Body size in the field cricket Gryllus integer (Orthoptera : Gryllidae) :heritability and male mating success

The influence of male body weight on the aggressive and mating behaviour of male Gryllus integer was studied under laboratory conditions. The relationship between adult age and weight was first determined; female weight increased and male weight decreased with age. Virgin males that had been isolated since the adult molt were paired for similar age and a difference in weight of greater than 200 mg. Paired males and a virgin female were observed in a glass arena for 24 minutes or until a mating occurred. Larger males mated significantly more often than smaller males. Larger males attacked more often, were more successful in aggressive encounters and had more contact with the female. Males that did not mate had lower rates of courtship and mounts than males that mated. Females in trials that did not result in a mating were signifcantly heavier than females in trials that resulted in a mating. Larger males that mated were significantly closer in weight to the weight of the female than larger males in trials that did not result in a mating. Larger males in trials that did not result in a mating had higher rates of aggressive stridulation than larger males that mated. Male weight is therefore important in mating success; fitness traits should theoretically show low genetic variability. However, significant heritability values were found for live weight, dry weight, head width, pronotum width and length, hind femur length and forewing length when estimated from the regression of offspring on mid-parent values, offspring and female and male values separately and full-sib correlations. The heritability of hind femur width was significant when estimated from the regression of offspring on male parent and from full-sib correlations. Heritability estimates of forewing length were significantly higher when estimated from the regression of offspring on female parent than when estimated from the regression of offspring on male parent. High phenotypic, genetic and environmental correlations were found between all pairs of traits. Data on male mating success and the heritability of fitness traits were discussed in terms of the maintenance of genetic variability.

Heritability of multiple mating by female field crickets, Gryllus integer (Orthoptera: Gryllidae)

The heritability of multiple mating in female Gryllus integer crickets was studied. Two preliminary experiments were conducted to determine when females first mate following the post-imaginal moult and to ascertain whether constant exposure to males affects female mating rate. Female Q. integer first mated at an average age of 3.6 days (S.D. = 2.3, Range = 0-8 days) . Exposing female crickets to courting males 24 hr daily did not significantly alter mating rates from those females in contact with males for only 5 hr per day. A heritability value of 0.690 ± 0.283 was calculated for multiple mating behavior in female Q. integer using a parent-offspring regression approach. Parental females mated between land 30 times (x 9.8, S . D. = 6. 6 ) and offspring matings ranged from 0 to 26 times (x 7 .3, S.D. = 3.4). Multiple mating is probably a sexually selected trait which functions as a mechanism of female choice and increases reproductive success through increased offspring production. Classical theory suggests that traits intimately related with fitness should exhibit negligible heritable variation. However, this study has shown that multiple mating, a trait closely linked with reproductive fitness, exhibits substantial heritability. These results are in concordance with a growing body of empirical evidence suggesting many fitness traits in natural populations demonstrate heritabilities far removed from zero. Various mechanisms which may maintain heritable variation for female multiple mating in wild, outbred Q. integer populations are discussed.

Mating behaviours of the field cricket (Gryllus integer) at different levels of male density

The reproductive behaviour of the field cricket, Gryllus integer, was systematically observed in indoor arenas to determine the extent of female Choice and male-male competition at different sex ratios representing two male densities (12:6 and 6:6). The costs and benefits to males and females in those two densities were analyzed according to the theory of the evolution o£ leks. Observations were conducted during the dark hours when most calling occurred since hourly rates of courtship song and mating did not fluctuate significantly over a 24 h period. Female mating rates were not significantly different between densities, therefore males at high densities were not advantaged because of increased female tendencies to mate when social stimulation was increased. Mean rates of acoustical signalling (calling and courtin"g) did not differ significantly between densities. Mean rates of fighting by males at the high density were significantly greater than those of males at the low density. Mating benefits associated with callin~courting and fighting were measured. Mating rates did not vary with rates of calling at either density. Calling was not a prerequisite to mating. Courtship song preceded all matings. There was a significant power fit between male mating and courting rates, and male mating and fighting rates at the low, but not at the high, density. Density differences in the benefits associated with increased courting and fighting may relate, in part, to greater economic defensibility and monopoly of females due to reduced male competition at the low density. Dominant males may be preferentially chosen by females or better able to monopolize mating opportunities than subordinate males. Three criteria were used to determine whether dominant males were preferentially chosen by females. The number of matings by males who won fights (within 30 min of mating) was significantly greater than the number of matings by males who were defeated in such fights. Mating rates did not vary significantly with rates of winning at either density. There was a significant power fit between male mating rates and the percentage of fights a male won (irrespective of his fighting-frequency) at the low density. The mean duration a male guarded the female after mating did not vary significantly between densities. There was a significant linear relationship between the duration a spermatophore was retained and the duration a male guarded the female after mating. Courtship song apparently stimulated spermatophore removal. Male guarding involved inter-male aggression and reduced courtship attempts by other males. Males at the high density received no apparent reproductive benefits associated with increased social stimulation. Conclusive evidence for preferential choice of males by females, using the criteria examined here, is lacking. Males at the lower density had fewer competitors and could monopolize females more effectively.

Sperm utilization patterns in Gryllus integer (orthoptera: gryllidae

Sperm competition is the competition for fertilizations between ejaculates, within a female, following multiple mating. There are four sperm utilization or precedence patterns: first male precedence, where the first male to mate fertilizes most of the eggs laid by a female; last male precedence, where the last male to mate fertilizes most of the eggs laid by a female; "all-or-none" pattern, where sperm from either male fertilizes all the eggs laid by a female but which male's sperm that is used is random; or sperm mixing, where sperm from each male is used equally in fertilizing eggs laid by a female. Intermediate utilization patterns are also possible. Sperm competition occurs in a wide variety of insect species as well as other animals. This study was undertaken to study sperm competition in the field cricket, Gryllus integer. Four experiments were conducted: a radiation and sterilization experiment, a diapause experiment, and 2 competition experiments. It was found that 7,000 rad of gamma radiation sterilized adult ~ integer males. There was no diapause in the laboratory in ~ integer eggs. In the first competition experiment, three groups of females were used: females mated with a normal male, then with a second normal male (NN group); females mated with a normal male, and then with a sterile male (NR group); and females mated with a sterile male, and then with a normal male (RN group). The results obtained from this experiment showed that the mean proportion of eggs hatched was significantly different between 3 groups of females, with the proportion hatched much greater in the NN group than in either the NR or RN groups. The pattern for the proportion of eggs hatched following a double mating most closely resembled a pattern expected if sperm mixing is occurring. Results obtained in the replicate competition experiment showed that the mean proportion of eggs hatched for the females in the NR group was significantly lower than the proportion hatched in the other two groups. This also supports a model of sperm mixing as a precedence pattern. Values calculated following Boorman and Parker (1976), for the proportion of eggs fertilized by the second male to mate following a double mating, were 0.57 in competition experiment 1 and 0.62 in the replicate. These values indicate that sperm mixing occurs in~ integer.

The effect of diet and parasite load on female phonotaxis in the Texas field cricket, Gryllus integer

Female crickets respond selectively to variations in species-specific male calling songs. This selectivity has been shown to be age-dependent; older females are less choosy. However, female quality should also affect female selectivity. The effect of female quality on mate choice was examined in Gryllus integer by comparing the phonotactic responses of females on different diets and with different parasite loads to various synthetic models of conspecific calling song. Test females were virgin, 11-14 days old, and had been maintained on one of five diets varying in protein and fat content. Phonotaxis was quantified using a non-compensating Kugel treadmill which generates vector scores incorporating the speed and direction of movement of each female. Test females were presented with four calling song models which differed in pulse rate, but were still within the natural range of the species for the experimental temperature. After testing, females were dissected and the number of gregarine parasites within the digestive tract counted. There were no significant effects of either diet or parasitism on female motivation to mate although the combined effects of these variables seem to have an effect with no apparent trend. Control females did not discriminate among song types, but there was a trend of female preferences for lower pulse rates which are closest to the mean pulse rate for the species. Heavily parasitized females did not discriminate among pulse rates altho~gh there was a similar trend of high vector scores for low pulse rates. Diet, however, affected selectivity with poorly-fed females showing significantly high vector scores for pulse rates near the species mean. Such findings raise interesting questions about energy allocation and costs and risks of phonotaxis and mate choice in acoustic Orthoptera. These results are discussed in terms of sexual selection and female mate choice.

The effect of gregarine parasite infections, age, and diet on calling song structure and mating behaviour in the Texas field cricket, Gryllus integer

In the past ten years, many researchers have focussed their attention on parasites regarding the role they may play in causing variations in male secondary sexual traits and subsequent effects on female choice. Male age has also been suggested to be an important factor in female choice if old age reflects superior genes. This study investigated the effects that gregarine gut parasites, age, and diet have on the calling and mating behaviour of the male Texas field cricket, Gryllus integer. Male calling songs were recorded in the laboratory using a Digital Signal Processing Network. The song parameters measured were: pulse rate, pulse width, burst duration, pulses per burst, interburst interval, and percent missing pulses. The effects of parasite load and age on the various calling song parameters was investigated in crickets that were fed two different diets varying in nutritional quality. None of the calling song parameters were affected by either parasite load or age in either diet grou p. Courtship behaviour was ob served and recorded using an Eventlog recorder on an IBM computer in the laboratory. Females mated equally with paras(tized and unparasitized males and with old and young males The total duration and proportion of time spent performing each of 9 courtship displays were recorded for males on each diet. Only one display was affected by parasite load. Highly parasitized males fed the nutritionally inferior diet juddered for a proportionately shorter time than males with low parasite loads. Also, older males performed juddering and shaking antennae proportionally longer and juddering and raising wings for longer durations than younger males. Males that successfully mated were observed for performance of 8 post-copulatory guarding behaviour displays. None of the guarding behaviours were affected by parasite load. However, one display was affected by age, with older males performing guard turning for shorter durations than younger males. Results are discuss,ed in terms of the influence of parasites and age on female choice.

Effect of age on female choice in the field cricket, Gryllus interger

Female choice is an important element of sexual selection that may vary among females of the same species. Few researchers have investigated the causes of variation in selectivity with respect to potential mates and overall level of motivation toward a stimulus source representative of a mate. This study demonstrates that female age may be one cause of variation in female choice. Females of different ages may have different mate preferences. As females age, they have less time left to reproduce, and their residual reproductive value decreases. This should correspond to a higher reproductive effort which may be represented as increased motivation and/or decreased selectivity. The effect of age on mate choice in Gryllus integer was investigated by using a non-compensating treadmill, called the Kugel, to measure female phonotaxis. Artificially generated male calling songs of varying pulse rates were broadcast in either a singlestimulus or a three-stimulus experimental design. The pulse rates used in the calling song stimuli were 70, 64, 76, 55 and 85 pulses per second. These corresponded to the documented mean pulse rate for the species at the experimental temperature, one standard deviation below and above the mean, and 2.5 standard deviations below and above the mean, respectively. Test females were either 11-14 days or 25-28 days post-ecdysis. Trials usually were conducted two to seven hours into the scotophase. In the single-stimulus experiment, females were presented with stimuli with only one pulse rate. Older females achieved higher vector scores than younger females, indicating that older females are more motivated to mate. Both groups showed little phonotactic response towards 55 or 85 pIs, both of which lie outside the natural range of G. integer calling song at the experimental temperature. Neither group discriminated among the three pulse rates that fell within the natural range of calling song. In the three-stimulus experiment, females were presented with stimuli with one of three pulse rates, 64, 70 or 76 pIs, In alternation. Both age groups had reduced responsiveness in this experiment, perhaps due to an increase in perceived male density. Additionally, younger females responded significantly more to 64 and 70 pIs than to the higher pulse rate, indicating that they are selective with respect to mate choice. Older females did not discriminate among the three pulse rates. Therefore, it was concluded that selectivity decreases with age. A further study was conducted to determine that these effects were due to age and not due to the differing periods without a mating between the two age groups. Again, stimuli were presented in a three-stimulus experimental design. Age was held constant at 28 days and time since last mating varied from 11 to 25 days. Females varyIng in time since last mating did not differ in their responses to the calling song pulse rates. This indicated that the increased motivation and decreased selectivity exhibited In the initial experiments were due to age and not to time without a mating. Neither time of trial nor female weight had an effect upon female phonotaxis. Data are discussed in terms of mate choice, residual reproductive value, and costs of choice.

Individual differences and factors affecting male behaviour in field crickets

Individual differences in male sexual behav~our and the factors influencing calling behaviour were studied in the field crickets Gryllus 2 integer and Q. veletis. In a large (13m) outdoor arena individually numbered adult male ~~ integer started calling at three to five days of age but thereafter the age of individual G. integer males did not affect nightly calling duration. Calling also did not correlate with individual weight. In this study individual male calling was continuously distributed from 0 hrs. per night to 3.5 hrs. per night, on average. A temporal effect on the number of G. integer males calling was observed. The number of males calling through the night was uniform, but a sharp increase in the number calling was observed in the early morning. No difference in calling times was observed between the night and dawn callers. AlsC)' males calling at dawn usually didnotc'all during the preceeding night. Calling and reproductive success in 1979 demonstrated a negative logarithmic relationship while in the 1980(initial) population a negative linear relationship was observed. No relationship was seen in the 1980 high density population. The ratio of non-callers to callers also affected the mating of individuals in the 1979 and1980(initial) densities:-non~callers (males calling .5 hrs. per night, on average, or less) obtained more females when the population contained a high number of callers, this being a negative logarithmic relationship to, No such relationship was observed in the 1980 high density population. Individual displacement varied nightly and was not correlated to amount of calling or reproductive success of individual G. integer males. G. integer males were displa~ed more when in a higher density in the outdoor arena Male G. integer and G. veletis behaviours were also observed in an indoor arena at different densities and, in G. veletis, with respect to female presence. When females were present in the arena, in G. veletis, male calling was reduced. Males of both species called less, on average, when in ~ higher density, than when they were in a lower density. Male displacement of both species increased on average when in a higher density as compared to displacement in a lower density. Aggression was measured by aggressive call-ing and fighting and was studied in regards to density.G. integer demonstrated less aggression in all but one comparison at higher density. No difference was observed in the ratio of aggressive calling to f.ighting comparison in G. integer. G. veletis demonstrated mixed results. No difference in aggression between densities was observed in comparisons. Less.aggression did occur in higher densities when comparisons invol.ved fighting behaviour. Male behaviour represents a competitive strategy against ot~er males, strategy being defined as a genetic (in part) alternative to other strategies. In this sense, the factors of time, density, male-male aggression, and female presence are conditions demonstrated to affect male behaviour in G. integer and G. veletis. Individual male differences and other considerations suggest that alternative male behaviours are represented by at least two conditional strategies. This possibility, and the transient 'or stable nature of genetic polymorphisms in field cricket behaviour are considered.

Sexual behavior and factors affecting female reproduction in house and field crickets

The objective of this investigation was to clarify the adaptive significance of female sexual behaviours in the house cricket, Acheta domesticus, and the Texas field cricket, Gryllus integer. Experiments were focussed primarily on: nutritional factors affecting female reproductive success; the ontogeny of female sexual behaviours; female mating frequency and progeny production; and the pattern of sperm competition. Reproduction of singly mated female A. domesticus assigned to 3 nutritional regimes was compared . Females fed a vitamin and protein-enriched mouse chow, cannibalistic females, and starved females produced on the average, 513 , 200 and 68 offspring, respectively. Cannibals probably could not obtain the same amounts of essential nutrients as females fed mouse chow. Reabsorption of oocytes was likely the major factor contributing to the decreased reproduction of starved females. In addition, female !. domesticus fed mouse chow, but allowed constant access to males produced 11 times as many offspring than did females fed corn meal. Females fed corn meal probably could not absorb or synthesize enough dietary lipids, thus resulting in poor ovariole growth. Female !. domesticus first mate at an average adult age of 7 days, closely corresponding to when they first exhibit positive phonotaxis. Females mate repeatedly and often consume the externally attached spermatophore. In ~. domesticus, females allowed constant access to males produced significantly more offspring than did single maters. Similarly, doubly mated G. integer females produced more offspring than did single maters. This difference resulted largely from the failure of many single maters to reproduce. Remating by female crickets partly functions in offsetting the possibility of a failed initial mating. Nymph production increased significantly with the time the spermatophore was attached in singly mated ~. domesticus. Spermatophore consumption by the female was not affected by male guarding behaviour, and the interval between mating and eating of the spermatophore may often be shorter than the time required for maximum insemination. Some degree of sperm depletion in singly mated !. domesticus and G. integer may have occurred. The patterns of daily offspring production of singly and multiplymated females suggests that a factor provided by a male during mating stimulates female oviposition and/or egg production. Female crickets also might acquire nutrition from spermatophore consumption, a benefit that is augmented by female multiple mating. The electrophoretic examination of various allozymes in ~. integer did not permit determination of a pattern of sperm competition. However, the possibility of last male sperm predominance is related to male guarding behaviour.

Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

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.

Multi-Objective Genetic Algorithms for the Single Allocation Hub Location Problem

Hub Location Problems play vital economic roles in transportation and telecommunication networks where goods or people must be efficiently transferred from an origin to a destination point whilst direct origin-destination links are impractical. This work investigates the single allocation hub location problem, and proposes a genetic algorithm (GA) approach for it. The effectiveness of using a single-objective criterion measure for the problem is first explored. Next, a multi-objective GA employing various fitness evaluation strategies such as Pareto ranking, sum of ranks, and weighted sum strategies is presented. The effectiveness of the multi-objective GA is shown by comparison with an Integer Programming strategy, the only other multi-objective approach found in the literature for this problem. Lastly, two new crossover operators are proposed and an empirical study is done using small to large problem instances of the Civil Aeronautics Board (CAB) and Australian Post (AP) data sets.

Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].