Temporal variation in the carrying capacity of a perennial grass population.

Density dependence and, therefore, K (carrying capacity, equilibrium population size) are central to understanding and predicting changes in population size (N). Although resource levels certainly fluctuate, K has almost always been treated as constant in both theoretical and empirical studies. We quantified temporal variation in K by fitting extensions of standard population dynamic models to 16 annual censuses of a population of the perennial bunchgrass Bouteloua rigidiseta. Variable-K models provided substantially better fits to the data than did models that varied the potential rate of population increase. The distribution of estimated values of K was skewed, with a long right tail (i.e., a few "jackpot" years). The population did not track K closely. Relatively slow responses to changes in K combined with large, rapid changes in K sometimes caused N to be far from K. In 13%-20% of annual intervals, K was so much larger than N that the population's dynamics were best described by geometric growth and the population was, in effect, unregulated. Explicitly incorporating temporal variation in K substantially improved the realism of models with little increase in model complexity and provided novel information about this population's dynamics. Similar methods would be applicable to many other data sets.

An evolutionary epidemiological mechanism, with applications to type A influenza.

In this paper I develop a model that describes an evolutionary epidemiological mechanism and apply this model to the epidemiology of type A influenza. This evolutionary epidemiological model differs from the classical nonevolutionary epidemiological model which has been applied to diseases like measles, rubella, and whooping cough in having a novel mechanism which causes susceptible individuals to be introduced into the host population. In the nonevolutionary model, susceptibles are continually introduced into the host population by demographic processes: most hosts that die are immune, while newborn hosts are susceptible. In this evolutionary model, the susceptible class is continually replenished because the pathogen changes genetically, and hence immunologically, from one epidemic to the next, causing previously immune hosts to become susceptible. I derive formulae which describe how the equilibrium number of infected hosts, the interepidemic period, and the probability that a host will become reinfected depend on the rate of amino acid substitution in the pathogen, m, a parameter describing the effect of these substitutions on host immunity, gamma, as well as the host population size, N, and the recovery rate, r. To apply the model to influenza, I show how the nondimensional parameter epsilon = m gamma N/r2 may be estimated from four types of data. The methods are applied to several data sets, and I conclude that epsilon much less than 1; sampling variation and inconsistencies between the various data sets do not permit epsilon to be estimated more precisely. The evolutionary epidemiological model has no threshold host population size, in contrast to the nonevolutionary model.

A quantitative study of command elements for abdominal positioning behavior in the crayfish Procambarus clarkii.

We develop a statistical method to estimate the total number of command elements devoted to abdominal positioning behavior in crayfish. We assumed that all command elements can be identified, that each identified cell is equivalent to a tagged individual in a population, and that the cells were sampled randomly. Samples of 29, 30, 20, and 35 cells from abdominal ganglia A3, A4, A5, and A6, respectively, were taken from our catalog. We characterized each cell using several morphological and physiological criteria, determined how many times each identified cell was present in the sample, and estimated the total number of command elements using both a maximum likelihood method and a modification of the Lincoln index. The larger the proportion of identified cells seen only once in the sample, the more identified cells there were that were unrepresented in the sample. We estimate there are approximately 34, 60, 86, and 98 command elements in ganglia A3, A4, A5, and A6, respectively. Using a slightly different data set we show that the motor output of unipolar cells is more often stronger in the direction of the cell's axonal projection. In bipolar command elements, the output strength was uncorrelated with the relative sizes of the two projecting axons. No two cells in our sample were completely identical, and this morphological variability sometimes made it difficult to determine whether or not two cells obtained from different individuals were the same identified cell. We discuss why caution should be exercised in studies requiring precision in cell identification.

Unexpected divergence among identified interneurons in different abdominal segments of the crayfish Procambarus clarkii.

The command elements that initiate and coordinate the abdominal movements in crayfish show little similarity between the various abdominal segments. Our criteria for similarity among interneurons were based on both cell morphology and electrophysiology. By contrast, previously published evidence shows much greater intersegmental similarity in the skeletal, muscular, motoneuronal, and sensory components of the abdominal system in crayfish, structures that are controlled by or send information to the command elements. Therefore, unlike the command elements, these structures have retained nearly identical form and function in the various segments. We also found in different ganglia examples of interneurons involved with abdominal positioning behavior that have similar morphology but different function and vice versa. Such interneurons could represent divergent pairs of serial homologues. It is unknown why so many of the abdominal positioning interneurons have become different. The various ganglia may perform subtly different functions, requiring differences in the positioning interneurons but not in the motor neurons or muscles. Alternatively, some of the abdominal positioning interneurons underlie more than one behavior; consequently, selection acting on these multiple functions may have changed these interneurons through evolution.

Consistency of interneuronal group formation in response to stimulation of identified cells.

In crayfish stimulation of abdominal positioning interneurons (APIs) recruits other interneurons producing various abdominal movements. We investigated whether: (1) the same API from different preparations activated a similar number or group of interneurons, (2) different APIs activated different groups, and (3) repeated stimulation of an API consistently affected a similar set of interneurons. To quantify the similarities and differences of the recruited interneuronal groups we compared the number of interneurons affected, their firing frequencies, and motor outputs. Three types of APIs (Curly Q, L and T) were identified and each type was stimulated in three preparations. Our results showed that for the Curly Q and L cells, each cell type activated interneuronal groups that were statistically similar in number and firing frequency. The T cell activated interneuronal groups that were more variable. Some APIs generally provided a repeatable motor output; all did not. The interneuronal groups activated by the Curly Q, L and T cells were very different from each other. Repeated stimulation of one Curly Q cell affected similar although not identical sets of interneurons. These data suggest that repeated motor outputs could be produced by a similar but not identical group of cells.