Control targets for the management of biological systems

Attention is focused on biological systems which are describable in terms of ordinary differential equations subject to human control inputs. The concept of an isochronal system is introduced in order to include systems for which the differential equations are valid only over regularly reoccurring time intervals.It is assumed that the control inputs are to be chosen so that an integral cost function of the state of the system, the control used, current time, and the time interval of the control program is minimized. Problems associated with minimizing this cost function over an infinitely long time interval is then considered. Difficulties inherent with minimizing a cost integral on an infinite time interval are shown to be avoided by minimizing an average of the cost function over an unknown but periodic time interval. Under proper circumstance, the optimal control program for the average cost function is either identical to or a good approximation to the optimal control program for the original cost function over an infinitely long time interval.Necessary conditions are obtained for minimizing an average cost function over an unspecified time interval subject to the system equations. For a given problem the necessary conditions will yield but a single system trajectory in the state space. For management purposes this trajectory may be thought of as a target to which the system should be driven and maintained.A number of examples illustrate the use of the necessary conditions to obtain control targets. Certain problems associated with the stability of the target solutions are illustrated with the examples.     

Sorption of Cu and Zn by bone charcoal

Bone charcoal is being developed as a treatment for decontaminating polluted water. In particular, its potential to adsorb metal species from contaminated water supplies is being examined. In this study, bone charcoal was used in batch and column experiments designed to investigate the sorption of two cationic metals Cu and Zn. The data from batch experiments fitted the Langmuir isotherm and so theoretical maximum binding capacities could be obtained. These values were compared with experimental values derived from the column experiments. The mechanisms involved in the immobilisation were also investigated.     

Growth of zinc granules in the barnacleElminius modestus

The growth of insoluble, membrane-limited spherical granules has been studied in the barnacleElminius modestus Darwin, collected on 26 March 1983 from the shore of the Huon River, Tasmania. X-ray microprobe analysis of these granules using a non-aqueous fixation method established their elemental composition (in order of abundance) to be phosphorus, zinc, potassium, sulphur and chlorine. Formation of granules is initiated on exposure to high zinc levels in the ambient seawater. Granules were first detected in barnacles transplanted from an area of low seawater zinc levels to one with high levels after 12 d exposure. Over a period of 5 mo, granules increased both in numbers and diameter and were concentrated in specialized cells around the gut, the stratum perintestinale. Barnacles positioned at mid-tide level in high ambient zinc levels, developed greater numbers of larger granules than those positioned below low-tide level. Rate of uptake of zinc was higher in the former group during the first month, after which similar rates were observed in the two groups. Barnacles transplanted from an area of high to one of low seawater zinc concentration, lost zinc slowly (0.3% body load per day over an 11 wk period). There was no evidence to suggest that zinc granules are excreted intact across the gut. We conclude that zinc granules represent a detoxification mechanism for surplus zinc.     

Age-specific social dominance affects habitat use by breeding American redstarts (Setophaga ruticilla): a removal experiment

Summary By removing older males from their breeding territories, we tested the hypothesis that age-related dominance behavior influenced the pattern of habitat selection by breeding American redstarts Setophaga ruticilla (Aves: Parulinae). Fifteen older male redstarts removed in five experimental replicates during three breeding seasons were replaced by ten yearling and five older males; no redstart males of either age colonized the control sites during the same time periods, although two yearlings disappeared. Significantly more yearling males (67%, n=9) colonized the vacated areas than were present in the redstart population at large (26.8%, n=209). We reject the alternative hypothesis that yearling male redstarts occupy different habitats from older males because of age-related (innate) habitat preferences. Redstarts that colonized the territories made vacant by our removals (i.e., floaters) were a behaviorally heterogeneous group of animals. The presence of both yearling and older male floaters indicates that suitable habitat is limiting for this species and that intraspecific competitive interactions are important in habitat distribution, and potentially in population regulation.     

The functional organization of resin work in honeybee colonies

Resin is an important building material in the nests of honeybees, but little is known about how it is handled within the nest and how its collection is controlled. We studied the functional organization of resin work to better understand how a colony adaptively controls its intake of resin. Two hypotheses have been proposed for how resin collectors stay informed of the need for additional resin: (1) the unloading difficulty hypothesis (resin need is sensed indirectly by the unloading delay) and (2) the caulking activity hypothesis (resin need is sensed directly while engaged in using resin). A falsifiable prediction of the latter hypothesis, but not of the former, is that resin collectors not only gather resin outside the hive but also regularly handle resin inside the hive (taking it from other bees and using it to caulk crevices). Consistent with this prediction are our findings that in the resin sector of a colony’s economy, unlike in the pollen, nectar, and water sectors, there is no strict division of labor between the collectors and the users of a material. Over the course of a day, bees seen collecting resin were also commonly seen using resin. Moreover, we found that the unloading locations of resin collectors are unlike those of water and nectar collectors, being deep inside the hive (at the sites of resin use) rather than at the hive entrance. This arrangement facilitates the engagement in resin use by resin collectors. We conclude that the caulking activity hypothesis is well-supported, but that the unloading difficulty hypothesis also remains viable, for we found that resin collectors experience variable delays in getting rid of their loads, from less than 15 min to more than an hour, consistent with this hypothesis. The stage is now set for experimental tests of these two hypotheses. Both may be correct, which if true will imply that social insect workers, despite their small brains, can acquire and integrate information from multiple sources to improve their knowledge of conditions within the colony.     

Honey bee foragers as sensory units of their colonies

Forager honey bees function not only as gatherers of food for their colonies, but also as sensory units shaped by natural selection to gather information regarding the location and profitability of forage sites. They transmit this information to colony members by means of waggle dances. To investigate the way bees transduce the stimulus of nectar-source profitability into the response of number of waggle runs, I performed experiments in which bees were stimulated with a sucrose solution feeder of known profitability and their dance responses were videorecorded. The results suggest that several attributes of this transduction process are adaptations to enhance a bee's effectiveness in reporting on a forage site. (1) Bees register the profitability of a nectar source not by sensing the energy gain per foraging trip or the rate of energy gain per trip, but evidently by sensing the energetic efficiency of their foraging. Perhaps this criterion of nectar-source profitability has been favored by natural selection because the foraging gains of honey bees are typically limited by energy expenditure rather than time availability. (2) There is a linear relationship between the stimulus of energetic efficiency of foraging and the response of number of waggle runs per dance. Such a simple stimulus-response function appears adequate because the range of suprathreshold stimuli (max/min ratio of about 10) is far smaller than the range of responses (max/min ratio of about 100). Although all bees show a linear stimulus-response function, there are large differences among individuals in both the response threshold and the slope of the stimulus-response function. This variation gives the colony a broader dynamic range in responding to food sources than if all bees had identical thresholds of dance response. (3) There is little or no adaptation in the dance response to a strong stimulus (tonic response). Thus each dancing bee reports on the current level of profitability of her forage site rather than the changes in its profitability. This seems appropriate since presumably it is the current profitability of a forage site, not the change in its profitability, which determines a site's attractiveness to other bees. (4) The level of forage-site quality that is the threshold for dancing is tuned by the bees in relation to forage availability. Bees operate with a lower dance threshold when forage is sparse than when it is abundant. Thus a colony utilizes input about a wide range of forage sites when food is scarce, but filters out input about low-reward sites when food is plentiful. (5) A dancing bee does not present her information in one spot within the hive but instead distributes it over much of the dance floor. Consequently, the dances for different forage sites are mixed together on the dance floor. This helps each bee following the dances to take a random sample of the dance information, which is appropriate for the foraging strategy of a honey bee colony since it is evidently designed to allocate foragers among forage sites in proportion to their profitability.     

Use of the ouput of a lead risk assessment model to establish soil lead cleanup levels

Three general methods to calculate soil contaminant cleanup levels are assessed: the truncated lognormal approach, Monte Carlo analysis, and the house-by-house approach. When these methods are used together with a lead risk assessment model, they yield estimated soil lead cleanup levels that may be required in an attempt to achieve specified target blood lead levels for a community. The truncated lognormal approach is exemplified by the Society for Environmental Geochemistry and Health (SEGH) model, Monte Carlo analysis is exemplified by the US EPA's LEAD Model, and the house-by-house approach is used with a structural equation model to calculate site-specific soil lead cleanup levels. The various cleanup methods can each be used with any type of lead risk assessment model. Although all examples given here are for lead, the cleanup methods can, in principle, be used as well with risk assessment models for other chemical contaminants to derive contaminant-specific soil cleanup levels.