Of grandmothers, grandfathers and wicked step-grandparents: differential impact of paternal grandparents on grandoffspring survival

'Historisch diente Verwandtschaft als die essentiellste Quelle für wirtschaftliche Unterstützung und Sicherheit. Aus einer evolutionären Perspektive gesehen jedoch sollten Investitionen in Bezug auf Angehörige den Grad von Vertrauen in genetische Verbundenheit reflektieren. Deshalb sollten patrilineale Verwandte weniger gewillt sein Unterstützung zu leisten als matrilineare Abgehörige, was erklären könnte, warum Großmütter mütterlicherseits sich oft als die am fürsorglichsten herausstellen, gefolgt von Großvätern mütterlicherseits, der Großmutter väterlicherseits und zuletzt dem Großvater väterlicherseits. Der Zweck der vorliegenden Studie ist es, großelterliche Investmentstrategien zu untersuchen, wenn beide Großeltern nahe bei ihren Nachkommen leben. In diesem Kontext bezieht sich geographische Nähe auf das Leben in derselben Dorfgemeinschaft. Demographische Informationen wurden aus den deutschen Dorfgenealogien Dannstadt/ Schauernheim (1480-1880) und Hochdorf/ Assenheim (1412-1912) entnommen. Alle empirischen Ergebnisse basieren auf Daten aus der Haushaltsebene. Betrachtete man die Rollen der Großeltern in Bezug auf das Überleben von Kleinkindern, wurde deutlich, dass Großeltern mütterlicherseits keine Auswirkungen zeigten, während Großeltern väterlicherseits scheinbar einen dazu differierenden Einfluss hatten. Die Mutter des Vaters hatte einen positiven Einfluss auf das Überleben ihrer Enkel. Nach dem ersten Geburtstag des Kindes gewann jedoch der förderliche Einfluss der Großmutter väterlicherseits eine statistische Bedeutung. Dieser Zeitpunkt implizierte eine großmütterliche Besorgnis direkt bezogen auf die Schwiegertochter und weniger auf das Enkelkind selbst. Im Gegensatz dazu übte der Großvater väterlicherseits einen negativen Einfluss auf die Überlebenschancen der Enkelkinder aus, was auf Konflikte in Bezug auf Ressourcen hinweisen könnte. Insgesamt ist anzunehmen, dass der eindeutige Ausgang der vorliegenden Studie durch geographische Nähe und strenge patriarchale Bindungen hätte unterstützt werden können, die beständig in bäuerlichen Familien vorgefunden wurden. Ländliche Gemeinden sind oft durch patrilineare Wohnverhältnisse, Arbeits- und Erbmuster charakterisiert, eingebunden in eine Generationenabfolge in der Landwirtschaft, weil landwirtschaftliches Auskommen Individuen an spezifische Ressourcen bindet.' (Autorenreferat)'Historically, kin served as the most essential source for economic assistance and security. However, from an evolutionary perspective, investments in next of kin should reflect the degree of confidence in genetic relatedness. Therefore, patrilineal relatives should be less willing to render support than matrilineal relatives, which might explain why the maternal grandmother is often found to be the most caring, followed by the maternal grandfather, the paternal grandmother, and lastly, the paternal grandfather. The purpose of the present study is to investigate grandparental investment strategies, when both sets of grandparents live close to their offspring. In this context, geographic proximity refers to living within the same village community. Demographic information was extracted from the German village genealogies of Dannstadt/ Schauernheim (1480-1880) and Hochdorf/ Assenheim (1412-1912). All empirical results are based on household-level data. When grandparental roles in infant survival were considered, it became evident that maternal grandparents were of no consequence, while paternal grandparents seemed to impact differentially. The father's mother had a positive influence on offspring survival. However, after the infant's first birthday, the beneficial impact of the paternal grandmother seized to be of statistical significance. This timing implies grandmaternal solicitude directly bestowed on the daughter-in-law, rather than the grandchild itself. In contrast, the paternal grandfather exerted a negative effect on grandoffspring survival, which may be indicative of resource conflicts. Overall, it is hypothesized that the unique outcome of the current study may have been fostered by geographic proximity and strong patriarchal ties invariably found in farm families. Rural communities are often characterized by patrilineal residence, work and inheritance patterns, tied in with a generation succession in farming, as agricultural subsistence ties individuals to specific resources.' (author's abstract

Almost all cop-win graphs contain a universal vertex

AbstractWe consider cop-win graphs in the binomial random graph G(n,1/2). We prove that almost all cop-win graphs contain a universal vertex. From this result, we derive that the asymptotic number of labelled cop-win graphs of order n is equal to (1+o(1))n2n2/2−3n/2+1

Properties of random graphs

The thesis describes new results for several problems in random graph theory. The first problem relates to the uniform random graph model in the supercritical phase; i.e. a graph, uniformly distributed, on $n$ vertices and $M=n/2+s$ edges for $s=s(n)$ satisfying $n^{2/3}=o(s)$ and $s=o(n)$. The property studied is the length of the longest cycle in the graph. We give a new upper bound, which holds asymptotically almost surely, on this length. As part of our proof we establish a result about the heaviest cycle in a certain randomly-edge-weighted nearly-3-regular graph, which may be of independent interest. Our second result is a new contiguity result for a random $d$-regular graph. Let $j=j(n)$ be a function that is linear in $n$. A $(d,d-1)$-irregular graph is a graph which is $d$-regular except for $2j$ vertices of degree $d-1$. A $j$-edge matching in a graph is a set of $j$ independent edges. In this thesis we prove the new result that a random $(d,d-1)$-irregular graph plus a random $j$-edge matching is contiguous to a random $d$-regular graph, in the sense that in the two spaces, the same events have probability approaching 1 as $n\to\infty$. This allows one to deduce properties, such as colourability, of the random irregular graph from the corresponding properties of the random regular one. The proof applies the small subgraph conditioning method to the number of $j$-edge matchings in a random $d$-regular graph. The third problem is about the 3-colourability of a random 5-regular graph. Call a colouring balanced if the number of vertices of each colour is equal, and locally rainbow if every vertex is adjacent to vertices of all the other colours. Using the small subgraph conditioning method, we give a condition on the variance of the number of locally rainbow balanced 3-colourings which, if satisfied, establishes that the chromatic number of the random 5-regular graph is asymptotically almost surely equal to 3. We also describe related work which provides evidence that the condition is likely to be true. The fourth problem is about the chromatic number of a random $d$-regular graph for fixed $d$. Achlioptas and Moore recently announced a proof that a random $d$-regular graph asymptotically almost surely has chromatic number $k-1$, $k$, or $k+1$, where $k$ is the smallest integer satisfying $d < 2(k-1)\log(k-1)$. In this thesis we prove that, asymptotically almost surely, it is not $k+1$, provided a certain second moment condition holds. The proof applies the small subgraph conditioning method to the number of balanced $k$-colourings, where a colouring is balanced if the number of vertices of each colour is equal. We also give evidence that suggests that the required second moment condition is true

Bounds on the Location of the Maximum Stirling Numbers of the Second Kind

Let K_n denote the smaller mode of the nth row of Stirling numbers of the second kind S(n, k). Using a probablistic argument, it is shown that for all n>=2, [exp(w(n))]-2<=K_n<=[exp(w(n))]+1, where [x] denotes the integer part of x, and w(n) is Lambert's W-function.Comment: accepted by Discrete Mathematic

»For Better or Worse, Till Death Us Do Part« – Spousal Age Gap and Differential Longevity: Evidence from Historical Demography

Based on a set of 2,371 family related entries dating from 1688 to 1921, the current study tried to verify longevity differentials due to interspousal age difference. For the purpose of the analysis, age-heterogamy was operationalized in terms of sample-specific marital age gap (3.2 years) with a standard deviation of 6.1 years. Based on this, five marriage groups were isolated. Female mean age at marriage experienced a slight increase over time, while the male mean at marriage decreased. This led to an appreciable narrowing of the spousal age gap. Age-homogamous unions were most prevalent in the lower socio-economic class (day-laborers, industrial workers) (p<0.01). In both husband- older and wife-older unions, the interspousal gap increased with marriage order. In accord with previous studies, mean age at death varied significantly by marriage group. Females, who married younger men, died later than females, who married older men. In contrast, male longevity was most depressed within age-similar marriages, while those who married older or younger wives displayed higher life spans. Overall, marriage to a younger spouse seemed to increase longevity prospects (p<0.05). These differentials were not exclusively a function of the marital age gap, but were affected by diverse confounders such as reproductive output and socio-economic status