Rings, Group Rings, and Their Graphs

We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. We define an undirected graph ᴦ(R) with nonzero zero-divisors as vertices and distinct vertices x and y are adjacent if xy=0 or yx=0. We investigate the Isomorphism Problem for zero-divisor graphs of group rings RG. Let Sk denote the sphere with k handles, where k is a non-negative integer, that is, Sk is an oriented surface of genus k. The genus of a graph is the minimal integer n such that the graph can be embedded in Sn. The annihilating-ideal graph of R is defined as the graph AG(R) with the set of ideals with nonzero annihilators as vertex such that two distinct vertices I and J are adjacent if IJ=(0). We characterize Artinian rings whose annihilating-ideal graphs have finite genus. Finally, we extend the definition of the annihilating-ideal graph to non-commutative rings.

The influence of investigator disturbance on aggressive behaviour and breeding success of ring-billed gulls (Larus delawarensis) /

Increased losses of eggs and chicks resulting from human intrusion (investigator or other) into seabird colonies has been well documented. In 1990/91, I studied the effects of investigator disturbance on aggressive behaviour and breeding success of individual pairs of ring-billed gulls nesting at two colonies near Port Colborne, Ontario. The insular colony was on an artificial breakwall, associated with the Welland Ship Canal, approximately 1 km off the north shore of Lake Erie. The mainland colony was adjacent to the canal approximately 1 km east of the breakwall. The frequencies of adult threat and assault behaviours, chick movement and adult attacks on chicks were recorded by continuous scan sampling 30 min prior to, 30 min during and 60 (2 X 30) min after investigator disturbance. The frequency of threat and assault behaviours increased during the period of investigator activity in the colony while the duration of wingpulls and beakpulls decreased. Significantly more chicks ran ("runners") from their natal territories during disturbances and "runners" were more frequently attacked than "territorial" chicks. No chicks were fatally attacked during disturbance and "runners" returned to their natal territories quickly after disturbance. Breeding success was determined for pairs nesting in study plots subjected to two levels of disturbance (normal and moderate). The disturbance level of each plot differed in visitation frequency and activities performed on each visit. Investigator disturbance had no effect on the hatching success or fledging success (taken as 21 days of age) of ring-billed gull study pairs at either colony.

Broad reduction and adoption in ring-billed gulls (Larus Delaworensis): the potential for inergenerational conflict

Patterns of intra-clutch egg size variation and intra-clutch hatch intervals in the Ring-billed gull (Larus delawarensis) were documented during the peak nesting period of two consecutive breeding seasons, at a colony near Port Colborne, Ontario. Egg size decreased with laying order; third laid eggs were significantly smaller than first laid eggs. Hatching of the third egg was delayed from that of first and second eggs. Intraclutch egg size differences established initial size disparities among chicks at hatch. Hatch intervals further exaggerated size disparities during the early post brood completion period. Competitive asymmetries among chicks were associated with increased mortality rates among third hatched chicks despite the lack of evidence of a sibling feeding hierarchy. Fledging success in 1987 was greater than in 1988. A "brood reduction strategy" appears to have enabled parents in 1987, to obtain an extra unit of reproductive fitness, while in 1988 parents were often unable to raise the entire brood and third chicks likely represented insurance reproductive value. Experimental broods (1988) were created in which hatch intervals were double those of natural intervals. The size disparities among chicks were significantly greater than in control broods, and the pattern of mortality among chicks suggested that first chicks benefited at a cost to second and third chicks. Parents of peak experimental broods achieved a fledging success rate similar to that of control broods. Characteristics of chick adoptions were also recorded. In each study year, 9 chicks abandoned their natal territories, 6 of which were adopted. Chicks consistently established themselves into broods where they were older than resident chicks. No direct evidence of cost to foster parents, or benefits to adopted chicks was obtained, although fledging success of adopted chicks was high.

Seasonal variation in hatching pattern and chick survival in the ring-billed gull Larus delawarensis

The general objective of my study was to monitor proximate causes and seasonal patterns of hatching asynchrony and chick survival in the Ring-billed Gull (Larus delawarensis). Two different plots were set up at a Ring-billed Gull colony near Port Colborne, Ontario in the summer of 1992. One group was from 'peak' nesting pairs (clutches initiated between 15 April and 1 May); a second group was from 'late' nesting pairs (clutches initiated between 9 .. 22 May). Despite equal intra-clutch egg laying intervals between the peak and late periods, intra-clutch hatching intervals lengthened as the season progressed (ie. hatching became more asynchronous). Clutches from both periods were monitored for nocturnal attendance and brood patch development of parents was monitored during the egg laying period. Late nesters were characterized by an absence of nocturnal desertion, substantial brood patch defeatheration at clutch initiation and a reduction in the number of chicks fledged per pair. Chick survival to 25 days (taken as fledging) reflected patterns of chick mass at brood completion and five days post-brood completion, in peak clutches. In late clutches, survival was poor for all chicks and, was partially independent of hatching order, due in part to stochastic events such as Herring Gull predation and adverse weather. In both the peak and late periods, last-hatched C-chicks realized the poorest survival to fledging among brood mates. An artificial hatching pattern (manipulated synchrony) and an artificial hatching order were created, in three-chick broods, through a series of egg exchanges. In peak and late clutches manipulated to hatch synchronously (s; 24 h): C-chick survival to fledging did not differ from the survival of A- and B-chicks, in the peak period. In the late period, the survival of C-chicks was significantly lower than that of A-chicks. In peak clutches manipulated such that chicks from last-laid eggs (C-chicks) hatched 24 h - 48 h ahead of the A- and B- chicks, C-chick survival was greater than in controls. Within those broods, C-chicks survived better on average than both A- and B- chicks.

Sex chromosome translocation and speciation : a Drosophila genetic model

Although exceptions may be readily identified, two generalizations concerning genetic differences among species may be drawn from the available allozyme and chromosome data. First, structural gene differences among species vary widely. In many cases, species pairs do not differ more than intraspecific populations. This suggests that either very few or no gene substitutions are required to produce barriers to reproduction (Avise 1976). Second, chromosome form and/or number differs among even closely related species (White 1963; 1978; Fredga 1977; Wright 1970). Many of the observed chromosomal differences involve translocational rearrangements; these produce severe fitness depression in heterozygotes and were, thus, long considered unlikely candidates for the fixation required of genetic changes leading to speciation (Wright 1977). Nonetheless, the fact that species differences are frequently translocational argues convincingly for their fixation despite prejudices to the contrary. Haldane's rule states that in the F of interspecific crosses, the heterogametic sex is absent or sterile in the preponderance of cases (Haldane 1932). This rule definitely applies in the genus Dr°sophila (Ehrman 1962). Sex chromosome translocations do not impose a fitness depression as severe as that imposed by autosomal translocations, and X-Y translocations may account for Haldane's rule (Haldane 1932). Consequently a study of the fit ness parameters of an X·yL and a yS chromosome in Drosophila melanogaster populations was initiated by Tracey (1972). Preliminary results suggested that x.yL//YSmales enjoyed a mating advantage with X·yL//X·yL females, that this advantage was frequency dependent, that the translocation produced sexual isolation and that interactions between the yL, yS and a yellow marker contributed to the observed isolation (Tracey and Espinet 1976; Espinet and Tracey 1976). Encouraged by the results of these prelimimary studies, further experiments were performed to clarify the genetic nature of the observed sexual isolation, S the reality of the y frequency dependent fitness .and the behavioural changes, if any, produced by the translocation. The results of this work are reported herein. Although the marker genes used in earlier studies, sparkling poliert an d yellow have both been found to affect activity,but only yellow effects asymmetric sexual isolation. In addition yellow effects isolation through an interaction with the T(X-y) chromosomes, yS also effects isolation, and translocational strains are isolated from those of normal karyotype in the absence of marker gene differences. When yS chromosomes are in competition with y chromosomes on an X.yL background, yS males are at a distinct advantage only when their frequency is less than 97%. The sex chromosome translocation alters the normal courtship pattern by the incorporation of circling between vibration and licking in the male repertoire. Finally a model of speciation base on the fixation of this sex chromosome translocation in a geographically isolated gene pool is proposed.

Viability interactions between the left and right arms of the second chromosome of Drosophila melanogaster

Inter and intrachromosomal viability interactions have been detected in a few experimental studies. Computer simulations and analytical models have led to postulation of nonadditivity of gene action. This study reports evidence of strong nonadditive interactions between the arms of the metacentric second chromosome of Drosophila melanogaster. Mean viability for 40 homozygous lines of the second chromosomes was 0.720+0.265 • Mean viability for 40 half homozygous second chromosomes was 0.928!O.)10 • Significant heterogeneity among and within lines was found in both groups of chromosomes, as well as a highly significant viability difference between the two groups. Comparison of observed viabilities with the expected values, according to the theories of additive and multi - plicative gene action. was made for both groups. Highly significant departures from the expected values were found for over 90% of the lines in both groups of chromosomes, for both additive and multiplicative models of gene action.