Density-dependent Limitation Research Articles

Evolutionary dynamics of structured populations with density-dependent limitation of juvenile survival

The paper considers evolutionary dynamics of a structured population with density-dependent regulation of juvenile survival. Such a type of density limitation is not unusual for natural populations. It occurs as either competition for food resources or sibling aggression, and, moreover, cannibalism or infanticide. Birth rate is assumed to change during the process of microevolution. The stability loss of non-trivial fixed points was shown to realize according to both the Neimark–Sacker​ scenario and the Feigenbaum one. The stability loss scenario is shown to be determined by both the mature individuals’ contribution to limiting juvenile survival and birth rate level. The bifurcations, dynamic modes and a possibility of their shifting are studied for the model proposed. The model reveals bistability and multistability both the population number and gene frequencies dynamics. There are bifurcations leading to fluctuations of gene frequencies in the proposed model. Thus, both monomorphic equilibriums and oscillation modes of the population genetic composition are simultaneously possible in the system. With the same values of population parameters in the case of variations in its current stage and/or genetic composition, such multistability can lead not only to a change in the dynamic mode due to an evolutionary growth of individual fitness, but also to a change in the evolution direction. As a result, different mechanisms of fluctuation emergence can be realized in a population at the same values of demographic parameters.

Validation of Body Condition Indicators for Monitoring Changes in Populations of Sika Deer (Cervus nippon) at a Landscape Scale

The estimated number of sika deer within the Tanzawa Mountains has decreased since the Kanagawa Prefecture sika deer management plan commenced. Meanwhile, unit-specific culling has resulted in various trends in deer density across small monitoring units. Deer abundance is usually surveyed within small monitoring units; therefore, the evaluation of deer abundance changes across the entire management area comprising individual units is difficult. We examined the relationship between deer body condition indicators and densities estimated at both individual unit and entire management scales in the Tanzawa Mountains during 2004–2015. Winter fawn body mass in the study area increased at least until 2011, irrespective of the increase/decrease in deer density in each unit. Observed variations in body mass were related to the estimated number of deer within the entire management area. Winter fawn hind foot length was not related to any density estimates. Inconsistencies between deer density changes in each unit and body mass might derive from the deer movement between units and mitigation of density-dependent food limitations caused by a reduction in the number of deer within the entire management area. We suggest that winter fawn body mass can provide additional evidence of deer abundance changes within management areas.

Effects of Lead Exposure, Environmental Conditions, and Metapopulation Processes on Population Dynamics of Spectacled Eiders

Abstract Spectacled eider Somateria fischeri numbers have declined and they are considered threatened in accordance with the US Endangered Species Act throughout their range. We synthesized the available information for spectacled eiders to construct deterministic, stochastic, and metapopulation models for this species that incorporated current estimates of vital rates such as nest success, adult survival, and the impact of lead poisoning on survival. Elasticities of our deterministic models suggested that the populations would respond most dramatically to changes in adult female survival and that the reductions in adult female survival related to lead poisoning were locally important. We also examined the sensitivity of the population to changes in lead exposure rates. With the knowledge that some vital rates vary with environmental conditions, we cast stochastic models that mimicked observed variation in productivity. We also used the stochastic model to examine the probability that a specific population will persist for periods of up to 50 y. Elasticity analysis of these models was consistent with that for the deterministic models, with perturbations to adult female survival having the greatest effect on population projections. When used in single population models, demographic data for some localities predicted rapid declines that were inconsistent with our observations in the field. Thus, we constructed a metapopulation model and examined the predictions for local subpopulations and the metapopulation over a wide range of dispersal rates. Using the metapopulation model, we were able to simulate the observed stability of local subpopulations as well as that of the metapopulation. Finally, we developed a global metapopulation model that simulates periodic winter habitat limitation, similar to that which might be experienced in years of heavy sea ice in the core wintering area of spectacled eiders in the central Bering Sea. Our metapopulation analyses suggested that no subpopulation is independent and that future management actions may be improved through a metapopulation framework. For example, management actions could include displacement of breeding females from “sink” areas that reduce the growth potential of the population as a whole. However, this action is contingent upon dispersal among local populations, for which there is limited information. Thus, we recommend that researchers examine dispersal behavior among areas on the Yukon-Kuskokwim Delta in western Alaska. The metapopulation framework could also be applied at the rangewide scale to address the density-dependent limitation of available polynya habitat during winter that may limit the recovery of small subpopulations, such as that on the Yukon-Kuskokwim Delta. Reductions in other subpopulations may be necessary to ensure an increase in the Yukon-Kuskokwim Delta population. Thus, we recommend that managers consider the interpopulation dynamics of spectacled eiders at different spatial scales in future management actions.

Decades of habitat use reveal food limitation of Newfoundland caribou

Abstract Identifying limiting factors is fundamental to understanding and conserving mammals, yet it often requires long-term data for long-lived species. Numerical changes of migratory caribou ( Rangifer tarandus ), for example, may unfold over decades, but few studies have examined habitat use at similar timeframes. We analyzed multiple decades of habitat use by caribou in Newfoundland, Canada, coincident with their numeric growth ( r = 0.064 in 1980s, 1990s) and decline ( r = −0.099 in 2000s). We examined 2 scales: selection of land cover, based on radiotracking of 520 adult females, and diet, based on microhistological analysis of feces and age-specific tooth wear from jawbones of harvested animals. Caribou responded at both scales. In contrast to previous decades, females during the population decline used proportionally less open coniferous and closed coniferous forests, they used more shrublands (in fall and winter) and barrens, open habitats with greater vascular plant resources. Patterns of selection also changed from nonselection to avoidance of open coniferous forest and from avoidance to nonselection or preference of barrens. The proportion of dietary moss increased at the expense of deciduous shrubs, especially during spring and summer and of ericaceous shrubs, graminoids, and lichens during winter. Teeth of both sexes exhibited premature wear, likely indicative of abrasion from low-quality forages and cropping of foods near the ground. These patterns mirror other responses, including declines in calf weight, female body size, number of male antler points, herd affinities, and time spent on the summer grounds. We surmise that they reflect density-dependent forage limitation of this island population.

Dynamics of ungulates in relation to climatic and land use changes in an insularized African savanna ecosystem

Land use change and human population growth are accelerating the fragmentation and insularization of wildlife habitats worldwide. The conservation and management of wildlife in the resultant ‘island’ ecosystems in the context of global warming is challenging due to the isolation and reduced size of the ecosystems and hence the scale over which ecosystem processes can operate. We analyzed trends in numbers of nine large herbivores in Kenya’s Lake Nakuru National Park to understand how rainfall and temperature variability, surrounding land use changes, and boundary fencing affected wildlife population dynamics inside the park during 1970–2011. Buffalo, zebra and Thomson’s gazelle numbers increased persistently. Grant’s gazelle and impala increased initially then gradually declined. Waterbuck and warthog numbers progressively declined to levels that potentially threatened their local population persistence. The total biomass of ungulates tripled from 1970 to 2011, with buffalo replacing waterbuck as the predominant species in biomass. Increased competition from buffalo and zebra, heightened predation and illicit human harvests probably all contributed to the declines by waterbuck and warthog. Density-dependent limitation of population growth within the park confines was evident for buffalo, impala, eland, giraffe, Grant’s and Thomson’s gazelles. Fluctuations in the lake level related to varying rainfall affected changes in animal abundance through expansion of the lake area and flooding of grasslands bordering the lake. Unusually, the most stressful conditions were associated with high water levels following high rainfall. There was also evidence of carry-over effects from prior habitat conditions affecting all species. The relatively stable populations of all species except warthog and waterbuck demonstrate the remarkable capacity of this small, insularized park to retain viable populations of most of the large herbivores, without much management intervention.

Diversity emerging: from competitive exclusion to neutral coexistence in ecosystems

In this communication, we present a unifying framework to understand the emergence and maintenance of diversity in ecological systems. We do this by developing a deterministic population model including density-dependent limitation in resources and available space. Our model shows that competitive exclusion and neutral coexistence represent different regimes of the same adaptive dynamics suggesting that neutrality is the general result of an adaptive process in a finite habitat with limited energetic resources. Our model explains the emergence of biodiversity through mutation and its maintenance through neutrality. We show that this framework provides the theoretical foundations to understand the emergence and maintenance of diversity in microbial ecosystems.

Two-Body Transients in Coupled Atomic-Molecular Bose-Einstein Condensates

We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found, and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett. 88, 090403 (2002)10.1103/PhysRevLett.88.090403], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating condensates of alkaline-earth atoms.

Rydberg Excitation of Bose-Einstein Condensates

Rydberg atoms provide a wide range of possibilities to tailor interactions in a quantum gas. Here, we report on Rydberg excitation of Bose-Einstein condensed 87Rb atoms. The Rydberg fraction was investigated for various excitation times and temperatures above and below the condensation temperature. The excitation is locally blocked by the van der Waals interaction between Rydberg atoms to a density-dependent limit. Therefore, the abrupt change of the thermal atomic density distribution to the characteristic bimodal distribution upon condensation could be observed in the Rydberg fraction. The observed features are reproduced by a simulation based on local collective Rydberg excitations.

Demographic responses of house mice to density and temperature on sub-Antarctic Marion Island

Recent changes in the climate of the sub-Antarctic may influence the number of house mouse (Mus musculus sensu lato) living on islands in the region. An increase in mouse numbers, as conditions became milder, could amplify the effects of climate change on native prey species. However, we have no direct evidence of the influence of climate on mouse numbers in the sub-Antarctic. We, therefore, assessed demographic trends in the mouse population on Marion Island between 1991 and 2001. Both the climate and mouse numbers were relatively stable during our study. Mice, however, increased their reproductive output in years when ambient temperatures were relatively high. Moreover, reduced reproductive output followed high densities at the onset of a breeding season, implying density-dependent limitation. We conclude that both temperature and density limited the increase in numbers during the summer breeding season. Major die-offs during winter probably limit population size and explain the relative stability in numbers across the 10 years of our study.

The Effect of Recycling on Plant Competitive Hierarchies

Evidence from field studies suggests that some plant species enhance their persistence by reinforcing patterns of N availability through differences in litter quality. Using mathematical models of nutrient flow, we explore whether and how recycling affects plant growth, competition, and coexistence and whether it leads to positive feedbacks. Two mechanisms are considered: the ability of plants to access two forms of soil N, complex (e.g., organic) and simple (e.g., nitrate), and the effect of density-dependent limitation of growth. Except in the trivial case of limitation by N in one form without density dependence, differences in litter quality can prevent the establishment of competitors. Feedback can, conversely, facilitate the invasion of competitors. At equilibrium, the rate of decomposition does not affect the outcome of competition. Species affect their long-term persistence if they alter the fraction of nitrogen that is returned to the soil and becomes available for plant uptake. Increasing the fraction of N that is recycled favors specialists in complex nitrogen and species that suppress the growth of others at high nitrogen availability. Increasing the rate of microbial decomposition of complex nitrogen favors specialists in simple nitrogen.

Demography of the over-exploited Mediterranean red coral (<i>Corrallium rubrum</i> L. 1758)

The precious octocoral, Corallium rubrum, endemic to the Mediterranean, has long been overexploited. A demographic approach to the conservation and management of this species would therefore be highly valuable. To this end, a coastal population of red coral was studied in detail. The population represents a true genetic unit, as it is mainly self-seeding. It is moreover gonocoric, and the sex ratio is significantly biased toward females. For this study, 4408 colonies, collected from 28, 300-cm2 samples, were divided into 10 size (age) classes. Recruits represent about half the population. The frequency of colonies in each class decreases exponentially with colony size. On these bases, an ad hoc life history table has been updated to include the mortality and reproduction coefficients actually measured in the population. The major reproductive output is due to the first 3 reproductive classes (79%), while larger colonies, although having higher reproductive coefficients, are sparse and only account for a small portion of the population overall reproductive output. The ratio of larval survival to adult density found indicates that some density-dependent limitation of population growth is likely at play in the population under study. Such results will be important for understanding dynamics of red coral disturbed or exploited populations.

Growth changes in plaice, cod, haddock and saithe in the North Sea: a comparison of (post-)medieval and present-day growth rates based on otolith measurements

Fishing effort has strongly increased in the North Sea since the mid-19th century, causing a substantial reduction in the population size of exploited fish stocks. As fisheries research has developed simultaneously with the industrialisation of the fisheries, our knowledge of population dynamics at low levels of exploitations is limited. Otoliths retrieved from archaeological excavations offer a unique opportunity to study growth rates in the past. This study compares historical and present-day growth rates for four commercially important demersal fish species. A total of 2532 modern otoliths (AD 1984–1999) and 1286 historical otoliths (AD 1200–1925) obtained from archaeological excavations in Belgium and Scotland were analysed. Comparison of the growth patterns between eras revealed a major increase in growth rate of haddock, whereas growth changes were not observed in saithe and only in the smaller size classes of plaice and cod. Comparison of our results with literature data indicates that the observed growth rate changes in plaice and cod occurred within the 20th century. Apparently the onset of industrialised fisheries has not greatly affected the growth of plaice, cod and saithe populations in the North Sea. This result contradicts the expectation of density-dependent limitation of growth during the era of pre-industrialised fishing, but is in agreement with the concentration hypothesis of Beverton (Neth. J. Sea Res. 34 (1995) 1) stating that species which concentrate spatially into nursery grounds during their early life-history may ‘saturate’ the carrying capacity of the juvenile habitat even though the adult part of the population is not limited by the adult habitat.

Onchocerca-Simulium complexes in Venezuela: can human onchocerciasis spread outside its present endemic areas?

The compatibility between sympatric and allopatric combinations of Onchocerca volvulus-anthropophilic species of Simulium was studied in the north-eastern focus of human onchocerciasis as well as in a densely populated locality of the Amazonas State in Venezuela. The objectives were to test the conjecture that local adaptation exists between the parasite and its vectors (the Onchocerca-Simulium complex hypothesis), and assess the possibility of the infection spreading from its present distributional range. For the homologous combination, O. volvulus-S. metallicum cytospecies E in Anzoátegui State (north-eastern focus), parasite yield was 45% in contrast to 1% for the heterologous, southern parasite-S. metallicum infection. This was significantly lower than the parasite yield (4-10%) expected after allowing for the effect of density-dependent limitation of infective larval output described in this paper for S. metallicum. The population of S. exiguum s.l. from southern Venezuela allowed no larval development beyond the L1 stage of either northern or southern parasites. Mechanisms for such refractoriness probably operate at the level of the thoracic muscles, not affecting microfilarial uptake or migration out of the bloodmeal. The parasite yield of southern O. volvulus in S. oyapockense s.l. flies biting man at Puerto Ayacucho (Amazonas) was about 1%, in agreement with the figures recorded for highly compatible sympatric combinations such as O. volvulus-S. ochraceum s.l. in Guatemala. No infective larval development of the northern parasite was observed in southern S. oyapockense. These results, together with considerations of typical worm burdens in the human host, presence/absence of armed cibaria in the simuliids, parasite-induced vector mortality, and fly biting rates, suggest a lower potential for onchocerciasis to spread between the northern and southern endemic areas of Venezuela than that between Amazonian hyperendemic locations and settlements outside this focus with high densities of S. oyapockense s.l.

Modelling nutrient-periphyton dynamics in streams: the importance of transient storage zones

The dynamics of a nutrient-limited periphyton community in a segment of stream was modeled. The stream segment was assumed to consist of two zones, free-flowing water and a boundary zone of zero water flow, which acted as a transient storage zone for nutrients. Studies with a biologically unreactive tracer solute (sodium chloride) were used to obtain parameters for diffusion of solute into the transient storage zone. Two simple alternative functional responses representing nutrient-limited periphyton growth were formulated, one with only nutrient limitation on periphyton growth and one that additionally included density-dependent limitation of periphyton growth. Attempts to fit the two alternative functional responses for periphyton growth and to predict nutrient levels in the transient storage zone showed that the two alternatives had very different implications for the steady state and dynamics of the storage zone. Empirical studies of periphyton biomass and nutrient turnover give support for the second alternative function. The model results suggests some additional experiments that can be performed to test the two alternatives.

Reproduction and Mortality of Finnish Semi-Domesticated Reindeer in Relation to Density and Management Strategies

We assessed the effects of management strategies during 1960-73 relative to strategies used during 1974-87 on the reproduction and mortality of 56 semi-domesticated herds of Finnish reindeer (Rangifer tarandus tarandus). During 1960-73, reindeer fed exclusively on natural forage growing on their range, and reindeer were harvested mostly as adults. These strategies were modified starting in 1974 to include supplemental feeding in the southern part of the Finnish reindeer range and calf harvesting throughout the range. We found significantly higher calf/female ratios, lower mortality, and less variation in both calf/female ratios and mortality during 1974-87 than during 1960-73. These changes occurred in spite of increased animal density. Coefficients of variation in calf/female ratio and mortality were negatively correlated with the prevalence of mature spruce forests, which are rich in arboreal lichens. Mean calf/female ratio and mortality rate depended on reindeer density only in the southern region during 1960-73. During 1974-87 these did not depend on density in any region. Within herds, calf/female ratio did not depend on density in most cases (98%), while in the later period the relationship between calf production and density was positive in some cases (25%). Mortality depended more often on density during the earlier (46% of herds) than the later (23% of herds) period. Calf harvesting influenced mortality more than supplemental feeding and virtually freed reindeer from density-dependent limitations. Supplemental feeding was used to compensate for deterioration of range resulting from overgrazing and logging of mature forests rich in arboreal lichens.Key words: reproduction, mortality, density dependence, reindeer, Rangifer tarandus, management, Finland

Foraging habitat and prey taken by least auklets at King Island, Alaska

MARINE ECOLOGY PROGRESS SERIES Mar. Ecol. Prog. Ser. Vol. 65: 141-150, 1990 Published August 2 Foraging habitat and prey taken by least auklets at King Island, Alaska George L. Hunt, Jr, Nancy M. Harrison* Department of Ecology a n d Evolutionary Biology, University of California, Irvine, California 92717, USA ABSTRACT: We examined the foraging distribution a n d prey use of least auklets Aethia pusilla breeding on King Island in the northern Bering Sea. The locat~on of the King Island colony, in Alaska Coastal Water, but within auklet flight range of the oceanic Anadyr Current and the Anadyr-influenced Bering Shelf Water, provided an opportunity to ident~fy the preferred foraging h a b ~ t a t of the least auklet. Least auklets fed on Neocalanus plumchrus, N. cnstatus, Eucalanus bungii, a n d shrimp larvae, all present in Anadyr Current and in Bering Shelf Water. In early J u n e 1984 a n d July 1985, auklet foraging was concentrated at and just beyond a front ca 30 km west of Klng Island, separating Alaska Coastal Water from Bering Shelf Water to the west, large copepods of oceanic ongin occurred throughout Bering Shelf Water. Data from 1985 indicated varlabllity In the path of the Anadyr Current; rapid changes also took place in the distribution of the least auklets' planktonic prey. In late July 1985, we documented an intrusion of Anadyr Water from 45 km to withln 25 km of King Island. Least auklets often overflew the Alaska Coastal Water and foraged in stratified Benng Shelf Water, a n d in Anadyr Water beyond the front. In 1986, Alaska Coastal Current Water overlaid Bering Shelf Water in much of the area to the west of King Island and a majority of auklets foraged where Bering Shelf Water w a s closest to the surface. Throughout the study, foraglng least auklets were absent from the Alaska Coastal Current near King Island, even though alternative prey, Calanus rnarshallae, taken elsewhere by breeding least auklets, w e r e present. We conclude that at King Island least auklets sought specific preferred prey in stratified water and near fronts a n d shifted their foraging over large distances in response to the mobile marine habitat in which their prey were abundant. INTRODUCTION Marine birds forage in habitats that are patchy and dynamic. Within habitats, prey patches are ephemeral, with large prey patches generally lasting longer than small patches (Steele 1976, Haury et al. 1978). Addi- tionally, the habitats themselves are mobile, with ani- mal communities carried by currents. Thus, breeding marine birds foraging from a central place not only have to locate patches of prey within a given habitat, but also must respond to movements of the water mass within which the patches of preferred prey occur. We report here the foraging distribution of least auklets Aethia pusilla breeding on King Island, northern Be- ring Sea, Alaska, in relation to water masses supporting different communities of zooplankton on which these auklets feed. Factors determining the distribution of foraging sea- Present address: Nature Conservancy Council, l? Rub~slaw Terrace, Aberdeen AB1 IXE, Scotland 0 Inter-Research/Printed in F. R. Germany birds in the vicinity of their breedlng colonies have long been of interest. Initial emphasis focused on the possi- bility of density-dependent limitation of seabird num- bers due to intraspecific competition for prey near colonies (e.g. Ashmole 1963, Gaston et al. 1983, Furness &Birkhead 1984, Hunt et al. 1986), and themechanisms for resource partitioning by which interspecific com- petition might be reduced (e.g. Ashmole & Ashmole 1967, Bedard 1969). Cody (1973) suggested that the principal means of resource partitioning in coexisting species of alcids (e.g. auks, puffins) was the use of foraging zones at different distances from their col- onies. Bedard (1976) showed that much of Cody's interpretation was flawed. Bedard suggested that the foraging distribution of alcids near their colonies was more likely to be determined by ' . . . the general water circulation and oceanographic conditions. . . ' in the vi- cinity of the colony. Recently, Kinder et al. (1983) found that frontal systems associated with shoaling of water near the Pribilof Islands (Alaska) supported higher numbers of foraglng birds than expected by chance.

Effects of host grooming on louse populations

Grooming behaviour by the host is increasingly recognized as an important determinant of feeding behaviour by blood-sucking arthropods. In general, grooming activity increases as a function of attack rate which, in some cases, provides a density-dependent limitation on the success of blood feeding. In turn this can lead to density dependence in population parameters of the arthropod, and can affect transmission of some arthropod-borne parasites in a similar way. But although insect-host interactions at this level are now being revealed in a variety of blood-sucking groups, such as mosquitoes, tsetse flies and triatomine bugs (see Box I), they are perhaps most clearly seen in, populations of ectoporositic insects such as lice, which ore permanently subject to defensive grooming behaviour by their hosts. As Durno Murray discusses here, host grooming has been a dominant factor in the evolution of lice, not only at the morphological level but also in terms of reproductive strategy.

Ecological Aspects of Disease and Human Populations

This paper shows how some basic ecological themes can be illustrated, in a very explicit and quantitative way, by examples drawn from the interactions between human hosts and their infectious diseases. I first discuss the population biology of infectious diseases, showing how basic reproductive rates and density dependent limitations may be estimated. Observed cycles in the incidence of childhood infections are discussed as examples of Lotka-Volterra prey-predator cycles. Trade-offs between virulence and transmissibility in the evolution of parasite life histories are discussed in general,with the Australian rabbit-myxoma virus story as a case study. I conclude by mentioning ways in which the interplay between population density and transmission thresholds may have influenced human history.

Measuring microzooplankton grazing on planktonic marine bacteria by its impact on bacterial production

Grazing on planktonic bacteria by microzooplankton was estimated by separating bacteria from the larger plankton with 1μm pore Nuclepore filtration and measuring changes in bacteria in filtered and unfiltered samples over 24 hours. In the absence of grazers, bacteria increased linearly. The regression coefficient of linear increase was used to estimatein situ bacterial production. When grazers were present, the changes in bacteria concentration usually took the form of a linear decline, and grazing was estimated by subtracting the regression coefficient of the unfiltered sample from that of the 1μm filtrate. Results from the Essex estuary-coastal system of northern Massachusetts show grazing and production at rates that indicate a daily turnover of the standing crop of bacteria, with highest values in mid-estuarine waters. Experiments on the size distribution of grazing showed that microzooplankton from 1-3μm were responsible for most of the observed decrease in bacteria. It was suggested that the basic pattern of linear increase of the bacteria in the absence of grazing reflects density-dependent limitation by substrate present at the outset of the incubation and is indicative of a population that has been maintained around the mid-point of the logistic growth curve by grazing.

Density-dependent limitation of growth and the regulation of cell replication by changes in the triggering level of the cell cycle switch

If the initiation/suppression of cell replication results from the operation of an intracellular switch, then proliferation control can be expected to occur through the modulation of its threshold setting or sensitivity. Assuming the existence of a threshold and the uptake of regulators by an equilibrium process, one can explain various types of dependency of the maximum cell density on the initial level of the regulator (e.g., serum) in the medium. Moreover it becomes theoretically possible to distinguish whether an altered threshold or equilibrium constant is responsible for modified proliferation characteristics. It is pointed out that some published data on transformed cells are more consistent with an altered threshold than the permeability change invoked. Other data suggests that transformation has produced more complex effects. The arguments presented indicate that while some cells may be more susceptible to control via changes in the relevant equilibrium constant, others may respond more markedly to threshold modulation. If control occurs through inhibition of replication, it is possible for the system to exhibit a critical “mass”: if this is exceeded (in ways discussed) proliferation could continue indefinitely provided adequate nutrients are available. An oscillator concept of the cell cycle accounts for the existence of a threshold and also permits a general understanding of its modulation by multiple agents. It is concluded that at least some forms of cancer are the result of altered thresholds.