Showing papers on "Foraging published in 2003"

From spatial orientation to food acquisition in echolocating bats

Abstract: Field research on echolocation behavior in bats has emphasized studies of food acquisition, and the adaptive value of sonar signal design as been considered largely in the context of foraging. However, echolocation tasks related to spatial orientation also differ among bats and are relevant to understanding signal structure. Here, we argue that the evolution of echolocation in bats is characterized by two key innovations: first, the evolution of echolocation for spatial orientation and, second, a later transition for prey acquisition. This conceptual framework calls for a new view on field data from bats orienting and foraging in different types of habitats. According to the ecological constraints in which foraging bats operate, four distinct functional groups or guilds can be defined. Within each group, signal design and echolocation behavior are rather similar.

Using first‐passage time in the analysis of area‐restricted search and habitat selection

Abstract: How animals change their movement patterns in relation to the environment is a central topic in a wide area of ecology, including foraging ecology, habitat selection, and spatial population ecology. To understand the underlying behavioral mechanisms in- volved, there is a need for methods to measure changes in movement patterns along a pathway through the landscape. We used simulated pathways and satellite tracking of a long-ranging seabird to explore the properties of first-passage time as a measure of search effort along a path. The first-passage time is defined as the time required for an animal to cross a circle with a given radius. It is a measure of how much time an animal uses within a given area. First-passage time is scale dependent, and a plot of variance in first-passage time vs. spatial scale reveals the spatial scale at which the animal concentrates its search effort. By averaging the first-passage time on a geographical grid, it is possible to relate first-passage time to environmental variables and the search pattern of other individuals.

Social learning in fishes : a review

Abstract: Animals acquire skills and knowledge from other animals, and fish are no exception. There is now strong experimental evidence that many species of fish exhibit social learning and traditional behaviours. Here, we review the literature pertaining to social learning in fish, focusing on (i) antipredator behaviour, (ii) migration and orientation, (iii) foraging, (iv) mate choice and (v) eavesdropping.

Bumblebees: Behaviour, Ecology, and Conservation

Abstract: Preface 1. Introduction 2. Thermoregulation 3. Social Organisation and Conflict 4. Finding a Mate 5. Natural Enemies 6. Foraging Economics 7. Exploitation of Patchy Resources 8. Choice of Flower Species 9. Intraspecific Floral Choices 10. Foraging Cues Gained from Other Bees 11. Competition and Niche Differentiation in Bumblebee Communities 12. Bumblebees as Pollinators 13. Conservation 14. Bumblebees Abroad Effects of Introduced Bees References Index

Levy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi)

Abstract: Scale invariant patterns have been found in different biological systems, in many cases resembling what physicists have found in other nonbiological systems. Here we describe the foraging patterns of free-ranging spider monkeys (Ateles geoffroyi) in the forest of the Yucatan Peninsula, Mexico and find that these patterns resemble what physicists know as Levy walks. First, the length of a trajectory s constituent steps, or continuous moves in the same direction, is best described by a power-law distribution in which the frequency of ever larger steps decreases as a negative power function of their length. The rate of this decrease is very close to that predicted by a previous analytical Levy walk model to be an optimal strategy to search for scarce resources distributed at random Viswanathan et al 1999). Second, the frequency distribution of the duration of stops or waiting times also approximates a power-law function. Finally, the mean square displacement during the monkeys first foraging trip increases more rapidly than would be expected from a random walk with constant step length, but within the range predicted for Levy walks. In view of these results, we analyze the different exponents characterizing the trajectories described by females and males, and by monkeys on their own or when part of a subgroup. We discuss the origin of these patterns and their implications for the foraging ecology of spider monkeys.

Psychophysics: bees trade off foraging speed for accuracy.

Abstract: Bees have an impressive cognitive capacity1,2,3,4, but the strategies used by individuals in solving foraging tasks have been largely unexplored. Here we test bumblebees (Bombus terrestris) in a colour-discrimination task on a virtual flower meadow and find that some bees consistently make rapid choices but with low precision, whereas other bees are slower but highly accurate. Moreover, each bee will sacrifice speed in favour of accuracy when errors are penalized instead of just being unrewarded. To our knowledge, bees are the first example of an insect to show between-individual and within-individual speed– accuracy trade-offs.

Honeybee foraging in differentially structured landscapes

Abstract: Honeybees communicate the distance and location of resource patches by bee dances, but this spatial information has rarely been used to study their foraging ecology. We analysed, for the first time to the best of the authors' knowledge, foraging distances and dance activities of honeybees in relation to landscape structure, season and colony using a replicated experimental approach on a landscape scale. We compared three structurally simple landscapes characterized by a high proportion of arable land and large patches, with three complex landscapes with a high proportion of semi-natural perennial habitats and low mean patch size. Four observation hives were placed in the centre of the landscapes and switched at regular intervals between the six landscapes from the beginning of May to the end of July. A total of 1137 bee dances were observed and decoded. Overall mean foraging distance was 1526.1 +/- 37.2 m, the median 1181.5 m and range 62.1-10037.1 m. Mean foraging distances of all bees and foraging distances of nectar-collecting bees did not significantly differ between simple and complex landscapes, but varied between month and colonies. Foraging distances of pollen-collecting bees were significantly larger in simple (1743 +/- 95.6 m) than in complex landscapes (1543.4 +/- 71 m) and highest in June when resources were scarce. Dancing activity, i.e. the number of observed bee dances per unit time, was significantly higher in complex than in simple landscapes, presumably because of larger spatial and temporal variability of resource patches in complex landscapes. The results facilitate an understanding of how human landscape modification may change the evolutionary significance of bee dances and ecological interactions, such as pollination and competition between honeybees and other bee species.

Bumblebees: their behaviour and ecology.

Abstract: 1. Introduction 2. Thermoregulation 3. Social organisation and conflict 4. Finding a mate 5. Natural enemies 6. Foraging Economics 7. Foraging range 8. Exploitation of patchy resources 9. Choice of flower species 10. Intraspecific floral choices 11. Communication during foraging 12. Competition in bumblebee communities 13. Bumblebees as pollinators 14. Conservation 15. Bumblebees abroad effects of introduced bees on native ecosystems

Spontaneous emergence of leaders and followers in foraging pairs

Abstract: Animals that forage socially often stand to gain from coordination of their behaviour. Yet it is not known how group members reach a consensus on the timing of foraging bouts. Here we demonstrate a simple process by which this may occur. We develop a state-dependent, dynamic game model of foraging by a pair of animals, in which each individual chooses between resting or foraging during a series of consecutive periods, so as to maximize its own individual chances of survival. We find that, if there is an advantage to foraging together, the equilibrium behaviour of both individuals becomes highly synchronized. As a result of this synchronization, differences in the energetic reserves of the two players spontaneously develop, leading them to adopt different behavioural roles. The individual with lower reserves emerges as the 'pace-maker' who determines when the pair should forage, providing a straightforward resolution to the problem of group coordination. Moreover, the strategy that gives rise to this behaviour can be implemented by a simple 'rule of thumb' that requires no detailed knowledge of the state of other individuals.

Surface‐water constraints on herbivore foraging in the kruger national park, south africa

Abstract: At a landscape scale, the combined influence of biotic and abiotic factors may determine the distribution patterns of large herbivores in African savanna ecosystems. Herbivores foraging in these ecosystems may become nutritionally stressed during an annual dry season when both forage quality and quantity are reduced. Additionally, the locations of water sources may impose a landscape-scale constraint on dry-season herbivore distri- butions. We used logistic regression to analyze 13 years of aerial census data collected in the Kruger National Park (KNP), South Africa, and evaluated hypotheses regarding the relative influences that surface water, forage quality, and forage quantity exert on the dry- season, landscape-scale distribution patterns of eight herbivore species. Hypotheses re- garding the degree of correlation between species' distributions and distance to water were developed using previous observations of species' relative water dependence. We also developed hypotheses regarding species' responses to the trade-off that may occur between surface-water constraints and nutritional requirements when either forage quality or quantity is reduced. In general, we expect an increase in species' mean distance to water as a result of individuals mitigating limitations in nutritional requirements (i.e., intake quality or quantity) by foraging farther from water. Our analyses suggest that the trade-off between nutritional requirements and surface-water constraints that species face varies according to the species' water dependence, size, and gut morphology. Of the four grazers considered in our analyses, waterbuck distributions appear to be constrained primarily by surface- water availability. Distributions of buffalo, a large ruminant grazer, suggest that individuals face a trade-off between nutritional requirements and surface-water constraints when forage quantity is reduced. Alternatively, distributions of wildebeest, a smaller ruminant grazer, suggest that individuals face this trade-off when access to high-quality forage is limited. In comparison to buffalo and wildebeest, the strength of this trade-off is moderate for zebra, a nonruminant similar in size to wildebeest, when either forage quality or quantity is reduced. Distribution patterns for browsers are characterized by a weak relationship with distance to water, as expected for these relatively water-independent species. Population densities relative to forage quality confound exploration of this trade-off for mixed feeders.

Social insects: Cuticular hydrocarbons inform task decisions

Abstract: Social insect colonies are organized without central control, and must not only accomplish many tasks, such as foraging and nest construction, but must also respond to changing conditions by adjusting the number of workers performing each task1,2. Here we use chemically treated, artificial ants to show that cuticular hydrocarbons, which differ according to task, are used by workers of the red harvester ant (Pogonomyrmex barbatus) to recognize the tasks of the ants that they encounter. Encounters with other ants thus inform a worker's decision on whether to perform a particular task.

Foraging by bats in cleared, thinned and unharvested boreal forest

Abstract: Summary 1 Modern silvicultural methods employ various styles of selective harvesting in addition to traditional clear-cutting. This can create a mosaic of patches with different tree densities that may influence habitat use by foraging bats. Use of forest patches may also vary among bat species due to variation in their manoeuvrability. Apart from studies investigating use of clear-cuts, few have tested for differences in use of forest patches by bats, or for differences among bat species. 2 We investigated the influence of various harvesting regimes, which created forest patches of different tree densities, on habitat selection by foraging bats in the boreal mixed-wood forest of Alberta, Canada. We also tested for variation in habitat selection among species related to differences in body size and wing morphology. 3 Over two summers we assessed habitat use by bats using ultrasonic detectors to count the echolocation passes of foraging bats. We measured activity in three forest types and four tree densities, ranging from intact (unharvested) forests to clear-cuts. 4 Smaller, more manoeuvrable, species (Myotis spp.) were less affected by tree density than the larger, less manoeuvrable, Lasionycteris noctivagans. Two Myotis spp. differed in their habitat use. Myotis lucifugus, an aerial insectivore, preferred to forage along the edge of clear-cuts, while M. septentrionalis, a species that gleans prey from surfaces, did not forage in clear-cuts but preferred intact forest. 5 The largest species in our study, L. noctivagans, preferred clear-cuts and avoided intact patches. There were therefore differences in habitat selection by foraging bats among the species in our study area, and these were correlated with size and wing morphology. 6 Synthesis and applications. Our results suggest that, in the short term, thinning has minimal effect on habitat use by bats. They also indicate that silvicultural methods have different immediate effects on different species of bats that may be obscured if the community is studied as a single entity. Management for forest-dwelling bats must take such species-specific effects into consideration. Harvesting that creates a mosaic of patches with different tree densities is likely to satisfy the requirements of more species than a system with less diverse harvesting styles.

Prey dynamics affect foraging by a pelagic predator (Stenella longirostris) over a range of spatial and temporal scales

Abstract: Studies have shown that pelagic predators do not overlap with their prey at small scales. However, we hypothesized that spinner dolphin foraging would be affected by the spatio-temporal dynamics of their prey at both small and large scales. A modified echosounder was used to simultaneously measure the abundance of dolphins and their prey as a function of space and time off three Hawaiian islands. Spinner dolphin abundance closely matched the abundance patterns in the boundary community both horizontally and vertically. As hypothesized, spinner dolphins followed the diel horizontal migration of their prey, rather than feeding offshore the entire night. Spinner dolphins also followed the vertical migrations of their prey and exploited the vertical areas within the boundary layer that had the highest prey density. Cooperative foraging by pairs of dolphins within large groups was evident. The geometric and density characteristics of prey patches containing dolphins indicate that dolphins may alter the characteristics of prey patches through this cooperative foraging. The overlap of Hawaiian spinner dolphins and their prey at many temporal and spatial scales, ranging from several minutes to an entire night and 20 m to several kilometers, indicates that the availability of truly synoptic data may fundamentally alter our conclusions about pelagic predator-prey interactions.

Supply of Dissolved Organic Matter to Aquatic Ecosystems: Autochthonous Sources

Abstract: 1 Trophic polymorphism is a common phenomenon in many species Trade-offs in foraging efficiency on different resources are thought to be a primary cause of such polymorphism2 To test for a tr

Morphology dependent foraging efficiency in perch: a trade-off for ecological specialization?

Abstract: The work in this thesis deals with the ecology and evolution of adaptive individual variation. Ecologists have long used niche theory to describe the ecology of a species as a whole, treating conspecific individuals as ecological equivalent. During recent years, research about individual variation in diet and morphology has gained interest in adaptive radiations and ecological speciation. Such variation among individual niche use may have important conservation implications as well as ecological and evolutionary implications. However, up to date we know very little about the extension of this phenomenon in natural populations and the mechanisms behind it.The results in this thesis show that the extension of individual diet specialization is widely spread throughout the animal kingdom. The variation in diet is mainly correlated to morphological variation but not always. Furthermore, this variation in diet and morphology among individuals could be both genetically determined and environmentally induced and it mainly comes from trade-offs in foraging efficiency between different prey types. The results from a number of studies of perch also show that individual perch differ in morphology and diet depending on habitat, where littoral perch has a deeper body compared to pelagic perch. This difference in morphology corresponds to functional expectations and is related to foraging efficiency trade-offs between foraging in the littoral and pelagic zone of a lake. The variation in morphology in perch is mainly due to phenotypic plasticity but there are also small genetic differences between the littoral and pelagic perch. Two separate studies show that both predation and competition may be important mechanism for the variation in morphology and diet in perch.In conclusion, the results in this thesis show that individual variation in diet and habitat choice is a common phenomenon with lots of ecological and evolutionary implications. However, there are many mechanisms involved in this phenomenon on which we are just about to start learning more about, and only further research in this area will give us the full insight.

Species difference in adaptive use of public information in sticklebacks

Abstract: Animals foraging on variable food sources can refine their estimates of patch quality by monitoring the success of others (i.e. collect 'public information'). Here, we show that both three-spined sticklebacks (Gasterosteus aculeatus) and nine-spined sticklebacks (Pungitius pungitius) use past cues provided by others to locate food but only nine-spined sticklebacks use prior public information to assess patch quality, regardless of whether demonstrators were conspecifics or heterospecifics. Moreover, nine-spined but not three-spined sticklebacks preferentially hid in vegetation during the demonstration, a position from which they could observe both patches simultaneously and collect public information. We conclude that species differences in the use of public information can be explained by variations in habitat choice and response to predation. Our findings expand current understanding of the scope of public-information use in animals by showing that fishes can use public-information in a foraging context and from heterospecifics. The study suggests that public-information use is an adaptation that allows animals vulnerable to predation to acquire valuable foraging information at low risk.

Energetics of a benthic diver: seasonal foraging ecology of the australian sea lion, neophoca cinerea

Abstract: This research examines the foraging energetics and diving behavior of the Australian sea lion, Neophoca cinerea. We examine whether the foraging ecology of the Australian sea lion is typical for an animal that has evolved to exploit benthic habitats. Such a strategy is in marked contrast to those utilized by some seabirds and other pinnipeds that feed in the midwater, where travel and search components of the time at sea become more important. Onshore and at-sea field metabolic rates (FMR) were measured using doubly labeled water in lactating sea lions at Kangaroo Island, South Australia, during the winter of 1988 (early lactation, breeding season 1) and the summer of 1990 (early lactation, breeding season 2). Dive behavior was also measured with dataloggers during these seasons, as well as in the summer of 1991 (late lactation, breeding season 2). The foraging behavior of Neophoca cinerea indicated that it works hard to exploit benthic habitats in the waters around its breeding site. Sea lions maximized ...

Variability in reproductive success viewed from a life-history perspective in baboons.

Abstract: Nonhuman primates, like humans, mature slowly and have low fertility during a relatively long life. As data have accumulated on life-history patterns of nonhuman primates, comparative studies have yielded important insights into the evolution of this slow life-history style of primates. However, in order to understand selection pressures and evolutionary potential within species, it is important to complement comparative studies with detailed studies of life-history variability within species and to identify sources of this variability. Here we present a summary of how foraging environment, social status, and group size (a measure of population density) contribute to within-population variance in reproductive success for savannah baboons. We also discuss the extent to which savannah baboons, with their highly flexible and adaptable behavior, change their foraging environments by shifting home ranges and seeking rich food sources and how low-ranking females, which disproportionately bear the costs of social life, may mitigate those costs.

Environmental enrichment and prior experience of live prey improve foraging behaviour in hatchery-reared Atlantic salmon

Abstract: Atlantic salmon salmo salar L. parr were reared for 3 months under standard hatchery conditions or in a structurally enriched tank (containing plants, rocks and novel objects). Half of each of these fish had prior exposure to live prey in the form of live bloodworm while the other half were fed hatchery-pellets. After 12 days all fish were tested on a novel live prey item (brine shrimp). A significant interaction between the two factors (prior exposure to live prey and rearing condition) revealed that foraging performance was only enhanced in fish that had been reared in a complex environment and exposed to live prey. It appears that the ability to generalize from one live prey type to another is only enhanced in fish that had been reared in an enriched environment. The findings support the assertion that the provision of enriched environments in combination with exposure to live prey prior to release may significantly improve the post-release survival rates of hatchery-reared fishes. As both the environmental enrichment and the prior foraging experience procedures were comparatively simple, the provision of such pre-release experiences are likely to prove cost effective to hatcheries.

Response to Comment on "Foraging Adaptation and the Relationship Between Food-Web Complexity and Stability"

Abstract: In their comment ( [1][1] ), Brose et al. analyzed extended models of adaptive food webs and found that, under their alternative assumptions, a positive complexity–stability relationship does not emerge. As they mention, my original model ( [2][2] ) made a number of simplifying assumptions, and

Behavioural effects of pesticides in bees--their potential for use in risk assessment.

Abstract: This paper reviews a wide variety of behavioural effects that have been reported in bees following exposure to pesticides, primarily insecticides. These range from effects on odour discrimination in the individual to the loss of foraging bees due to disruption of their homing behaviour. Some of these effects have the potential to have a significant impact on the development and survival of colonies. However, there is currently little guidance available on the types of behavioural data which should be collected during laboratory, semi-field or field regulatory studies or how they should be included and interpreted in risk assessment. Further work is required to allow risk assessment to include significant behavioural effects and their longer term consequences on colony survival and development. Such an approach will require a larger base set of data to predict the longer-term consequences on colonies of short-term effects on individuals, e.g. through population modelling.

Are honey bees' foraging preferences affected by pollen amino acid composition?

Abstract: . 1. Although pollen is a vital nutritional resource for honey bees, Apis mellifera, the influence of pollen quality on their foraging behaviour is little understood. 2. In choice-test experiments, bees showed no innate pollen-foraging preferences, but preferred oilseed rape Brassica napus pollen over field bean Vicia faba pollen after previous foraging experience of oilseed rape. 3. The free amino acid content of oilseed rape and field bean pollen was compared using high-performance liquid chromatography. Oilseed rape pollen contained a greater proportion of the most essential amino acids required by honey bees (valine, leucine, and isoleucine) than field bean, suggesting that oilseed rape pollen is of greater nutritional quality for honey bees than is field bean pollen. 4. Honey bee foraging preferences appeared to reflect pollen quality. The hypothesis that pollen amino acid composition affects the foraging behaviour of honey bees is discussed.

Learning of foraging skills by fish

Abstract: This chapter outlines the relationships between a number of key factors that influence learning and memory, and illustrates them by reference to studies on the foraging behaviour of fish. Learning can lead to significant improvements in foraging performance in only a few exposures, and at least some fish species are capable of adjusting their foraging strategy as patterns of patch profitability change. There is also evidence that the memory window for prey varies between fish species, and that this may be a function of environmental predictability. Convergence between behavioural ecology and comparative psychology offers promise in terms of developing more mechanistically realistic foraging models and explaining apparently 'suboptimal' patterns of behaviour. Foraging decisions involve the interplay between several distinct systems of learning and memory, including those that relate to habitat, food patches, prey types, conspecifics and predators. Fish biologists, therefore, face an interesting challenge in developing integrated accounts of fish foraging that explain how cognitive sophistication can help individual animals to deal with the complexity of the ecological context.

Lithic Source Use and Paleoarchaic Foraging Territories in the Great Basin

Abstract: Paleoarchaic (11.5–8.0 ka) occupants of the Great Basin encountered numerous lithic sources as they moved across foraging territories. Source provenance and lithic technologic analyses applied to the tools manufactured from these source materials elucidate several aspects of mobility, including the geographic scale of material conveyance and extent and possible routes of population movement. This research indicates that central Great Basin groups traversed large subsistence territories, extending more than 400 km from north to south, with mobility tactics probably keyed to the distribution of resource-rich wetlands. Changes in source representation parallel warming and drying trends, suggesting that Paleoarchaic foraging ranges shifted as wetlands diminished after about 9.5–8.5 ka.

Information acquisition and time allocation in insect parasitoids

Abstract: All animals face the problem of finding resources for growth, maintenance and reproduction. Foraging in a heterogeneous (i.e. patchy) environment requires seemingly complex decisions, such as where to forage, and for how long. To make such decisions, animals need to acquire relevant information from their environment. Recent studies of how parasitoids acquire information and allocate their time to the exploitation of host patches use a combination of functional (evolutionary) and causal (mechanistic) approaches. They show that parasitoids can allocate foraging time to patches in an adaptive way and that members of the same species can respond differently to the same environmental cues, depending on their physiological state and previous experiences or on genetic differences. Functional models now help to explain these contrasting responses.

Day length, latitude and behavioural (in)flexibility in baboons (Papio cynocephalus ursinus )

Abstract: Annual cycles in day length are an important consideration in any analysis of seasonal behaviour patterns, since they determine the period within which obligate diurnal or nocturnal animals must conduct all of their essential activities. As a consequence, seasonal variation in day length may represent an ecological constraint on behaviour, since short winter days restrict the length of the time available for foraging in diurnal species (with long summer days, and thus short nights, a potential constraint for nocturnal species). This paper examines monthly variation in activity patterns over a 4-year study of chacma baboons (Papio cynocephalus ursinus) at De Hoop Nature Reserve, South Africa. Time spent feeding, moving, grooming and resting are all significant positive functions of day length, even before chance events such as disease epidemics and climatically mediated home range shifts have been accounted for. These results provide strong support for the idea that day length acts as an ecological constraint by limiting the number of daylight hours and thus restricting the active period at certain times of year. Day length variation also has important implications across populations. Interpopulation variation in resting time, and non-foraging activity in general, is a positive function of latitude, with long summer days at temperate latitudes apparently producing an excess of time that cannot profitably be devoted to additional foraging or social activity. However, it is the short winter days that are probably of greatest importance, since diurnal animals must still fulfil their foraging requirements despite the restricted number of daylight hours and elevated thermoregulatory requirements at this time of year. Ultimately this serves to restrict the maximum ecologically tolerable group sizes of baboon populations with increasing distance from the equator. Seasonal variation in day length is thus an important ecological constraint on animal behaviour that has important implications both within and between populations, and future studies at non-equatorial latitudes must clearly be mindful of its importance.

Scale–dependent hierarchical adjustments of movement patterns in a long–range foraging seabird

Abstract: Foraging animals are expected to adjust their path according to the hierarchical spatial distribution of food resources and environmental factors. Studying such behaviour requires methods that allow for the detection of changes in pathways' characteristics across scales, i.e. a definition of scale boundaries and techniques to continuously monitor the precise movement of the animal over a sufficiently long period. We used a recently developed application of fractals, the changes in fractal dimension within a path and applied it to foraging trips over scales ranging across five orders of magnitude (10 m to 1000 km), using locations of wandering albatrosses (Diomedea exulans) recorded at 1 s intervals with a miniaturized global positioning system. Remarkably, all animals consistently showed the same pattern: the use of three scale-dependent nested domains where they adjust tortuosity to different environmental and behavioural constraints. At a small scale (ca. 100 m) they use a zigzag movement as they continuously adjust for optimal use of wind; at a medium scale (1-10 km), the movement shows changes in tortuosity consistent with food-searching behaviour; and at a large scale (greater than 10 km) the movement corresponds to commuting between patches and is probably influenced by large-scale weather systems. Our results demonstrate the possibility of identifying the hierarchical spatial scales at which long-ranging animals adjust their foraging behaviour, even in featureless environments such as oceans, and hence how to relate their movement patterns to environmental factors using an objective mathematical approach.