Predicting the unpredictable: transmission of drug-resistant HIV

We use a mathematical model to understand (from 1996 to 2001) and to predict (from 2001 to 2005) the evolution of the epidemic of drug-resistant HIV in San Francisco. We predict the evolutionary trajectories for 1,000 different drug-resistant strains with each strain having a different fitness relative to a drug-sensitive strain. We calculate that the current prevalence of resistance is high, and predict it will continue to rise. In contrast, we calculate that transmission of resistance is currently low, and predict it will remain low. We show that the epidemic of resistance is being generated mainly by the conversion of drug-sensitive cases to drug-resistant cases, and not by the transmission of resistant strains. We also show that transmission of resistant strains has not increased the overall number of new HIV infections. Our results indicate that transmission of resistant strains is, and will remain, a relatively minor public health problem.     

Nonvulnerability of ecosystems in unpredictable environments

One way to bracket the effects of a real environment on an ecosystem during a finite time interval is to use the concept of vulnerability. If a deterministic model ecosystem has a good Lyapunov function, it may be possible to derive simple and useful tests for the system to be nonvulnerable. For a subset of Lotka-Volterra models, the system is nonvulnerable if the smallest eigenvalue of a certain matrix is not only positive, but is greater than a positive number, which depends on a priori estimates for the bounds on the unpredictable forcing functions. The bounded but unknown functions which act on the Lotka-Volterra equations also can be interpreted as errors in the system's equations which can be tolerated without a qualitative change in the behaviour of its solutions.     

Arterial thrombosis--insidious, unpredictable and deadly

The formation of blood clots--thrombosis--at sites of atherosclerotic plaque rupture is a major clinical problem despite ongoing improvements in antithrombotic therapy. Progress in identifying the pathogenic mechanisms regulating arterial thrombosis has led to the development of newer therapeutics, and there is general anticipation that these treatments will have greater efficacy and improved safety. However, major advances in this field require the identification of specific risk factors for arterial thrombosis in affected individuals and a rethink of the 'one size fits all' approach to antithrombotic therapy.     

Protected polymorphism in the two-locus haploid model with unpredictable fitnesses

 In an unpredictable environment, the distributions of alleles from which polymorphism can be maintained forever belong to a certain set, the C-viability kernel. Such a set is calculated in the two-locus haploid model, as well as the corresponding fitnesses at any time which make this maintenance possible. The dependence of the C-viability kernel on the set U of admissible fitnesses and on the recombination rate r is studied. Notably, the C-viability kernel varies rapidly in the neighborhood of equal fitness of AB and ab; it becomes empty when ab has a fitness below a certain function, which is delineated, of the recombination rate. The properties of the two-locus model under constraints, out of equilibrium and with unpredictable selection are thus presented. Received: 20 May 1999     

Site fidelity in predictable and unpredictable habitats

Summary Site fidelity, the tendency to return to a previously occupied location, has been observed in numerous species belonging to at least three phyla. In this paper I develop a general model using dynamic programming to investigate conditions under which fidelity to a previously occupied territory will be advantageous. The results predict that site fidelity should be inversely related to heterogeneity in territory quality and the animal's lifespan and positively related to the cost of changing territories, age and probability of mortality in the habitat. The predictability of reproductive outcome (defined as the probability that next period's outcome will be the same as this period's outcome) also affects site fidelity. In predictable habitats, changing territories may be favoured after a bad previous outcome. In contrast, settlement should be independent of the previous outcome in unpredictable habitats. Individuals should also be site-faithful in unpredictable habitats, as long as the mean territory quality is equal among available territories. I also investigate the success of two potential decision rules (always stay and win-stay: lose-switch) relative to the optimal settlement strategy. The results show that these rules may perform as well as the optimal strategy under certain conditions. The always stay strategy does well in unpredictable habitats, when the mean quality within a territory is equal among territories. In contrast, the win-stay: lose-switch strategy performs best in predictable habitats.     

Timing of avian reproduction in unpredictable environments

Organisms living in periodically varying environments adjust their life history events to the changes in food availability. When these changes are not entirely predictable animals face a trade-off between maintaining physiological preparedness (which can be costly) and being unprepared (which decreases the chances of successful reproduction). To investigate this problem, we developed an optimal annual routine model of gonad regulation in birds. Most birds regress their reproductive organs during non-breeding periods, but to start breeding again they need to have functional gonads. Maintaining the gonads in this state is costly, but because it takes time to achieve this state, if gonads are not functional the bird may miss a possible breeding opportunity. We explore the resolution of this trade-off in environments where favorable periods can occur at any time of the year and variability in the length of good and bad periods can be altered. Consistent with empirical studies of reproductive behavior in unpredictable environments, we find that birds maintain the gonads partially activated during unfavorable conditions in many cases. However, gonad regulation may differ strikingly depending on the consistency of the good and bad periods. Furthermore, seasonal changes in food availability lead to the entrainment of reproduction and the segregation of the breeding and non-breeding season, even if the magnitude of seasonality is small compared to the degree of environmental fluctuations. These results indicate that several aspects of the environment need to be taken into account to understand reproductive behavior in unpredictable environments. Given that the trade-off between the costs and benefits of maintaining physiological preparedness is not limited to birds, our results have implications for understanding behavioral flexibility in other organisms as well.     

Temporally unpredictable supplementary feeding may benefit endangered scavengers

The monitoring of an experimental feeding station established in northern Spain allowed the evaluation of how this type of resource, predictable in space but not in time, was exploited by a guild of avian scavengers in relation to factors such as season, hour of disposal and presence of the dominant species. The presence of Egyptian Vultures Neophron percnopterus at carcasses was more likely during spring, and richness and diversity of avian scavengers was lower during the summer and when Griffon Vultures Gyps fulvus arrived earlier. The temporal unpredictability of the resource may favour exploitation by smaller and less competitive scavengers. New European regulations may present an opportunity to develop effective conservation measures to support functional scavenger assemblages.     

Population differentiation of temperate amphibians in unpredictable environments

Amphibians are a globally distributed and diverse lineage, but much of our current understanding of their population genetic structure comes from studies in mesic temperate habitats. We characterize the population genetic structure of two sympatric explosive breeding amphibians in the southwestern deserts of the United States: the Great Plains toad ( Anaxyrus cognatus ) and Couch's spadefoot toad ( Scaphiopus couchii ). For both species, we find limited genetic differentiation even between populations in adjacent valleys separated by dispersal barriers such as mountainous habitats. To understand how population genetic patterns in these two arid-adapted species compare to taxa in more mesic environments, we computed a standardized measure of population differentiation for A. cognatus , S. couchii , and for pond-breeding amphibians that inhabit mesic temperate environments. Our results indicate that the arid-adapted species have lower population genetic structure at fine and moderate scales than most other amphibian species we surveyed. We hypothesize that stochasticity in the availability of appropriate breeding sites as well as landscape homogeneity may result in increased population connectivity in desert-adapted frogs. Future work examining fine-scale population structure in amphibians from a diversity of habitats will test the generality of our findings. Intraspecific comparisons among localities with varied seasonality and habitats will be particularly useful for investigating the interaction between species-typical population dynamics and environmental characteristics as determinants of population connectivity in pond-breeding amphibians.