫能够进行多次交配,随寄生蜂雄蜂交配次数的增加,雄蜂体内精子减少,雌蜂获得的精子数量减少,产下更多的单倍体卵,发育为雄性后代;一些单寄生性的寄生蜂雌蜂一生仅能够交配1次。描述了蝇蛹金小蜂雌雄蜂的交配行为,探讨了雄蜂交配次数对雌蜂后代产量等的影响以及雌蜂的可交配次数。结果表明,交配过程包括求偶、交尾前期、交尾和交尾后期;雄蜂已交配的次数并不能够显著影响其配偶的寿命、产卵期和后代总数量,但显著影响到其配偶的雌、雄后代数量和性比。随雄蜂交配次数的增加,与之交配的雌蜂的后代雄性百分比显著增大,雌蜂在产卵期内更早地出现较多雄性后代,体内精子不足的现象更加明显。无论已交配的蝇蛹金小蜂雌蜂在产卵期中是否出现精子不足,均不能再次完成交配。     

A model of the plant-to-plant movement of aphids I. Description of the model

The plant-to-plant movement of insects in one of the factors determining the distribution of individuals in insect populations. In this report the movement of barley aphids was analyzed by a statistical model. The model is represented as the convolution of three probability functions:

1. The probability that s individuals are found on a plant at time t₀:Q(s);
2. The probability that i individuals leave the plant and remain on the ground from time t₀ to t₁:_sC_ipⁱq^s−i and p+q=1, where p and q are the proportions of individuals which do not leave a plant and which leave it once or more, respectively;
3. The probability that j individuals climb a plant between time t₀ to t₁ and stay there at time t₁:e^−λλ^j/λ^!, where λ is the mean of the individuals.

The probability that l individuals are located on a plant at time t₁ is represented by the following equation It was shown by simple experiments that the experimental populations were well fitted to the model.     

THE KINETICS OF PENETRATION : I. EQUATIONS FOR THE ENTRANCE OF ELECTROLYTES

When the only solute present is a weak acid, HA, which penetrates as molecules only into a living cell according to a curve of the first order and eventually reaches a true equilibrium we may regard the rate of increase of molecules inside as See PDF for Equation where P_M is the permeability of the protoplasm to molecules, M_o, denotes the external and M_i the internal concentration of molecules, A_i denotes the internal concentration of the anion A^- and See PDF for Equation (It is assumed that the activity coefficients equal 1.) Putting P_MF_M = V_M, the apparent velocity constant of the process, we have See PDF for Equation where e denotes the concentration at equilibrium. Then See PDF for Equation where t is time. The corresponding equation when ions alone enter is See PDF for Equation. where K is the dissociation constant of HA, P_A is the permeability of the protoplasm to the ion pair H⁺ + A^-, and A_ie denotes the internal concentration of A_i at equilibrium. Putting P_AKF_M = V_A, the apparent velocity constant of the process, we have See PDF for Equation and See PDF for Equation When both ions and molecules of HA enter together we have See PDF for Equation where S_i = M_i + A_i and S_ie is the value of S_i at equilibrium. Then See PDF for Equation V_M, V_A, and V_MA depend on F_M and hence on the internal pH value but are independent of the external pH value except as it affects the internal pH value. When the ion pair Na⁺ + A^- penetrates and Na_i = BA_i, we have See PDF for Equation and See PDF for Equation where P _NaA is the permeability of the protoplasm to the ion pair Na⁺ + A^-, Na_o and Na_i are the external and internal concentrations of Na⁺, See PDF for Equation, and V _Na is the apparent velocity constant of the process. Equations are also given for the penetration of: (1) molecules of HA and the ion pair Na⁺ + A^-, (2) the ion pairs H⁺ + A^- and Na⁺ + A^-, (3) molecules of HA and the ion pairs Na⁺ + A^- and H⁺ + A^-. (4) The penetration of molecules of HA together with those of a weak base ZOH. (5) Exchange of ions of the same sign. When a weak electrolyte HA is the only solute present we cannot decide whether molecules alone or molecules and ions enter by comparing the velocity constants at different pH values, since in both cases they will behave alike, remaining constant if F_M is constant and falling off with increase of external pH value if F_M falls off. But if a salt (e.g., NaA) is the only substance penetrating the velocity constant will increase with increase of external pH value: if molecules of HA and the ions of a salt NaA. penetrate together the velocity constant may increase or decrease while the internal pH value rises. The initial rate See PDF for Equation (i.e., the rate when M_i = 0 and A_i = 0) falls off with increase of external pH value if HA alone is present and penetrates as molecules or as ions (or in both forms). But if a salt (e.g., NaA) penetrates the initial rate may in some cases decrease and then increase as the external pH value increases. At equilibrium the value of M_i equals that of M_o (no matter whether molecules alone penetrate, or ions alone, or both together). If the total external concentration (S_o = M_o + A_o) be kept constant a decrease in the external pH value will increase the value of M_o and make a corresponding increase in the rate of entrance and in the value at equilibrium no matter whether molecules alone penetrate, or ions alone, or both together. What is here said of weak acids holds with suitable modifications for weak bases and for amphoteric electrolytes and may also be applied to strong electrolytes.     

Sperm (ejaculate) competition in Drosophila melanogaster, and the reproductive value of females to males in relation to female age and mating status

• 1 In double mating experiments with Drosophila melanogaster in which one male had been irradiated, it was confirmed that sperm displacement is extensive, i.e. the second male to mate displaces most of the previously-stored sperm.
• 2 The predominance of the second ejaculate over the first increases with the interval between the two matings, from about P₂= 0.83 (second mating on the first day after the first mating) to about P₂= 0.99 (interval between mating = 14 days) where P₂ is the proportion of offspring fathered by the second male.
• 3 A more accurate method for calculating P₂ values is developed for experiments in which sperm are ‘labelled’ by irradiation treatment (equation 1).
• 4 Observations of the reducing egg production of the female throughout life were also obtained. A model is examined which incorporates both the sperm competition and egg production data to predict the reproductive value to a male of a mating with a given type of female, varying in age and mating status. The relative value (in terms of probable numbers of progeny gained) of a mating with a virgin or 4 day post-mating female is about twice that of a 14 day post-mating female, mainly because of the fecundity difference.
• 5 Some evolutionary aspects of sperm competition and multiple mating in insects are reviewed and discussed.

     

The rate of convergence of a generalized stable population

In an age-structured population that grows exponentially, each age groupP _i(t) at periodt is asymptotically equivalent tox ₀ ^t for some positive number x₀. In this paper we show that the speed at which the ith age group reaches its exponential state of equilibrium can be measured by the rate at which the ratio v_i(t)=P_i(t)/p_i(t–1) converges tox ₀. The age specific rate of convergence is determined by considering a quantityr satisfyingv _i(t)-x ₀ ¦ r ^t whent is large;R _i=Infr (over all initial populations,r satisfying the above inequality) is the R-factor used in numerical analysis to measure the rate at which the sequencev _i (t) converges tox ₀;S _i =- In R_i is then defined as the rate of convergence to stability of the ith age group. The case of constant net maternity rates is studied in detail; in this contextS ₀ is compared to the population entropyH, which was proposed by Tuljapurkar (1982) as a measure of the rate of convergence to stability.     

An Unbalanced Nested Model with Random Effects Having Unequal Variances

Consider the model Y_ijk=μ + a_i + b_ij + e_ijk (i=1, 2,…, t; j=1,2,…, B_i; k=1,2…,n_ij), where μ is a constant and a¹,b_ij and e_ijk are distributed independently and normally with zero means and variances σ²_ad_ij and σ², respectively, where it is assumed that the d_i's and d_ij's are known. In this paper procedures for estimating the variance components (σ², σ²_a and σ²_b) and for testing the hypothesis σ²_b = 0 and σ²_a = 0 are presented. In the last section the mixed model y_ijk, where x_ijkkm are known constants and β_m's are unknown fixed effects (m = 1, 2,…,p), is transformed to a fixed effect model with equal variances so that least squares theory can be used to draw inferences about the β_m's.     

Value of male remating and functional sterility in redback spiders

In the Australian redback spider, Latrodectus hasselti, males typically use their paired copulatory organs (palps) to copulate twice with a single female then sacrifice themselves to their cannibalistic mates in a strategy that increases their paternity in that one mating, but leads to death. This type of terminal investment in one mating is predicted only if the expected value of future matings is low for males relative to the value of repeated mating with the same female. In this laboratory study, we quantified the reproductive value of mating more than once with the same female (repeated mating) and mating with more than one female (multiple mating) for male redback spiders. We tested two natural selection hypotheses for repeated mating, sperm limitation and reproductive insurance, but found no support for either hypothesis. We show that, in the absence of sperm competition or cannibalism, male lifetime reproductive output is the same whether a male copulates once, twice, or several times with a given female. Repeated mating does not increase the probability of successful fertilization, nor does it increase the number of offspring produced in successful matings. Although male repeated mating is not favoured because of increased fertility of mates, other studies suggest it may be important in sperm competition. Here we show that the relative reproductive value of the first two copulations is very high for redback males because they are functionally sterile after each palp has been used once; nonvirgin males are unable to father offspring. Functional sterility and repeated mating by male redbacks may be favoured by the same factors that lead to male sacrifice behaviour: ecological constraints on multiple mating combined with competitive benefits of maximal investment in the first mating. Copyright 2002 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.     

Mononuclear copper(I) complexes of O-t-butyl-1,1-dithiooxalate and of O-t-butyl-1-perthio-1-thiooxalate

Described are the syntheses and structures of a phosphonium salt of the anionic ligand O-t-butyl-1,1-dithiooxalate, [PPh₃Bz][i-dto^tBu] ([PPh₃Bz][1]), and of two Cu(I) complexes of this anion, Cu(PPh₃)₂(η²-i-dto^tBu) (2) and Cu(dmp)(PPh₃)(η¹-i-dto^tBu) (3, dmp = 2,9-dimethyl-1,10-phenanthroline). In addition, it was found that the reaction of CuBr₂ with i-dto^tBu⁻ gives a O-t-butyl-1-perthio-1-thiooxalato complex of copper(I), [BzPh₃P][Cu(Br)(S-i-dto^tBu)] ([BzPh₃P][4]), where [S-i-dto^tBu]⁻ is a disulfide-containing anionic ligand. The electronic structure and absorption spectrum of this species were investigated by time dependent DFT methods.     

The Levels of a Universally Conserved tRNA Modification Regulate Cell Growth

N⁶-Threonylcarbamoyl-adenosine (t⁶A) is a universal modification occurring at position 37 in nearly all tRNAs that decode A-starting codons, including the eukaryotic initiator tRNA (tRNA_i^Met). Yeast lacking central components of the t⁶A synthesis machinery, such as Tcs3p (Kae1p) or Tcs5p (Bud32p), show slow-growth phenotypes. In the present work, we show that loss of the Drosophila tcs3 homolog also leads to a severe reduction in size and demonstrate, for the first time in a non-microbe, that Tcs3 is required for t⁶A synthesis. In Drosophila and in mammals, tRNA_i^Met is a limiting factor for cell and animal growth. We report that the t⁶A-modified form of tRNA_i^Met is the actual limiting factor. We show that changing the proportion of t⁶A-modified tRNA_i^Met, by expression of an un-modifiable tRNA_i^Met or changing the levels of Tcs3, regulate target of rapamycin (TOR) kinase activity and influences cell and animal growth in vivo. These findings reveal an unprecedented relationship between the translation machinery and TOR, where translation efficiency, limited by the availability of t⁶A-modified tRNA, determines growth potential in eukaryotic cells.     

An Unbalanced Two-way Model With Random Effects Having Unequal Variances

Consider the model y_ijk=u ± a_i ± b_i ± c_ij ± e_ijk i=1, 2,…, t; j=1, 2,…b; k=1, 2,…,n_ij where μ is a constant and a_i, b_i, c_ij are distributed independently and normally with zero means and variances Δ₂ Δ2/bd_ij and δ₂ respectively. It is assumed that d_i's, and d_ij's are known (positive) constants (for all i and j). In this paper procedures for estimating the variance components (Δ₂, Δ²_b and Δ²_a) and for testing the hypothesis H_oc:Δ²_c/Δ² = y₃ and H_oa:Δ²_b/Δ² = y₄ (where y₂, y₃, and y₄, are specified constants) are presented. A generalization for the mixed model case is discussed in the last section.     

Vibratory courtship in a web-building spider: signalling quality or stimulating the female?

Courtship behaviour in spiders in the form of premating vibrations by males may function (1) as a male identity signal used for species recognition, (2) in suppression of female aggressiveness, (3) to stimulate female mating behaviour, or (4) as a quality signal used in female choice. We investigated the function of web vibration by male Stegodyphus lineatus in a series of experiments. Regardless of vibratory performance, all males mated successfully with virgin females but only 56.4% of males mated with nonvirgin females. Vibratory performance did not influence male mating success, but heavier males had a higher probability of mating with mated females. Males vibrated less often and produced fewer vibrations when introduced on the web of a mated female. Males that vibrated webs of virgin females mated faster than nonvibrating males, but there was no effect of vibration rate or body mass. There was no effect of male vibratory effort or vibration rate on female reproductive success measured as time to egg laying, clutch size, number of hatched young, number of dispersed young and offspring body mass after a single mating. Males vibrated on abandoned virgin female webs but the response decreased with increasing duration of female absence, suggesting that females produce a web-borne pheromone, which elicits male vibrating behaviour. Mated females were less receptive and not stimulated by male vibrating behaviour. We conclude that male premating vibrations in S. lineatus do not function as a male quality signal selected via female choice. Rather, the primary function of this behaviour may be to stimulate a receptive female to mate. Copyright 2003 Published by Elsevier Ltd on behalf of The Association for the Study of Animal Behaviour.      

Metabolic Inhibition Strongly Inhibits Na-Dependent Mg Efflux in Rat Ventricular Myocytes

We measured intracellular Mg²⁺ concentration ([Mg²⁺]_i) in rat ventricular myocytes using the fluorescent indicator furaptra (25°C). In normally energized cells loaded with Mg²⁺, the introduction of extracellular Na⁺ induced a rapid decrease in [Mg²⁺]_i: the initial rate of decrease in [Mg²⁺]_i (initial Δ[Mg²⁺]_i/Δt) is thought to represent the rate of Na⁺-dependent Mg²⁺ efflux (putative Na⁺/Mg²⁺ exchange). To determine whether Mg²⁺ efflux depends directly on energy derived from cellular metabolism, in addition to the transmembrane Na⁺ gradient, we estimated the initial Δ[Mg²⁺]_i/Δt after metabolic inhibition. In the absence of extracellular Na⁺ and Ca²⁺, treatment of the cells with 1 μM carbonyl cyanide p-(trifluoromethoxy)phenylhydrazone, an uncoupler of mitochondria, caused a large increase in [Mg²⁺]_i from ∼0.9 mM to ∼2.5 mM in a period of 5-8 min (probably because of breakdown of MgATP and release of Mg²⁺) and cell shortening to ∼50% of the initial length (probably because of formation of rigor cross-bridges). Similar increases in [Mg²⁺]_i and cell shortening were observed after application of 5 mM potassium cyanide (KCN) (an inhibitor of respiration) for ≥90 min. The initial Δ[Mg²⁺]_i/Δt was diminished, on average, by 90% in carbonyl cyanide p-(trifluoromethoxy)phenylhydrazone-treated cells and 92% in KCN-treated cells. When the cells were treated with 5 mM KCN for shorter times (59-85 min), a significant decrease in the initial Δ[Mg²⁺]_i/Δt (on average by 59%) was observed with only a slight shortening of the cell length. Intracellular Na⁺ concentration ([Na⁺]_i) estimated with a Na⁺ indicator sodium-binding benzofuran isophthalate was, on average, 5.0-10.5 mM during the time required for the initial Δ[Mg²⁺]_i/Δt measurements, which is well below the [Na⁺]_i level for half inhibition of the Mg²⁺ efflux (∼40 mM). Normalization of intracellular pH using 10 μM nigericin, a H⁺ ionophore, did not reverse the inhibition of the Mg²⁺ efflux. From these results, it seems likely that a decrease in ATP below the threshold of rigor cross-bridge formation (∼0.4 mM estimated indirectly in the this study), rather than elevation of [Na⁺]_i or intracellular acidosis, inhibits the Mg²⁺ efflux, suggesting the absolute necessity of ATP for the Na⁺/Mg²⁺ exchange.     

Male traits associated with attractiveness in Conambo,Ecuador

This study investigated male attractiveness rankings in a small-scale Amazonian society. In the rural community of Conambo, Ecuador, men and women practice self-sufficient horticulture, men hunt, and, traditionally, men have experienced a high rate of mortality due to homicide. We tested whether male attractiveness rankings would be related to male age, warriorship, hunting ability, status, coalitional affiliation, and female age. Twenty-five women aged between 14 and 78 years ranked photographs of 29 local men aged between 16 and 74 years for attractiveness in addition to warriorship, hunting ability, and status. Results revealed that male age was negatively correlated (r=?.683, p=.01) with female rankings of male attractiveness. Warriorship (r=.517, p=.005), status (r=.489, p=.008), and hunting ability (r=.577, p=.001) were found to be positively correlated with attractiveness, after controlling for age. Additionally, females showed a bias for males in their in-group when ranking attractiveness (one-sample t test: T₂₉=16.727, p<.001). Attention is given to male age and coalitional affiliation as factors important in attractiveness rankings; warriorship and hunting ability also serve as ecologically salient features of male social worth. These findings contribute to a broader understanding of human attractiveness research by adding a new case study to the literature that documents previously unreported findings from a cultural context that is significantly different from the standard university-level student sample.