Comparing organic farming and land sparing: optimizing yield and butterfly populations at a landscape scale

Organic farming aims to be wildlife-friendly, but it may not benefit wildlife overall if much greater areas are needed to produce a given quantity of food. We measured the density and species richness of butterflies on organic farms, conventional farms and grassland nature reserves in 16 landscapes. Organic farms supported a higher density of butterflies than conventional farms, but a lower density than reserves. Using our data, we predict the optimal land-use strategy to maintain yield whilst maximizing butterfly abundance under different scenarios. Farming conventionally and sparing land as nature reserves is better for butterflies when the organic yield per hectare falls below 87% of conventional yield. However, if the spared land is simply extra field margins, organic farming is optimal whenever organic yields are over 35% of conventional yields. The optimal balance of land sparing and wildlife-friendly farming to maintain production and biodiversity will differ between landscapes.

Scale matters: the impact of organic farming on biodiversity at different spatial scales

There is increasing recognition that ecosystems and their services need to be managed in the face of environmental change. However, there is little consensus as to the optimum scale for management. This is particularly acute in the agricultural environment given the level of public investment in agri-environment schemes (AES). Using a novel multiscale hierarchical sampling design, we assess the effect of land use at multiple spatial scales (from location-within-field to regions) on farmland biodiversity. We show that on-farm biodiversity components depend on farming practices (organic vs. conventional) at farm and landscape scales, but this strongly interacts with fine- and coarse-scale variables. Different taxa respond to agricultural practice at different spatial scales and often at multiple spatial scales. Hence, AES need to target multiple spatial scales to maximize effectiveness. Novel policy levers may be needed to encourage multiple land managers within a landscape to adopt schemes that create landscape-level benefits.

The dynamics of phenotypic change and the shrinking sheep of St. Kilda

Environmental change, including climate change, can cause rapid phenotypic change via both ecological and evolutionary processes. Because ecological and evolutionary dynamics are intimately linked, a major challenge is to identify their relative roles. We exactly decomposed the change in mean body weight in a free-living population of Soay sheep into all the processes that contribute to change. Ecological processes contribute most, with selection--the underpinning of adaptive evolution--explaining little of the observed phenotypic trend. Our results enable us to explain why selection has so little effect even though weight is heritable, and why environmental change has caused a decline in the body size of Soay sheep.

Variation in dispersal mortality and dispersal propensity among individuals: the effects of age, sex and resource availability

1. Dispersal of individuals between habitat patches depends on both the propensity to emigrate from a patch and the ability to survive inter-patch movement. Environmental factors and individual characteristics have been shown to influence dispersal rates but separating the effects of emigration and dispersal mortality on dispersal can often be difficult. In this study, we use a soil mite laboratory system to investigate factors affecting emigration and dispersal mortality. 2. We tested the movement of different age groups in two-patch systems with different inter-patch distances. Differences in immigration among age groups were primarily driven by differences in emigration but dispersal mortality was greater for some groups. Immigration declined with increasing inter-patch distance, which was due to increasing dispersal mortality and decreasing emigration. 3. In a second experiment, we compared the dispersal of recently matured males and females and tested the impact of food availability during the developmental period on their dispersal. Dispersal was found to be male biased but there was no significant sex bias in dispersal mortality. There was some evidence that food availability could affect emigration and dispersal mortality. 4. These results demonstrate that both emigration and dispersal mortality can be affected by factors such as individual age and resource availability. Understanding these effects is likely to be important for predicting the fitness costs and population consequences of dispersal.

The influence of context-dependent maternal effects on population dynamics: an experimental test

Parental effects arise when either the maternal or paternal phenotype influences the phenotypes of subsequent generations. Simple analytical models assume maternal effects are a mechanism creating delayed density dependence. Such models predict that maternal effects can very easily lead to population cycles. Despite this, unambiguous maternal-effect mediated cycles have not been demonstrated in any system. Additionally, much evidence has arisen to invalidate the underlying assumption that there is a simple positive correlation between maternal performance and offspring performance. A key issue in understanding how maternal effects may affect population dynamics is determining how the expression of parental effects changes in different environments. In this study, we tested the hypothesis that maternal effects influence population dynamics in a context-dependent way. Populations of the soil mite, Sancassania berlesei, were set up at high density (500 eggs) or low density (50 eggs), with eggs that were either laid by young mothers or old mothers (a previously documented maternal effect in this system). The influence of maternal age on both population and egg and body-size dynamics was only observed in the populations initiated under low density rather than high density. This difference was attributable to the context-dependence of maternal effects at the individual level. In low-density (high food) conditions, maternal effects have an impact on offspring reproductive performance, creating an impact on the population growth rate. In high density (low food), maternal effects impact more on juvenile survival (not adult size or reproduction), creating a smaller impact on the population growth rate. This context dependence of effects at the population level means that, in fluctuating populations, maternal effects cause intermittent delayed density dependence that does not lead to persistent cycles.

Indirect population dynamic benefits of altered life-history trade-offs in response to egg harvesting

Variations in demographic rates due to differential resource allocation between individuals are important considerations in the development of accurate population dynamic models. Systematic harvesting can alter age structure and/or reduce population density, conferring indirect positive benefits on the source population as a result of a consequent redistribution of resources between the remaining individuals. Independently of effects mediated through changes in density and competition, demographic rates can also be influenced by within-individual competition for resources. Harvesting dependent life stages can reduce an individual's current reproductive costs, allowing increased investment in its future fecundity and survival. Although such changes in demographic rates are well known, there has been little exploration of the potential impact on population dynamics. We use empirical data collected from a successfully reintroduced population of the Mauritius kestrel Falco punctatus to explore the population consequences of manipulating reproductive effort through harvesting. Consequent increases in an individual's future fecundity and survival allow source populations to withstand longer and more intensive harvesting regimes without being exposed to an increase in extinction risk, increasing maximum sustainable yields. These effects may also buffer populations against the impacts of stochastic events, but directional shifts in environmental conditions that increase reproductive costs may have detrimental population-level effects.

Accelerating invasion rates result from the evolution of density-dependent dispersal

Evolutionary processes play an important role in shaping the dynamics of range expansions, and selection on dispersal propensity has been demonstrated to accelerate rates of advance. Previous theory has considered only the evolution of unconditional dispersal rates, but dispersal is often more complex. For example, many species emigrate in response to crowding. Here, we use an individual-based model to investigate the evolution of density dependent dispersal into empty habitat, such as during an invasion. The landscape is represented as a lattice and dispersal between populations follows a stepping-stone pattern. Individuals carry three 'genes' that determine their dispersal strategy when experiencing different population densities. For a stationary range we obtain results consistent with previous theoretical studies: few individuals emigrate from patches that are below equilibrium density. However, during the range expansion of a previously stationary population, we observe evolution towards dispersal strategies where considerable emigration occurs well below equilibrium density. This is true even for moderate costs to dispersal, and always results in accelerating rates of range expansion. Importantly, the evolution we observe at an expanding front depends upon fitness integrated over several generations and cannot be predicted by a consideration of lifetime reproductive success alone. We argue that a better understanding of the role of density dependent dispersal, and its evolution, in driving population dynamics is required especially within the context of range expansions.

How range shifts induced by climate change affect neutral evolution

We investigate neutral evolution during range shifts in a strategic model of a metapopulation occupying a climate gradient. Using heritable, neutral markers, we track the spatio-temporal fate of lineages. Owing to iterated founder effects ('mutation surfing'), survival of lineages derived from the leading range limit is enhanced. At trailing limits, where habitat suitability decreases, survival is reduced (mutations 'wipe out'). These processes alter (i) the spatial spread of mutations, (ii) origins of persisting mutations and (iii) the generation of diversity. We show that large changes in neutral evolution can be a direct consequence of range shifting.

How to Put All Your Eggs in One Basket: Empirical Patterns of Offspring Provisioning throughout a Mother’s Lifetime

Maternal effects arise when a mother's phenotype or the environment she experiences influences the phenotype of her progeny. Most studies of adaptive maternal effects are a "snapshot" of a mother's lifetime offspring provisioning and do not generally consider the effects of earlier siblings on those produced later. Here we show that in soil mites, offspring provisioning strategies are dynamic, changing from an emphasis on egg number in young females to egg size in older females. This pattern may be adaptive if it increases the survival of younger offspring that must compete with older, larger siblings. The dynamic shift in egg provisioning was greater in high-food environments in which females lived longer, creating increasing asymmetry in offspring competitive abilities. Females reared in isolation and in the presence of a high-density colony had identical provisioning strategies, suggesting that, unlike males in this species, females do not use pheromones to assess colony size. Our findings suggest that the adaptive significance of maternal effects may be misinterpreted when studies consider only a snapshot of a female's offspring provisioning strategy or when components of the offspring provisioning strategy are studied in isolation.

Microcosm experiments can inform global ecological problems

Global-scale environmental problems are rarely regarded as amenable to traditional scientific experiment. We argue here that small-scale experiments using 'model organisms' in microcosms or mesocosms can be a useful approach for apparently intractable global problems, such as ecosystem responses to climate change or managing biodiversity through the design of nature reserves. An experimental, small-scale research programme can easily be coupled with the development of theory and act as a stimulus to further research, thereby hastening both understanding of the issues and development of practical solutions. This process--from microcosm experiment to the development of practical application--has previously been influential but also has a long time lag. We suggest short-cuts in an attempt to stimulate the use of small-scale experiments to address globally urgent issues with meaningful policy implications.

Complex population dynamics and complex causation: devils, details and demography

Population dynamics result from the interplay of density-independent and density-dependent processes. Understanding this interplay is important, especially for being able to predict near-term population trajectories for management. In recent years, the study of model systems-experimental, observational and theoretical-has shed considerable light on the way that the both density-dependent and -independent aspects of the environment affect population dynamics via impacting on the organism's life history and therefore demography. These model-based approaches suggest that (i) individuals in different states differ in their demographic performance, (ii) these differences generate structure that can fluctuate independently of current total population size and so can influence the dynamics in important ways, (iii) individuals are strongly affected by both current and past environments, even when the past environments may be in previous generations and (iv) dynamics are typically complex and transient due to environmental noise perturbing complex population structures. For understanding population dynamics of any given system, we suggest that 'the devil is in the detail'. Experimental dissection of empirical systems is providing important insights into the details of the drivers of demographic responses and therefore dynamics and should also stimulate theory that incorporates relevant biological mechanism.

How effective are maternal effects at having effects?

The well studied trade-off between offspring size and offspring number assumes that offspring fitness increases with increasing per-offspring investment. Where mothers differ genetically or exhibit plastic variation in reproductive effort, there can be variation in per capita investment in offspring, and via this trade-off, variation in fecundity. Variation in per capita investment will affect juvenile performance directly--a classical maternal effect--while variation in fecundity will also affect offspring performance by altering the offsprings' competitive environment. The importance of this trade-off, while a focus of evolutionary research, is not often considered in discussions about population dynamics. Here, we use a factorial experiment to determine what proportion of variation in offspring performance can be ascribed to maternal effects and what proportion to the competitive environment linked to the size-number trade-off. Our results suggest that classical maternal effects are significant, but that in our system, the competitive environment, which is linked to maternal environments by fecundity, can be a far more substantial influence.

Estimating individual contributions to population growth: evolutionary fitness in ecological time

Ecological and evolutionary change is generated by variation in individual performance. Biologists have consequently long been interested in decomposing change measured at the population level into contributions from individuals, the traits they express and the alleles they carry. We present a novel method of estimating individual contributions to population growth and changes in distributions of quantitative traits and alleles. An individual's contribution to population growth is an individual's realized annual fitness. We demonstrate how the quantities we develop can be used to address a range of empirical questions, and provide an application to a detailed dataset of Soay sheep. The approach provides results that are consistent with those obtained using lifetime estimates of individual performance, yet is substantially more powerful as it allows lifetime performance to be decomposed into annual survival and fecundity contributions.

Context-dependent intergenerational effects: the interaction between past and present environments and its effect on population dynamics

Intergenerational effects arise when parents' actions influence the reproduction and survival of their offspring and possibly later descendants. Models suggest that intergenerational effects have important implications for both population dynamical patterns and the evolution of life-history traits. However, these will depend on the nature and duration of intergenerational effects. Here we show that manipulating parental food environments of soil mites produced intergenerational effects that were still detectable in the life histories of descendents three generations later. Intergenerational effects varied in different environments and from one generation to the next. In low-food environments, variation in egg size altered a trade-off between age and size at maturity and had little effect on the size of eggs produced in subsequent generations. Consequently, intergenerational effects decreased over time. In contrast, in high-food environments, variation in egg size predominantly influenced a trade-off between fecundity and adult survival and generated increasing variation in egg size. As a result, the persistence and significance of intergenerational effects varied between high- and low-food environments. Context-dependent intergenerational effects can therefore have complex but important effects on population dynamics.

The impact of environmental fluctuations on structured discrete time population models: Resonance, synchrony and threshold behaviour

External forcing of a discrete time ecological system does not just add variation to existing dynamics but can change the dynamics. We study the mechanisms that can bring this about, focusing on the key concepts of excitation and suppression which emerge when analysing the power spectra of the system in linear approximation. Excitation, through resonance between the system dynamics and the external forcing, is the greater the closer the system is to the boundary of the stability region. This amplification means that the extinction of populations becomes possible sooner than expected and, conversely, invasion can be significantly delayed. Suppression and the consequent redistribution of power within the spectrum proves to be a function both of the connectivity of the network graph of the system and the way that external forcing is applied to the system. It is also established that colour in stochastic forcing can have a major impact, by enhancing resonance and by greater redistribution of power. This can mean a higher risk of extinction through larger fluctuations in population numbers and a higher degree of synchrony between populations. The implications of external forcing for stage-structured species, for populations in competition and for trophic web systems are studied using the tools and concepts developed in the paper.

Changes in maternal investment in eggs can affect population dynamics

The way that mothers provision their offspring can have important consequences for their offspring's performance throughout life. Models suggest that maternally induced variation in life histories may have large population dynamical effects, even perhaps driving cycles such as those seen in forest Lepidoptera. The evidence for large maternal influences on population dynamics is unconvincing, principally because of the difficulty of conducting experiments at both the individual and population level. In the soil mite, Sancassania berlesei, we show that there is a trade-off between a female's fecundity and the per-egg provisioning of protein. The mother's position on this trade-off depends on her current food availability and her age. Populations initiated with 250 eggs of different mean sizes showed significant differences in the population dynamics, converging only after three generations. Differences in the growth, maturation and fecundity of the initial cohort caused differences in the competitive environment for the next generation, which, in turn, created differences in their growth and reproduction. Maternal effects in one generation can therefore lead to population dynamical consequences over many generations. Where animals live in environments that are temporally variable, we conjecture that maternal effects could result in long-term dynamical effects.

The Evolution of Oscillatory Behavior in Age‐Structured Species

A major challenge in ecology is to explain why so many species show oscillatory population dynamics and why the oscillations commonly occur with particular periods. The background environment, through noise or seasonality, is one possible driver of these oscillations, as are the components of the trophic web with which the species interacts. However, the oscillation may also be intrinsic, generated by density-dependent effects on the life history. Models of structured single-species systems indicate that a much broader range of oscillatory behavior than that seen in nature is theoretically possible. We test the hypothesis that it is selection that acts to constrain the range of periods. We analyze a nonlinear single-species matrix model with density dependence affecting reproduction and with trade-offs between reproduction and survival. We show that the evolutionarily stable state is oscillatory and has a period roughly twice the time to maturation, in line with observed patterns of periodicity. The robustness of this result to variations in trade-off function and density dependence is tested.

Causes and consequences of animal dispersal strategies: relating individual behaviour to spatial dynamics

Knowledge of the ecological and evolutionary causes of dispersal can be crucial in understanding the behaviour of spatially structured populations, and predicting how species respond to environmental change. Despite the focus of much theoretical research, simplistic assumptions regarding the dispersal process are still made. Dispersal is usually regarded as an unconditional process although in many cases fitness gains of dispersal are dependent on environmental factors and individual state. Condition-dependent dispersal strategies will often be superior to unconditional, fixed strategies. In addition, dispersal is often collapsed into a single parameter, despite it being a process composed of three interdependent stages: emigration, inter-patch movement and immigration, each of which may display different condition dependencies. Empirical studies have investigated correlates of these stages, emigration in particular, providing evidence for the prevalence of conditional dispersal strategies. Ill-defined use of the term 'dispersal', for movement across many different spatial scales, further hinders making general conclusions and relating movement correlates to consequences at the population level. Logistical difficulties preclude a detailed study of dispersal for many species, however incorporating unrealistic dispersal assumptions in spatial population models may yield inaccurate and costly predictions. Further studies are necessary to explore the importance of incorporating specific condition-dependent dispersal strategies for evolutionary and population dynamic predictions.

Age and size at maturity: sex, environmental variability and developmental thresholds

In most organisms, transitions between different life-history stages occur later and at smaller sizes as growth conditions deteriorate. Day and Rowe recently proposed that this pattern could be explained by the existence of developmental thresholds (minimum sizes or levels of condition below which transitions are unable to proceed). The developmental-threshold model predicts that the reaction norm of age and size at maturity will rotate in an anticlockwise manner from positive to a shallow negative slope if: (i) initial body size or condition is reduced; and/or (ii) some individuals encounter poor growth conditions at increasingly early developmental stages. We tested these predictions by rearing replicated populations of soil mites Sancassania berlesei (Michael) under different growth conditions. High-food environments produced a vertical relationship between age and size at maturity. The slope became increasingly shallow as food was reduced. By contrast, high food in the maternal environment reduced the slope of the reaction norm of age and size at maturity, whereas low food increased it. Overall, the reaction norm of age and size at maturity in S. berlesei was significantly nonlinear and differed for males and females. We describe how growth conditions, mother's environment and sex determine age and size at maturity in S. berlesei.

Large amplification in stage-structured models: Arnol'd tongues revisited

The coexistence of periodic and point attractors has been confirmed for a range of stage-structured discrete time models. The periodic attractor cycles have large amplitude, with the populations cycling between extremely low and surprisingly high values when compared to the equilibrium level. In this situation a stable state can be shocked by noise of sufficient strength into a state of high volatility. We found that the source of these large amplitude cycles are Arnol'd tongues, special regions of parameter space where the system exhibits periodic behaviour. Most of these tongues lie entirely in that part of parameter space where the system is unstable, but there are exceptions and these exceptions are the tongues that lead to attractor coexistence. Similarity in the geometry of Arnol'd tongues over the range of models considered might suggest that this is a common feature of stage-structured models but in the absence of proof this can only be a useful working hypothesis. The analysis shows that although large amplitude cycles might exist mathematically they might not be accessible biologically if biological constraints, such as non-negativity of population densities and vital rates, are imposed. Accessibility is found to be highly sensitive to model structure even though the mathematical structure is not. This highlights the danger of drawing biological conclusions from particular models. Having a comprehensive view of the different mechanisms by which periodic states can arise in families of discrete time models is important in the debate on whether the causes of periodicity in particular ecological systems are intrinsic, environmental or trophic. This paper is a contribution to that continuing debate.

Rising burden of immature sheep ticks (Ixodes ricinus) on red grouse (Lagopus lagopus scoticus) chicks in the Scottish uplands

The sheep tick Ixodes ricinus (L.) (Acari: Ixodidae) is an ectoparasite of major economic and pathogenic importance in Scotland. Its distribution in the Scottish uplands is assumed to be governed by the abundance and distribution of its definitive hosts (deer and sheep) and climatic variables such as temperature and rainfall. As the numbers of its major host in Scotland, red deer, have increased dramatically and climatic conditions have become more favourable, the level of parasitism could have been expected to rise. We use data gathered from tick counts on over 4000 red grouse chicks Lagopus lagopus scoticus Latham (Galliformes: Tetraonidae) in various experiments over the past 19 years to ascertain whether the intensity and prevalence of parasitism has been increasing. From 1985 to 2003 the average tick burden of a parasitized red grouse chick has grown from 2.60 +/- 1.12 ticks per chick to 12.71 +/- 1.44. Over this period the percentage of chicks of a given brood parasitized has also increased from 4 +/- 2% to 92 +/- 3%. The possible implications of this increase in parasitism for red grouse production are discussed.

Talkin' 'bout my generation: environmental variability and cohort effects

In variable environments, it is probable that environmental conditions in the past can influence demographic performance now. Cohort effects occur when these delayed life-history effects are synchronized among groups of individuals in a population. Here we show how plasticity in density-dependent demographic traits throughout the life cycle can lead to cohort effects and that there can be substantial population dynamic consequences of these effects. We show experimentally that density and food conditions early in development can influence subsequent juvenile life-history traits. We also show that conditions early in development can interact with conditions at maturity to shape future adult performance. In fact, conditions such as food availability and density at maturity, like conditions early in development, can generate cohort effects in mature stages. Based on these data, and on current theory about the effects of plasticity generated by historical environments, we make predictions about the consequences of such changes on density-dependent demography and on mite population dynamics. We use a stochastic cohort effects model to generate a range of population dynamics. In accordance with the theory, we find the predicted changes in the strength of density dependence and associated changes in population dynamics and population variability.

The amplification of environmental noise in population models: causes and consequences

Environmental variability is a ubiquitous feature of every organism's habitat. However, the interaction between density dependence and those density-independent factors that are manifested as environmental noise is poorly understood. We are interested in the conditions under which noise interacts with the density dependence to cause amplification of that noise when filtered by the system. For a broad family of structured population models, we show that amplification occurs near the threshold from stable to unstable dynamics by deriving an analytic formula for the amplification under weak noise. We confirm that the effect of noise is to sustain oscillations that would otherwise decay, and we show that it is the amplitude and not the phase that is affected. This is a feature noted in several recent studies. We study this phenomenon in detail for the lurchin and LPA models of population dynamics. We find that the degree of amplification is sensitive to both the noise input and life-history stage through which it acts, that the results hold for surprisingly high levels of noise, and that stochastic chaos (as measured by local Lyapunov exponents) is a concomitant feature of amplification. Further, it is shown that the temporal autocorrelation, or "color," of the noise has a major impact on the system response. We discuss the conditions under which color increases population variance and hence the risk of extinction, and we show that periodicity is sharpened when the color of the noise and dynamics coincide. Otherwise, there is interference, which shows how difficult it is in practice to separate the effects of nonlinearity and noise in short time series. The sensitivity of the population dynamics to noise when close to a bifurcation has wide-ranging consequences for the evolution and ecology of population dynamics.

Trophic interactions and population growth rates: describing patterns and identifying mechanisms

While the concept of population growth rate has been of central importance in the development of the theory of population dynamics, few empirical studies consider the intrinsic growth rate in detail, let alone how it may vary within and between populations of the same species. In an attempt to link theory with data we take two approaches. First, we address the question 'what growth rate patterns does theory predict we should see in time-series?' The models make a number of predictions, which in general are supported by a comparative study between time-series of harvesting data from 352 red grouse populations. Variations in growth rate between grouse populations were associated with factors that reflected the quality and availability of the main food plant of the grouse. However, while these results support predictions from theory, they provide no clear insight into the mechanisms influencing reductions in population growth rate and regulation. In the second part of the paper, we consider the results of experiments, first at the individual level and then at the population level, to identify the important mechanisms influencing changes in individual productivity and population growth rate. The parasitic nematode Trichostrongylus tenuis is found to have an important influence on productivity, and when incorporated into models with their patterns of distribution between individuals has a destabilizing effect and generates negative growth rates. The hypothesis that negative growth rates at the population level were caused by parasites was demonstrated by a replicated population level experiment. With a sound and tested model framework we then explore the interaction with other natural enemies and show that in general they tend to stabilize variations in growth rate. Interestingly, the models show selective predators that remove heavily infected individuals can release the grouse from parasite-induced regulation and allow equilibrium populations to rise. By contrast, a tick-borne virus that killed chicks simply leads to a reduction in the equilibrium. When humans take grouse they do not appear to stabilize populations and this may be because many of the infective stages are available for infection before harvesting commences. In our opinion, an understanding of growth rates and population dynamics is best achieved through a mechanistic approach that includes a sound experimental approach with the development of models. Models can be tested further to explore how the community of predators and others interact with their prey.

The effects of grades on course enjoyment: did you get the grade you wanted?

BACKGROUND

Students tend to rate university courses more positively if they do well. Greenwald and Gillmore (1997a) suggested that it is not students' absolute grades that are important but rather how these grades compare to their expectations. However, this hypothesis is difficult to evaluate because few studies have measured grade expectations at the beginning of courses.

AIM

By measuring students' grade expectations and enjoyment at several stages during a course, we hoped to evaluate the extent to which expectations modulate the impact of grades on course enjoyment.

SAMPLE

Participants were 242 students in a university course in psychology.

METHOD

Students were asked what grades they expected, and how much they were enjoying the course, at four stages. The effect of grades and grade expectations on enjoyment were analysed using restricted maximum likelihood (REML) and regression analyses.

RESULTS

The best predictor of course enjoyment varied somewhat at different stages, but in general it was the extent to which students' grades surpassed their expectations. Students' expectations at the beginning of the course proved particularly influential.

CONCLUSIONS

Grade expectations do influence how students react to course grades, but the prominent role of pre-course expectations suggests that it may be important to distinguish between grade aspirations and grade expectations. It appears to be students' aspirations--the grades they hope to achieve--that most strongly shape their emotional reactions, rather than the more realistic expectations they may form later in a course.

Elasticity analysis as an important tool in evolutionary and population ecology

Elasticity analysis estimates the proportional change in the population growth rate for a proportional change in a vital rate (i.e. survival, growth or reproduction). It can be used to pinpoint those parts of an organism's life history that should be the focus of management effort, or those that contribute most to fitness. Recent theoretical work has emphasized some limitations of the technique, has overcome other problems, and has shown that it is robust to some violations of its underlying assumptions. Thus, although care is needed, elasticity analysis is a simple first step in answering important questions in evolutionary and population ecology.

The Impact of Environmental Variation on Demographic Convergence of Leslie Matrix Population Models: An Assessment Using Lyapunov Characteristic Exponents

In a constant environment, the rate of convergence of a density-independent Leslie matrix model to stable age distribution is determined by the damping ratio (the ratio of the absolute magnitudes of the first and second eigenvalues of the projection matrix). In a stochastic environment, the difference between the first two Lyapunov exponents is known to be analogous to the logarithm of the damping ratio, but there has been no systematic investigation of the consequences of enviromnental variation on convergence rates. In this study, the Lyapunov spectrum has been calculated for a wide variety of density-independent projection matrices subject to random variations in vital rates. This allows the impact of these random variations on convergence rates to be assessed. For rapidly convergent life histories, stochastic variation leads to a decrease in convergence rate. For life histories which are slow to converge, stochastic variation speeds up convergence. These effects are, however, relatively minor, and the value of the damping ratio for the mean matrix is a good predictor of the damping ratio in a stochastic environment. Consequently, when only an approximate indication of convergence rates is needed, the damping ratio for the mean projection matrix gives a very good guide. Detailed calculations of the Lyapunov spectrum would only be necessary to make comparisons between similar life histories or if very precise information on convergence rates were needed.