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Mathematical models of mimicry are attempts to simplify the complexity of real mimetic situations with only a few parameters. As such, they cannot be expected to mirror reality accurately. Nevertheless, they have stimulated much further thought, the collection of further field data, experimental testing in the laboratory, and further elaboration of the mathematical models. The succession of models has seen increasing preciseness of definition, increased scope of applicability, and increased accuracy in the depiction of mimetic situations. Their prediction of ecological and evolutionary relationships has been quite valuable. Even when mathematical models have been shown to be deficient, they have proven to have heuristic value in stimulating thought and discussion. The quarter of a century since they were first proposed has seen no diminution in the vigor of the work on these models, and we can expect this situation to continue.

The ecology and life history of Desmognathus ochrophaeus inhabiting wet rock faces at high elevations near Highlands, North Carolina, were studied. Comparisons were made with rock-face populations in Great Smoky Mountains National Park and with woodland populations at Rabun Bald, Scaly Mountain, and Blue Valley in the Blue Ridge Mountains. The reproductive cycle in rock-face populations is annual; spawning occurs mostly in July and August, and females begin to emerge from brooding as early as late August. The new spermatogenic cycle begins in May and June. Animals on rock faces average 40-45 cm in movements between successive captures and appear to have a limited range. Animals displaced to the base of the rock face and higher on the rock face can return to their home range. Population density is high (up to 25 individuals/M2), diurnal activity is nearly as high as nocturnal activity (correlated with subdued body colors), and at least a moderate level of activity occurs during warm winter periods. Animals mature at 2 years of age as in woodland populations, but at a smaller size, and grow more slowly thereafter. Small body size is not due to paucity of food on the rock faces. The high population densities on the wet rock faces indicate that they are highly favorable habitats for D. ochrophaeus. Differences between rock-face and forest-floor populations are attributable to modified selective pressures in the two different ecological settings. Variation among rock-face populations is attributed to the intensity of selection for small body size and cryptic coloration, the size of the rock face, and variation among forestfloor populations from which they were derived. Since rock-face populations are linked genetically to surrounding forest-floor populations of D. ochrophaeus, they cannot be considered examples of taxonomic variation, but rather of ecotypic variation.

Over one hundred years ago, Bates (1862) proposed that palatable prey should gain an advantage if they resembled and were mistaken for less palatable prey by predators. Seventeen years later, Muller (1889) proposed that a mutual advantage accrued to aposematic prey that converged in pattern to reduce predator error. Several recent workers (Huheey, 1961; Brower and Brower, 1964; Brower et al., 1970; Pough et al., 1973) have discussed the idea, first suggested by Dixey (1908) and clarified by Darlington (1938) and Fisher (1958), that there is no sharp dividing line between classical Batesian mimicry in which an innocuous mimic resembles a noxious model, and Miillerian mimicry in which two or more noxious models resemble each other. All cases in which two models, M1 and M2, do not have identical noxiousness will lie on a spectrum between the two limiting extremes of classical Batesian mimicry (noxiousness of M2 = 0) and classical Miillerian mimicry (noxiousness of M2 = noxiousness of M1). There has been some discussion of the evolution of Batesian and Miillerian mimicry in terms of this spectrum, but little of a quantitative nature has been attempted. Although the idea of a continuity of possibilities from Batesian mimicry at one extreme to Miillerian mimicry at the other is not a radical concept, surprisingly it does lead to several seeming contradictions. There are a number of tenets of mimicry theory that have been developed over the years (Carpenter, 1937; Sheppard, 1958; Wickler, 1968). In quite a large number of cases, the tenets for Batesian mimicry are diametrically opposed to those for Millerian mimicry (see Fisher (1958, p. 166) for, a concise and vivid description). The existence of a Batesian-Miullerian spectrum suggests that the supposed differences between the two be re-examined. Since the development of a mathematical model to describe Batesian mimicry (Huheey, 1964) has led to considerable work and interesting conclusions (Brower et al., 1970; Pough et al., 1973; Estabrook and Jesperson, 1975; Huheey, in ms.; Bobisud and Potratz, 1976; S. Arnold, Univ. of Chicago, pers. comm.), a similar study of Miillerian mimicry should prove useful.

The origin of right-handedness as the predominant chirality in humans seems to be related to the tendency of human (and presumably prehuman) mothers to hold infants on the left side. The latter practice has previously been ascribed to imprinting and the soothing sound of the mother's heartbeat on the infant. Given the practice of holding the child in this manner, dextral mothers will be more skillful at manipulation of objects and selectively favored.

Chickens found brown efts unpalatable. They hesitated longer in attacking efts compared with control Desmognathus ochrophaeus, attacked them less frequently, and for a shorter duration. Only one of 50 efts was killed (not eaten), whereas 47 of 50 D. ochrophaeus were eaten. When one red eft and one specimen of Pseudotriton montanus diastictus were offered to each of five chickens that had previous experience with brown efts, time to attack on both was the same as on D. ochrophaeus, showing that the chickens discriminated between these red sala- manders and brown efts. Duration of attack on red efts resembled that on brown efts, but was much longer on P. m. diastictus regardless of which reddish species was offered first. No red eft was killed; all five specimens of P. m. diastictus were killed but only one eaten. Palatability of P. m. diastictus was clearly less than that of D. ochrophaeus. Brown efts seem to be exposed to greater risk of damage by predators than are red efts because their skin toxins are not reinforced by bright skin coloring; in nature, however, this risk may be reduced by defensive posturing that exposes yellow underparts.

Laboratory experiments were conducted using toads, Bufo terrestris, and tree- frogs, Hyla cinerea, as predators and honeybees, Apis mellifera, as models. Bees from which the stinging apparatus had been removed served as mimics. Model and mimic bees were offered randomly with the models at frequencies of 10%, 30%, and 50% to the toads and 10%, 20%, and 50% to the treefrogs. The corresponding percentages of the model-mimic population eaten were 53.6%, 35.3%, and 19.8% (toads) and 29.6%, 17.4%, and 7.0% (treefrogs). The frequencies of bees eaten as a function of percent models in the prey population can be described by the mathematical model of predation presented previously (Huheey, 1964, 1976). Predator memory values (n) of 8.0 (toads) and 28.7 (treefrogs) were obtained. Various factors affecting the behavior of the predator with respect to the value of n are discussed: toxicity vs. distastefulness, alternate prey, and predator strategy. It is concluded that n is better viewed as a risk-taking strategy on the part of the predator than as a simple memory parameter.

its, it has been considered rare, and its range was long thought to be from South Carolina to Louisiana. Recent collecting has brought new specimens to light, and the recorded range has been extended from Virginia to Texas. It is the purpose of this study to delimit the range and explore the regional variation exhibited by this species. It has been found that the specimens fall into three distinct populations which appear to warrant subspecific recognition. A total of 255 specimens was examined, including sizable series from most areas of the range. Alabama, western Georgia, and North Carolina are sparsely represented. The following persons and institutions made specimens or data available (initials in parentheses are those used in subsequent references to these specimens): W. Frank Blair, University of Texas (TNHC); W. E. Brode, Gulf Coast Research Laboratory (GCRL); Bryce C. Brown (BCB), Strecker Museum, Baylor University (SM); E. Milby Burton, Charleston Museum (ChM); Fred R. Cagle, Tulane University (TU); Charles C. Carpenter, University of Oklahoma (UOMZ); Doris M. Cochran, United States National Museum

One of the principal tenets of the Batesian theory of mimicry is that the effectiveness of pseudaposematic coloration is reduced as the incidence of models decreases in relation to that of the mimics. This is to be expected since learning efficiency of predators will be reduced if models become scarce. Field studies (Carpenter 1932, 1949; Ford 1936) have shown that mimicry is, indeed, less effective where the frequency of models is low. Unfortunately, the following generalization is often assumed: if the model outnumbers the mimic, the pseudaposematic coloration is effective, whereas if the mimic outnumbers the model, the system breaks down. Sometimes the principle is stated qualitatively: the mimic must be rare with respect to the model. However, as pointed out by Sheppard (1959) and. Brower (1960), there is nothing unique about the 50-50% ratio. In studies by Brower using caged starlings as predators and meal worms as artificial models and mimics, it was found that the effectiveness of mimicry in a population containing 60% mimics was of the same order of magnitude as that of one containing only 30%. The effectiveness of aposematic and pseudaposematic coloration depends upon a number of variables in addition to model frequency. One is the ability of the predator to remember the aposematic signal. This in turn depends upon the inherent ability of the predator to learn, the nature of the warning signal, and the intensity of the stimulus that the predator receives upon sampling the model. Sheppard (1958) has called attention to the last factor: "An animal sufficiently obnoxious to make predators avoid its colour pattern, even when having encountered only one, could give protection to a mimetic form as common as, or commoner than, the model." In addition, the effectiveness of pseudaposematic coloration depends on the degree of similarity of the model and mimic. Other variables such as hunger, although influencing behavior strongly, may be considered relatively unimportant since their effects would be averaged out over a large sample. It would be advantageous if a mathematical model could be used to describe the situation obtaining between a model and a mimic. Although it should be possible to construct such a model employing all of the variables mentioned above, a simplified model is less cumbersome to handle, and at our present state of knowledge appears entirely adequate. As more data accumulate, it may become desirable to elaborate the simple model presented here. The following assumptions are made: (1) The effectiveness of the mimic pattern is 100%, i.e., the mimic cannot be distinguished visually from the model. This is patently untrue except in the case of artificial models and mimics analyzed below, but it must be admitted that in many cases of known mimicry this condition is approached closely. (2) The strength of the model's stimulus and the ability of the predator to remember it can be expressed in terms of a single parameter, n. This parameter corresponds to the total number of individuals (including the original model) protected by the predator rejecting the model, remembering the stimulus received from it, and thus avoiding both models and mimics until it forgets and renews sampling.

A divergence factor (D) is defined which indicates the rate of species replacement in a given area. All geographical points having equal values of D may be connected by a contour line (isometabasis). The resulting contour map indicates regions of little change (equivalent to biotic provinces) and regions of rapid change (equivalent to province boundaries). This procedure reduces the possibility of subjective bias in analyzing zoogeographic data. The herptofaunal data from the state of Illinois are used to illustrate the potential advantages of the method.