On random genetic drift in a subdivided population

1968 ◽  
Vol 5 (2) ◽  
pp. 314-333 ◽  
Author(s):  
Edward Pollak

SummaryGenerations are assumed to be non-overlapping. We consider a haploid population divided into K parts, each of which contain N adults in any generation. These are obtained by a random sampling of the offspring of the previous generation. We assume that the probability of an adult offspring of an individual in one subpopulation being in some other subpopulation is the same small positive number, no matter what two subpopulations are considered.If the population initially has individuals of two types, A and a, it is of interest to study approximations, if n is large, to (1)the rate at which A or a is lost between generations n-1 and n,(2)the probability that A and a are still present in generation n,(3)the joint distribution of frequencies of A in the subpopulations.A solution is given for the first problem. It is found that if the mean number of migrants per generation from one subpopulation to another is at least as large as 1, the population behaves almost as if it were not subdivided. But if this number is considerably less that 1, then the rate at which one or the other gene is lost is slower than in an undivided population. The other two problems are discussed for K = 2.

1968 ◽  
Vol 5 (02) ◽  
pp. 314-333
Author(s):  
Edward Pollak

Summary Generations are assumed to be non-overlapping. We consider a haploid population divided into K parts, each of which contain N adults in any generation. These are obtained by a random sampling of the offspring of the previous generation. We assume that the probability of an adult offspring of an individual in one subpopulation being in some other subpopulation is the same small positive number, no matter what two subpopulations are considered. If the population initially has individuals of two types, A and a, it is of interest to study approximations, if n is large, to (1) the rate at which A or a is lost between generations n-1 and n, (2) the probability that A and a are still present in generation n, (3) the joint distribution of frequencies of A in the subpopulations. A solution is given for the first problem. It is found that if the mean number of migrants per generation from one subpopulation to another is at least as large as 1, the population behaves almost as if it were not subdivided. But if this number is considerably less that 1, then the rate at which one or the other gene is lost is slower than in an undivided population. The other two problems are discussed for K = 2.


1969 ◽  
Vol 73 (700) ◽  
pp. 255-270
Author(s):  
H. Caplan

The purpose of this prologue is to outline how I have approached the arrogant and impossible task of surveying an unborn century of law. I may also be able to illustrate that the nature and quality of the task is completely different from that attempted in the preceding papers. In the whole paper I have done little more than infer repeatedly, in different ways (a) that the shape of the future so far as law is concerned will be determined by the methods of communication adopted between sectors of the aerospace community and between the aerospace community and society at large, and (b) that the search for effective methods of communication is urgent. But my target is not the lawyers of our community—who I am not qualified to advise. I write for the other members of the Royal Aeronautical Society and I return to the task of persuading them that they have a role to play in evolving future laws for aerospace activities.


2015 ◽  
Vol 47 ◽  
pp. 485-491

Brief in which King Henry III recalls that as there are people who might perhaps convey to the lord pope and cardinals certain business which has recently been transacted by him as a result of the advice of his magnates and vassals, who may put a malicious interpretation on it, and as the affair might be a potential hindrance to him, he (so the recipients are better prepared to argue against the cunning deceits of such men) is minded to explain here the whole sequence of certain of his affairs, so that they may not be uninformed about what has passed, on which it may happen that they or others might otherwise be deceived. [2] So they are to be aware that whereas, at the time when the bishop of Norwich was legate (1218–1221), the earl Marshal still occupied the castles of Marlborough and Ludgershall, and was proposing to marry the sister of Count Robert of Dreux, and there were also other magnates in England who were endeavouring to distance him from the king by injurious alliances, the idea of betrothing the earl to one of the king's sisters was discussed between the legate, his justiciar and certain other magnates, partly because the political alliance with foreigners was thought alarming should the earl marry the sister of the count of Dreux – so as not to render England more accessible to foreigners, especially since Richard Marshal, the brother of the earl, might obtain all the Marshal lands in Normandy – and partly because of fear of the malice of those people who endeavoured to seduce the earl's allegiance from the king; and indeed because the castles of Marlborough and Ludgershall ought to be returned to him (which many times the earl promised) so that the other magnates might the more readily be persuaded likewise to return to the king his castles which they also held. [3] Because of his tender years and the fragile state of his kingdom, one of the king's sisters was destined for the said Marshal, by the authority of the legate and the counsel of certain magnates. The said Marshal swore to marry her, if it pleased the king and the magnates of the realm. The justiciar swore to hand her over to the Marshal, if the magnates of the kingdom agreed. The legate, the justiciar and others who were present faithfully promised that they would approach this matter conscientiously. The said castles were handed back to the legate, so that if the contract were not fulfilled within a space of time long now expired, they should be given back promptly to the Marshal. [4] Further to this, when these matters were communicated to other magnates, notably to the earl of Chester who at that point returned from the Holy Land (July 1220) – the earl strongly approved the match and many others agreed, with no dissenters. But afterwards, when certain dissensions had emerged, some people demurred, claiming – just as indeed was said on their behalf in the papal curia – that the king should have no greater an aid for his own marriage as for his sisters, as a result of which his sisters’ marriage arrangements would be impeded, about which he was negotiating a considerable treaty in foreign parts, and so at that time the Marshal arrangement remained unfulfilled. [5] But when recently (June 1222) the same Marshal obtained a papal mandate addressed to the archbishop of Canterbury and bishop of Salisbury, that either they should cause him to be entirely absolved from the conditions of the oath, or the marriage contract be confirmed, the Marshal insisted vociferously that one of those options should be followed, since he cared for nothing other than that he be married. So now as before it is a worry that Marshal – a man of great power in England as much as Ireland – might marry the sister of the said count of Dreux or a daughter of the duke of Brabant, who was likewise offered to him – which on account of the matters already alluded to would assist the king in no way – or even the sister of the king of Scots, where similarly no small danger might arise, for by how much nearer Scotland is to Ireland and the Marshal lands, so much the more dangerous would the marriage be to the king. [6] So having considered the energy and power of the said Marshal, as well as the faithful service he has openly and strenuously performed for the king especially in the region of Wales – his castles which Llywelyn prince of Gwynedd held which Marshal vigorously reclaimed (in April 1223) would scarcely have been taken without his capacity and hard work – and also bearing in mind the example of Philip, the late king of France (died 14 July 1223) – who for a long time freely married off his daughters, sisters, and nieces to the likes of the counts of Namur and Ponthieu and others of his men rather than to foreigners, just as the current king of France recently married off his niece, the daughter of Guichard de Beaujeu to the count of Champagne (after August 1223); because of all these precedents and the great things which are hoped for from the Marshal, it should not be objectionable to the king and his council – all things considered – that he may at some time permit him to marry his sister to his advantage and honour. The king, on the advice of such and such men, having discussed this business extensively, conceded the Marshal his younger sister, without lessening of his lands, castles or money. [September 1223 × January 1224]A= Kew, National Archives (PRO), SC1/2/109.Printed, Royal Letters, 1: 244–246; Diplomatic Documents, 95–97.


1958 ◽  
Vol 11 (1) ◽  
pp. 70-72
Author(s):  
Frank C. White

Even in good weather, visual collision avoidance by pilots is unsatisfactory for reasons which include the following:(i) When on a collision course the other aircraft has no relative motion across the windscreen and is indistinguishable from other marks on the windscreen until danger is very close.(ii) There is a tendency to focus the eyes on nearby objects on the windscreen instead of at infinity, especially in the absence of conspicuous cloud and at high altitude. This can cause ‘empty field myopia’ whereby a normal pilot becomes nearsighted, his eyes focusing on a location less than six feet away.(iii) In modern jet fighter aircraft the pilot must give much of his visual attention to instruments in the cockpit, such as the altimeter, owing to the difficulty of maintaining longitudinal stability, especially when heavily loaded. In clear air above 35,000 ft, it is estimated the pilot flies half contact and half on instruments.


2018 ◽  
Vol 102 (554) ◽  
pp. 233-245
Author(s):  
John D. Mahony

In a recent and illuminating article that provided much food for thought [1], the problem of tethering a goat at the edge of a circular pasture so as to restrict its attentions to only one half of the grazing supply was elegantly addressed and developed further to embrace the corresponding three-dimensional scenario involving a bird. The exercises resulted in mathematical formulations that required the use of numerical methods to extract practical results. Following the article, various questions and different scenarios sprang to my mind. The following poser perhaps best illustrates one of these, and it is the purpose of this Article to address this particular conundrum:A grazier has three troublesome beasts that are water averse, eat grass and who will, given half a chance, eat one another also in some fashion. The first will eat the other two and the second will eat only the third, which eats just grass. Having stabled and fed them in separate stalls during the winter months he plans to release them in the spring to an arbitrarily elliptic shaped pasture up to the water's edge in the middle of a lake. He has at his disposal: (1)A drum of tethering rope from which he can cut just once any required length, TBD (To Be Determined).(2)Slip rings and two tethering pegs that can be positioned only on the pasture boundary (i.e. at the water's edge).


1971 ◽  
Vol 8 (04) ◽  
pp. 828-834 ◽  
Author(s):  
Asha Seth Kapadia

Kingman (1962) studied the effect of queue discipline on the mean and variance of the waiting time. He made no assumptions regarding the stochastic nature of the input and the service distributions, except that the input and service processes are independent of each other. When the following two conditions hold: (a) no server sits idle while there are customers waiting to be served; (b) the busy period is finite with probability one (i.e., the queue empties infinitely often with probability one); he has shown that the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in order of their arrival. Conditions (a) and (b) will henceforward be called Kingman conditions and a queueing system satisfying Kingman conditions will be referred to in the text as a Kingman queue.


1966 ◽  
Vol 112 (486) ◽  
pp. 429-441 ◽  
Author(s):  
Alistair Munro

This article presents the results of a study in which a number of social, familial and demographic aspects of primary depressive illness were examined under carefully-controlled conditions. The following factors are particularly considered: 1.The size of the sibship in the depressive's family of upbringing;2.the ordinal position of the depressive in that sibship;3.the depressive's position in the sibship relative to the other sibs;4.the age of the parents at the time of the depressive individual's birth;5.the presence of a family history of severe mental illness;6.celibacy and marriage in depressive individuals;7.the fertility of depressives;8.the social class distribution of depressive illness.


1992 ◽  
Vol 135 ◽  
pp. 266-272
Author(s):  
Paul Couteau

I.We recall the main surveys: J. Herschel (1826), W. Struve (1825), A.W. Burnham and G.W. Hough (1880), R.G. Aitken and W.J. Hussey (1910), R. Jonckeere and T.E. Espin (1910), W.H. van den Bos (1925), R.A. Rossiter (1950). Presently the classical surveys are continuing with P. Muller, W.D. Heintz, and P. Couteau. The interferometric survey with large telescopes is carried out at CHARA.II.The results of old surveys, up to 1950, amount to 700 known orbits out of more than 35000 found binaries. The new surveys since 1965, both visual and interferometric, had checked 4000 new binaries giving already about 30 orbits. The periods are shorter and shorter: the mean period is 200 years for Struve (1825) binaries, 75 years for Aitken’s (1910), 25 years for Couteau and Muller’s (1970), and 7 years for CHARA’s. The number of known orbits increases exponentially with time.III.The “classical” surveys will have to be performed again within fifty years with refractors.The interferometric and aperture syntheses surveys will be able to observe every binary, even those in contact with each other. With HIPPARCOS’ results, astronomers will dispose of a complete set of data for new theories of stellar evolution.


1964 ◽  
Vol 5 (38) ◽  
pp. 191-206
Author(s):  
John R. Reid

AbstractA highly deformed area in the Ross Ice Shelf near the Bay of Whales was studied during the 1958–59 Antarctic summer season. A series of snow-firn folds up to 8 m. high and with a wavelength of approximately 100 m. occurs here. Along one of these folds, a unique ice layer formed during the 1952–53 season through refreezing of melt water. From sites along this layer approximately 2,300 ice grains were measured using the root mean square method with the least circle diameter. The data obtained indicate the following:The mean diameter of the ice grains ranges from 4.5 mm. in the ice from the crest of the anticline to 2.5 mm. in the zone of maximum shear stress and/or in sections having a high air bubble content.The large diameter of the ice grains at the crest is attributed to greater solar radiation resulting from their proximity to the 1958–59 snow surface, and because they are near the surface of the exposed crevasse wall.The area of maximum shear stress, which is represented by small ice grains and the presence of secondary folds, is located almost halfway between the crest and the trough.Grains in the trough are larger than those in the shear zone because of less stress, and smaller than those at the crest because of deeper burial and the presence of a crevasse bridge which eliminates all direct radiation here.The growth of the ice grains is therefore controlled by temperature, stress and impurities.


1966 ◽  
Vol 70 (670) ◽  
pp. 951-952 ◽  
Author(s):  
J. A. C. Marsden

In preparation for the wind tunnel testing of a series of aerodynamic research models a strain-gauged balance was sought which could be successfully made without the use of sophisticated tools. The principal requirements which influenced the design of the balance were:(a)It must enable lift, drag and pitching moment to be measured.(b)Deformation of the balance under the aerodynamic loads to be small.(c)Use of only basic workshop tools.(d)Short manufacturing time.Further, the models were to be sting mounted at one end of the balance with their span vertical. The other end of the balance was to be rigidly fixed to a supporting stand which would be mounted on the wind tunnel turntable to permit incidence variation (Fig. 5).


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