The importance of carrying capacity,fertility, and viability for the competitive ability of populations

Summary A simple mathematical model is analyzed which describes the behaviour of a population under the influence of viability and fertility as well as carrying capacity and competition by another species. One locus with two alleles determining viability, fertility, and carrying capacity is considered. Throughout the analysis absolute rather than relative numbers are used. The following results have been obtained: 1. The species producing more zygotes wins the competition. 2. Absolute numbers must be used for viability and fertility in theoretical considerations, because the outcome of competition may be changed by using different absolute numbers of the same relation. 3. Differences in viability are amplified by limiting the number of individuals. 4. Differences in every parameter can be compensated by any other parameter.     

Predicting how populations decline to extinction

Global species extinction typically represents the endpoint in a long sequence of population declines and local extinctions. In comparative studies of extinction risk of contemporary mammalian species, there appear to be some universal traits that may predispose taxa to an elevated risk of extinction. In local population-level studies, there are limited insights into the process of population decline and extinction. Moreover, there is still little appreciation of how local processes scale up to global patterns. Advancing the understanding of factors which predispose populations to rapid declines will benefit proactive conservation and may allow us to target at-risk populations as well as at-risk species. Here, we take mammalian population trend data from the largest repository of population abundance trends, and combine it with the PanTHERIA database on mammal traits to answer the question: what factors can be used to predict decline in mammalian abundance? We find in general that environmental variables are better determinants of cross-species population-level decline than intrinsic biological traits. For effective conservation, we must not only describe which species are at risk and why, but also prescribe ways to counteract this.     

Minimum requirements for modelling bivalve carrying capacity

The concept of carrying capacity of an ecosystem fornatural populations is derived from the logisticgrowth curve in population ecology, and defined as themaximum standing stock that can be supported by agiven ecosystem for a given time. This definitionneeds to be modified for the exploitation ofecosystems. Carrying capacity for exploitation isdefined as the standing stock at which the annualproduction of a marketable cohort is maximized. Forbivalve suspension feeders, the dominant factordetermining the exploitation carrying capacity at theecosystem scale is primary production. At a localscale carrying capacity depends on physicalconstraints such as substrate, shelter and food supplyby tidal currents.We evaluate critically some existing models ofexploited ecosystems for shellfish cultivation inorder to formulate the minimum requirements of ageneric carrying capacity model. Generic models canbe developed for both the ecosystem scale and thelocal scale, depending on the aim of the modelling.Transport processes, sediment dynamics and submodelsfor organism and population level processes areminimum requirements for carrying capacity modelling. This revised version was published online in August 2006 with corrections to the Cover Date.     

On evolutionary stability of carrying capacity driven dispersal in competition with regularly diffusing populations

Two competing populations in spatially heterogeneous but temporarily constant environment are investigated: one is subject to regular movements to lower density areas (random diffusion) while the dispersal of the other is in the direction of the highest per capita available resources (carrying capacity driven diffusion). The growth of both species is subject to the same general growth law which involves Gilpin–Ayala, Gompertz and some other equations as particular cases. The growth rate, carrying capacity and dispersal rate are the same for both population types, the only difference is the dispersal strategy. The main result of the paper is that the two species cannot coexist (unless the environment is spatially homogeneous), and the carrying capacity driven diffusion strategy is evolutionarily stable in the sense that the species adopting this strategy cannot be invaded by randomly diffusing population. Moreover, once the invasive species inhabits some open nonempty domain, it would spread over any available area bringing the native species diffusing randomly to extinction. One of the important technical results used in the proofs can be interpreted in the form that the limit solution of the equation with a regular diffusion leads to lower total population fitness than the ideal free distribution.     

Predicting the consequences of carry-over effects for migratory populations

Migratory animals present a unique challenge for predicting population size because they are influenced by events in multiple stages of the annual cycle that are separated by large geographic distances. Here, we develop a model that incorporates non-fatal carry-over effects to predict changes in population size and show how this can be integrated with predictive models of habitat loss and deterioration. Examples from Barn swallows, Greater snow geese and American redstarts show how carry-over effects can be estimated and integrated into the model. Incorporation of carry-over effects should increase the predictive power of models. However, the challenge for developing accurate predictions rests both on the ability to estimate parameters from multiple stages of the annual cycle and to understand how events between these periods interact to influence individual success.     

Predicting survival time for cold exposure

The prediction of survival time (ST) for cold exposure is speculative as reliable controlled data of deep hypothermia are unavailable. At best, guidance can be obtained from case histories of accidental exposure. This study describes the development of a mathematical model for the prediction of ST under sedentary conditions in the cold. The model is based on steady-state heat conduction in a single cylinder comprised of a core and two concentric annular shells representing the fat plus skin and the clothing plus still boundary layer, respectively. The ambient condition can be either air or water; the distinction is made by assigning different values of insulation to the still boundary layer. Metabolic heat production (M) is comprised of resting and shivering components with the latter predicted by temperature signals from the core and skin. Where the cold exposure is too severe forM to balance heat loss, ST is largely determined by the rate of heat loss from the body. Where a balance occurs, ST is governed by the endurance time for shivering. End of survival is marked by the deep core temperature reaching a value of 30° C. The model was calibrated against survival data of cold water (0 to 20° C) immersion and then applied to cold air exposure. A sampling of ST predictions for the nude exposure of an average healthy male in relatively calm air (1 km/h wind speed) are the following: 1.8, 2.5, 4.1, 9.0, and >24 h for –30, –20, –10, 0, and 10° C, respectively. With two layers of loose clothing (average thickness of 1 mm each) in a 5 km/h wind, STs are 4.0, 5.6, 8.6, 15.4, and >24 h for –50, –40, –30, –20, and –10° C. The predicted STs must be weighted against the extrapolative nature of the model. At present, it would be prudent to use the predictions in a relative sense, that is, to compare or rank-order predicted STs for various combinations of ambient conditions and clothing protection.     

On the capacity of macroparasites to control insect populations

A graphical model of the population dynamics of macroparasites and their hosts is developed. Three principal means by which the parasites can be regulated are considered: reduction in host density as a result of parasite-induced host mortality, reduction in host density as a result of parasite-induced host sterility, and competition among parasites within multiply-infected hosts. The means by which parasites are regulated has a major effect on the degree to which they can depress host population densities. In particular, a parasite that sterilizes its host is expected to reduce host density more than one that causes an equivalent decline in host fitness through increased mortality. A special case of the model is developed for herbivorous insects that, in the absence of parasites, are limited by larval food resources. Parasites that are regulated via parasite-induced host sterility will control the insect populations below the level set by larval resources if the threshold host density for the parasites (N(T)) is less than the ratio of carrying capacity to net reproductive rate of the insects (K/R). Data are presented showing that all three means of parasite regulation, but especially parasite-induced host sterility, can operate in Howardula aoronymphium, a nematode parasite of mycophagous Drosophila flies. Data from a field cage experiment show that, if these nematodes are regulated primarily via reductions in host density due to this sterility, the parameters N(T), K, and R are such that Howardula is likely to play an important role in controlling Drosophila populations. However, this conclusion must be tempered by the fact that these nematodes also cause increased host mortality and experience within-host competition, making the conditions for parasite control of the flies more stringent.     

Predicting the response of Cabomba caroliniana populations to biological control agent damage

Abstract  Cabomba caroliniana is a submerged aquatic plant from South America that is becoming a serious weed worldwide. It spreads by seed and by fragmentation and has an extremely wide climatic range, invading lakes and ponds from tropical (Darwin, Australia: latitude 12°) to cold temperate regions (Peterborough, Canada: latitude 45°). There are currently no effective methods of managing cabomba infestations and funding has been allocated to research biological methods. Surveys have examined cabomba in its native range and have identified several potential biological control agents. The most promising are a stem boring weevil ( Hydrotimetes natans ) and an aquatic moth ( Paracles spp.). Here we predict the change in cabomba populations after the introduction of the biological control agents. Our predictions are based on quantitative surveys of cabomba populations at three lakes in south-east Queensland, qualitative observations of cabomba in its native range, and conceptual knowledge of how the realised niche of cabomba might be affected by herbivore damage.     

Predicting cumulated response to directional selection in finite panmictic populations

Summary Accurate prediction of the cumulated genetic gain requires predicting genetic variance over time under the joint effects of selection and limited population size. An algorithm is proposed to quantify at each generation the effects of these factors on average coefficient of inbreeding, genetic variance, and genetic mean, under a purely additive polygenic model, with no mutation, and under the assumption of absence of inbreeding depression on viability affecting selection differentials. This algorithm is relevant to populations where mating is at random and generations do not overlap. It was tested via Monte Carlo simulation on a population of 3 males and 25 females mass selected out of 50 candidates of each sex, over 30 generations. For two values of the initial heritability of the selected trait, 0.5 and 0.9 (to represent high accuracy in index selection), predicted values of the genetic variance are in agreement with observed results up to the 12th and 19th generations, respectively. Beyond these generations, the variance is overestimated, due to an underestimation of the effect of selection on the rate of inbreeding. Finally, the algorithm provides predictions of the cumulated responses close to the observed values in both selected populations. It is concluded that, as regards the hypotheses of the study, the proposed algorithm is satisfactory, and could be used to optimize selection methods with respect to the cumulated genetic gain in the mid- or long-term. Possible extensions of the algorithm to more realistic situations are discussed.     

Predicting the annual effective size of livestock populations

Effective population size (Ne) is an important parameter determining the genetic structure of small populations. In natural populations, the number of adults (N) is usually known and Ne can be estimated on the basis of an assumed ratio Ne/N, usually found to be close to 0.5. In farm animal populations, apart from using pedigrees or genetic marker information, Ne can be estimated from the number N of breeding animals, and a value of 1 is commonly assumed for the ratio Ne/N. The purpose of this paper is to show the relation between effective population size and breeding herd size in livestock species. With overlapping generations, Ne can be predicted knowing the number of individuals entering the population per generation and the variance of family size, the latter being directly related to the survival pattern (or replacement policy) in the breeding herd. Assuming an ideal survivorship leading to a geometric age distribution, it can be shown that the number of breeding animals tends to overestimate effective size, particularly in early-maturing species. The ratio of annual effective size to the number of breeding animals is shown to be equal to [1 + (a- 1)(1 - s)]2/(1 - s2), where a is the age at first offspring and s is the survival rate (including culling) of the parents between successive births. This expression shows to what extent inbreeding may be determined by demography or culling policy independently of the actual herd size. In many situations a fast replacement or an early culling will increase annual effective size. Consequences for the management of small populations are discussed.     

Student responses to a hands-on kinesthetic lecture activity for learning about the oxygen carrying capacity of blood

This article describes a new hands-on, or "kinesthetic," activity for use in a physiology lecture hall to help students comprehend an important concept in cardiopulmonary physiology known as oxygen carrying capacity. One impetus for designing this activity was to address the needs of students who have a preference for kinesthetic learning and to help increase their understanding and engagement during lecture. This activity uses simple inexpensive materials, provides an effective model for demonstrating related pathophysiology, and helps promote active learning. The activity protocol and its implementation are described here in detail. We also report data obtained from student surveys and assessment tools to determine the effectiveness of the activity on student conceptual learning and perceptions. A brief multiple-choice pretest showed that although students had already been introduced to the relevant concepts in lecture, they had not yet mastered these concepts before performing the activity. Two postactivity assessments showed that student performance was significantly improved on the posttest compared with the pretest and that information was largely retained at the end of the course. Survey data showed that one-half of the students stated kinesthetic learning as among their learning preferences, yet nearly all students enjoyed and were engaged in this hands-on kinesthetic activity regardless of their preferences. Most students would recommend it to their peers and expressed a desire for more kinesthetic learning opportunities in the lecture curriculum.     

Properties of sodium and potassium channels of the squid giant axon far below 0 degrees C

Squid giant axon could be excited in concentrated glycerol solutions containing normal concentrations of electrolytes, when osmolalities of solutions inside and outside the axon were matched. These glycerol solutions did not freeze at the temperature as low as -19 degrees C. The nerve excitation in these solutions were observed at this low temperature. The excitation process at this low temperature was slowed down and time constants of the excitation kinetics were several hundredfold larger than those in normal seawater at 10 degrees C, under which temperature the squid habituated. The temperature coefficients for the electrophysiological membrane parameters under this condition were larger than those in normal seawater above 0 degrees C. The Q10 value for the conduction velocity was 2.0 and that of the duration of the action potential was around 8.5. The time course of the membrane currents was also slowed with the Q10 value of around 5 and the magnitude decreased with the Q10 value of around 2 as the temperature was lowered. The Q10 values for the kinetics of the on process of the Na-channel were around 4.5 and were almost the same as those of the off process of the Na-channel in the wide range of the temperature below 0 degrees C. The Q10 value of the on process of K-channel was around 6.5 and was larger than those for Na-channel. The Q10 values increased gradually as the temperature was lowered.     

Predicting the potential of open-pollinating populations for the production of superior F1 hybrids

Summary The distributive properties of a single population or of a population resulting from a cross between two populations are reproduced when inbreds randomly extracted from the population itself or from the two parental populations are randomly paired. Hence, population parameters that are usually obtained during a breeding programme can be used to predict the performance of the F₁ hybrids that can be derived from them at that stage. Multiple allelism, epistasis and deviations from Hardy-Weinberg equilibria should not cause biasis to the predictions. While in theory genotype x environment interaction and linkage disequilibrium may disturb the predictions, in practice they are unlikely to create problems that cannot be accommodated. Genotypic and phenotypic predictions of the proportions of the F₁ hybrid distribution scoring above or below a given standard are made and analysed for three characters, weight of the ears, plant height and height of the ear, in two populations of maize per se and their interpopulational cross. Because no random inbred lines from the experimental populations are presently available we cannot check our predictions. However, genotypic and phenotypic predictions and observations of F₁ hybrids obtained from populations created by computer simulation are provided to illustrate our procedures.J. F. F. de Toledo is a geneticist on leave from Centro National de Pesquisa de Soja-EMBRAPA, Caixa Postal 1061, 86100-Londrina-Pr, BrazilJ. B. de Miranda Filho is Professor of Genetics at Escola Superior de Agriculture Luiz de Queiroz-ESALQ, Caixa Postal 83, 13400-Piracicaba-SP, Brazil     

Predicting response to selection on a quantitative trait: a comparison between models for mixed-mating populations

Two different theoretical frameworks have been developed to predict response to selection in a mixed mating population (in which reproduction occurs by a mixture of outcrossing and self-fertilization). The genotypic covariance model (GCM) and the structured linear model (SLM) rely on the same assumptions regarding quantitative trait inheritance, but use different genetic summary statistics. Here, we demonstrate the algebraic relationships between the various genetic metrics used in each theory. This is accomplished by reformulating the GCM in terms of the Wright-Kempthorne equation. We use stochastic simulations to investigate the relative accuracy of each theory for a range of selfing rates. The SLM is generally more accurate than the GCM, the most pronounced differences emerging in simulations with inbreeding depression for fitness. In fact, with strong inbreeding depression and high selfing rates, evolution can occur opposite the direction predicted by the GCM. The simulations also indicate that direct application of random mating models to partially selfing populations can produce very inaccurate predictions if quantitative trait loci exhibit dominance.     

Predicting extinction risks for plants: environmental stochasticity can save declining populations

An emerging generalization from theoretical and empirical studies on conservation biology is that high levels of environmental stochasticity increase the likelihood of population extinction. However, coexistence theory has illustrated that there are circumstances under which environmental stochasticity can increase the chance of population persistence. These theoretical studies have shown that the sign of the effect of environmental stochasticity on population persistence is determined by interactions between life history and environmental stochasticity. These interactions mean that the stochastic and deterministic rates of population growth might differ fundamentally. Although difficult to demonstrate in real systems, observed life histories and variance in the vital rates of populations suggest that this phenomenon is likely to be common, and is therefore of much relevance to conservation biologists.     

Red deer range and problems of carrying capacity in the Scottish Highlands

Some general principles underlying the concept of carrying capacity and problems in using the term are illustrated by reference to herbivore/vegetation inter-relationships in intensive pasture systems, regimes of range management and wildlife systems. The approach to management of the deer/range system in Scotland does not fit into any of these categories of land use. Ecological deficiencies arise because deer, rather than the soils and vegetation, are regarded as the resource. Hence, management of the range is animal orientated. It is based on techniques such as burning which give temporary benefits to the animal component of the system. It is argued that this inversion of priorities in management has the long-term effect of encouraging vegetational successions that aggravate problems of animal management, especially on the poorer soils. The characteristics of the deer and the vegetation, and trends of change are considered in this context. It is concluded that within the present framework of management there is little scope for radical improvement. A restructuring of the system is required to give greater control over the biological performance of the deer and of the trends in the vegetation.     

Predicting response to reassurances and uncertainties in bioterrorism communications for urban populations in New York and California

Recent national plans for recovery from bioterrorism acts perpetrated in densely populated urban areas acknowledge the formidable technical and social challenges of consequence management. Effective risk and crisis communication is one priority to strengthen the U.S.'s response and resilience. However, several notable risk events since September 11, 2001, have revealed vulnerabilities in risk/crisis communication strategies and infrastructure of agencies responsible for protecting civilian populations. During recovery from a significant biocontamination event, 2 goals are essential: (1) effective communication of changing risk circumstances and uncertainties related to cleanup, restoration, and reoccupancy; and (2) adequate responsiveness to emerging information needs and priorities of diverse populations in high-threat, vulnerable locations. This telephone survey study explored predictors of public reactions to uncertainty communications and reassurances from leaders related to the remediation stage of an urban-based bioterrorism incident. African American and Hispanic adults (N=320) were randomly sampled from 2 ethnically and socioeconomically diverse geographic areas in New York and California assessed as high threat, high vulnerability for terrorism and other public health emergencies. Results suggest that considerable heterogeneity exists in risk perspectives and information needs within certain sociodemographic groups; that success of risk/crisis communication during recovery is likely to be uneven; that common assumptions about public responsiveness to particular risk communications need further consideration; and that communication effectiveness depends partly on preexisting values and risk perceptions and prior trust in leaders. Needed improvements in communication strategies are possible with recognition of where individuals start as a reference point for reasoning about risk information, and comprehension of how this influences subsequent interpretation of agencies' actions and communications.