Biomedical subjects

Mark Rees

Publications and source records attributed to Mark Rees.

15 recordsLinked to original sources

PubMed2006

Stochastic stable population growth in integral projection models: theory and application.

Stochastic matrix projection models are widely used to model age- or stage-structured populations with vital rates that fluctuate randomly over time. Practical applications of these models rest on qualitative properties such as the existence of a long term population growth rate, asymptotic log-normality of total population size, and weak ergodicity of population structure. We show here that these properties are shared by a general stochastic integral projection model, by using results in (Eveson in D. Phil. Thesis, University of Sussex, 1991, Eveson in Proc. Lond. Math. Soc. 70, 411-440, 1993) to extend the approach in (Lange and Holmes in J. Appl. Prob. 18, 325-344, 1981). Integral projection models allow individuals to be cross-classified by multiple attributes, either discrete or continuous, and allow the classification to change during the life cycle. These features are present in plant populations with size and age as important predictors of individual fate, populations with a persistent bank of dormant seeds or eggs, and animal species with complex life cycles. We also present a case-study based on a 6-year field study of the Illyrian thistle, Onopordum illyricum, to demonstrate how easily a stochastic integral model can be parameterized from field data and then applied using familiar matrix software and methods. Thistle demography is affected by multiple traits (size, age and a latent "quality" variable), which would be difficult to accommodate in a classical matrix model. We use the model to explore the evolution of size- and age-dependent flowering using an evolutionarily stable strategy (ESS) approach. We find close agreement between the observed flowering behavior and the predicted ESS from the stochastic model, whereas the ESS predicted from a deterministic version of the model is very different from observed flowering behavior. These results strongly suggest that the flowering strategy in O. illyricum is an adaptation to random between-year variation in vital rates.

Ecosystem↗

PubMed2006

Seed dormancy and delayed flowering in monocarpic plants: selective interactions in a stochastic environment.

We explore the effects of temporal variation in multiple demographic rates on the joint evolution of delayed reproduction and seed dormancy using integral projection models (IPMs). To do this, we extend the standard IPM to include a discrete state variable representing the number of seeds in the seed bank, density-dependent recruitment, and temporal variation in demography. Parameter estimates for Carlina vulgaris and Carduus nutans are obtained from long-term studies. Carlina is relatively long lived and has a short-lived seed bank, whereas most Carduus plants flower in their first year and the seed bank is long lived. Using the evolutionarily stable strategy (ESS) approach, we predict the observed flowering and germination strategies. There is excellent agreement between the predictions and the field observations. The effects of temporal variation on the joint ESS are partitioned into components arising from nonlinear averaging (systematic changes in the mean resulting from the interaction between variability and nonlinearity) and nonequilibrium dynamics (fluctuations in fitness caused by temporal variation). This shows that temporal variation can have substantial effects on the observed flowering and germination strategies and that covariance between demographic processes is important. We extend the models to include spatial population structure and assess the robustness of the results from the nonspatial models.

Asteraceae↗

PubMed2006

Integral projection models for species with complex demography.

Matrix projection models occupy a central role in population and conservation biology. Matrix models divide a population into discrete classes, even if the structuring trait exhibits continuous variation (e.g., body size). The integral projection model (IPM) avoids discrete classes and potential artifacts from arbitrary class divisions, facilitates parsimonious modeling based on smooth relationships between individual state and demographic performance, and can be implemented with standard matrix software. Here, we extend the IPM to species with complex demographic attributes, including dormant and active life stages, cross-classification by several attributes (e.g., size, age, and condition), and changes between discrete and continuous structure over the life cycle. We present a general model encompassing these cases, numerical methods, and theoretical results, including stable population growth and sensitivity/elasticity analysis for density-independent models, local stability analysis in density-dependent models, and optimal/evolutionarily stable strategy life-history analysis. Our presentation centers on an IPM for the thistle Onopordum illyricum based on a 6-year field study. Flowering and death probabilities are size and age dependent, and individuals also vary in a latent attribute affecting survival, but a predictively accurate IPM is completely parameterized by fitting a few regression equations. The online edition of the American Naturalist includes a zip archive of R scripts illustrating our suggested methods.A zip archive of R scripts illustrating our suggested methods is also provided.

Biological Evolution↗

PubMed2006

Decoupling the direct and indirect effects of nitrogen deposition on ecosystem function.

Elevated nitrogen (N) inputs into terrestrial ecosystems are causing major changes to the composition and functioning of ecosystems. Understanding these changes is challenging because there are complex interactions between 'direct' effects of N on plant physiology and soil biogeochemistry, and 'indirect' effects caused by changes in plant species composition. By planting high N and low N plant community compositions into high and low N deposition model terrestrial ecosystems we experimentally decoupled direct and indirect effects and quantified their contribution to changes in carbon, N and water cycling. Our results show that direct effects on plant growth dominate ecosystem response to N deposition, although long-term carbon storage is reduced under high N plant-species composition. These findings suggest that direct effects of N deposition on ecosystem function could be relatively strong in comparison with the indirect effects of plant community change.

Ecosystem↗

PubMed2005

Niches, rather than neutrality, structure a grassland pioneer guild.

Pioneer species are fast-growing, short-lived gap exploiters. They are prime candidates for neutral dynamics because they contain ecologically similar species whose low adult density is likely to cause widespread recruitment limitation, which slows competitive dynamics. However, many pioneer guilds appear to be differentiated according to seed size. In this paper, we compare predictions from a neutral model of community structure with three niche-based models in which trade-offs involving seed size form the basis of niche differentiation. We test these predictions using sowing experiments with a guild of seven pioneer species from chalk grassland. We find strong evidence for niche structure based on seed size: specifically large-seeded species produce fewer seeds but have a greater chance of establishing on a per-seed basis. Their advantage in establishment arises because there are more microsites suitable for their germination and early establishment and not directly through competition with other seedlings. In fact, seedling densities of all species were equally suppressed by the addition of competitors' seeds. By the adult stage, despite using very high sowing densities, there were no detectable effects of interspecific competition on any species. The lack of interspecific effects indicates that niche differentiation, rather than neutrality, prevails.

Ecosystem↗

PubMed2004

Effects of temporal variability on rare plant persistence in annual systems.

Traditional conservation biology regards environmental fluctuations as detrimental to persistence, reducing long-term average growth rates and increasing the probability of extinction. By contrast, coexistence models from community ecology suggest that for species with dormancy, environmental fluctuations may be essential for persistence in competitive communities. We used models based on California grasslands to examine the influence of interannual fluctuations in the environment on the persistence of rare forbs competing with exotic grasses. Despite grasses and forbs independently possessing high fecundity in the same types of years, interspecific differences in germination biology and dormancy caused the rare forb to benefit from variation in the environment. Owing to the buildup of grass competitors, consecutive favorable years proved highly detrimental to forb persistence. Consequently, negative temporal autocorrelation, a low probability of a favorable year, and high variation in year quality all benefited the forb. In addition, the litter produced by grasses in a previously favorable year benefited forb persistence by inhibiting its germination into highly competitive grass environments. We conclude that contrary to conventional predictions of conservation and population biology, yearly fluctuations in climate may be essential for the persistence of rare species in invaded habitats.

California↗

PubMed2004

Periodic local disturbance in host-parasitoid metapopulations: host suppression and parasitoid persistence.

Within many agricultural systems, insect pests and their natural enemies are forced to persist as a metapopulation, continuously recolonizing patches following disturbance through harvesting or spraying with insecticides. Despite the need to understand factors influencing biocontrol success, few theoretical studies of host-parasitoid interactions have examined the potential impact of local disturbance within a metapopulation framework. Here, we add periodic local mortality to series of classical host-parasitoid models to examine its effect on host suppression and parasitoid persistence. Using a deterministic lattice model, we show that despite the wide range of complex dynamics generated at the patch level, the region wide pattern of disturbance is the key factor influencing host suppression. The level of host suppression achieved can be understood in terms of both the strength of density dependent parasitism, and the relative amounts of host and parasitoid mixing amongst patches of different ages. Local dispersal among patches is sufficient to ensure coexistence of the host and parasitoid, though persistence is not necessarily associated with the formation of self-organized spatial structures reported in previous studies. Finally, a stochastic version of the model is developed, in order to highlight how the effects of demographic stochasticity may influence biocontrol success in highly disturbed agricultural systems.

Animals↗

PubMed2004

Evolution of size-dependent flowering in a variable environment: partitioning the effects of fluctuating selection.

In a stochastic environment, two distinct processes, namely nonlinear averaging and non-equilibrium dynamics, influence fitness. We develop methods for decomposing the effects of temporal variation in demography into contributions from nonlinear averaging and non-equilibrium dynamics. We illustrate the approach using Carlina vulgaris, a monocarpic species in which recruitment, growth and survival all vary from year to year. In Carlina the absolute effect of temporal variation on the evolutionarily stable flowering strategy is substantial (ca. 50% of the evolutionarily stable flowering size) but the net effect is much smaller (ca. 10%) because the effects of temporal variation do not influence the evolutionarily stable strategy in the same direction.

Analysis of Variance↗

PubMed2004

Evolution of size-dependent flowering in a variable environment: construction and analysis of a stochastic integral projection model.

Understanding why individuals delay reproduction is a classic problem in evolutionary biology. In plants, the study of reproductive delays is complicated because growth and survival can be size and age dependent, individuals of the same size can grow by different amounts and there is temporal variation in the environment. We extend the recently developed integral projection approach to include size- and age-dependent demography and temporal variation. The technique is then applied to a long-term individually structured dataset for Carlina vulgaris, a monocarpic thistle. The parameterized model has excellent descriptive properties in terms of both the population size and the distributions of sizes within each age class. In Carlina, the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy approach. Considering each year separately, we show that both the direction and the magnitude of selection on the flowering strategy vary from year to year. Provided the flowering strategy is constrained, so it cannot be a step function, the model accurately predicts the average size at flowering. Elasticity analysis is used to partition the size- and age-specific contributions to the stochastic growth rate, lambda(s). We use lambda(s) to construct fitness landscapes and show how different forms of stochasticity influence its topography. We prove the existence of a unique stochastic growth rate, lambda(s), which is independent of the initial population vector, and show that Tuljapurkar's perturbation analysis for log(lambda(s)) can be used to calculate elasticities.

Asteraceae↗

PubMed2003

Evolution of complex flowering strategies: an age- and size-structured integral projection model.

We explore the evolution of delayed age- and size-dependent flowering in the monocarpic perennial Carlina vulgaris, by extending the recently developed integral projection approach to include demographic rates that depend on size and age. The parameterized model has excellent descriptive properties both in terms of the population size and in terms of the distributions of sizes within each age class. In Carlina the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy (ESS) approach. Despite accurately predicting the mean size of flowering individuals, the model predicts a step-function relationship between the probability of flowering and plant size, which has no age component. When the variance of the flowering-threshold distribution is constrained to the observed value, the ESS flowering function contains an age component, but underpredicts the mean flowering size. An analytical approximation is used to explore the effect of variation in the flowering strategy on the ESS predictions. Elasticity analysis is used to partition the agespecific contributions to the finite rate of increase (lambda) of the survival-growth and fecundity components of the model. We calculate the adaptive landscape that defines the ESS and generate a fitness landscape for invading phenotypes in the presence of the observed flowering strategy. The implications of these results for the patterns of genetic diversity in the flowering strategy and for testing evolutionary models are discussed. Results proving the existence of a dominant eigenvalue and its associated eigenvectors in general size- and age-dependent integral projection models are presented.

Adaptation, Biological↗

PubMed2002

Population growth rates: issues and an application.

Current issues in population dynamics are discussed in the context of The Royal Society Discussion Meeting 'Population growth rate: determining factors and role in population regulation'. In particular, different views on the centrality of population growth rates to the study of population dynamics and the role of experiments and theory are explored. Major themes emerging include the role of modern statistical techniques in bringing together experimental and theoretical studies, the importance of long-term experimentation and the need for ecology to have model systems, and the value of population growth rate as a means of understanding and predicting population change. The last point is illustrated by the application of a recently introduced technique, integral projection modelling, to study the population growth rate of a monocarpic perennial plant, its elasticities to different life-history components and the evolution of an evolutionarily stable strategy size at flowering.

Biological Evolution↗

PubMed2002

Evolution of flowering strategies in Oenothera glazioviana: an integral projection model approach.

The timing of reproduction is a key determinant of fitness. Here, we develop parameterized integral projection models of size-related flowering for the monocarpic perennial Oenothera glazioviana and use these to predict the evolutionarily stable strategy (ESS) for flowering. For the most part there is excellent agreement between the model predictions and the results of quantitative field studies. However, the model predicts a much steeper relationship between plant size and the probability of flowering than observed in the field, indicating selection for a 'threshold size' flowering function. Elasticity and sensitivity analysis of population growth rate lambda and net reproductive rate R(0) are used to identify the critical traits that determine fitness and control the ESS for flowering. Using the fitted model we calculate the fitness landscape for invading genotypes and show that this is characterized by a ridge of approximately equal fitness. The implications of these results for the maintenance of genetic variation are discussed.

Biological Evolution↗

PubMed2002

Evolution in the real world: stochastic variation and the determinants of fitness in Carlina vulgaris.

Empirical studies of life histories often ignore stochastic variation, despite theoretical demonstrations of its potential impact on life-history evolution. Here we use a novel approach to explore the effects of stochastic variation on life-history evolution and estimate the selection pressures operating on the monocarpic perennial Carlina vulgaris, in which flowering may be delayed by up to eight years. The approach is novel in that we use modern theoretical techniques to estimate selection pressures and the fitness landscape from a fully parameterised individual-based model. These approaches take into account temporal variation in demographic rates and density dependence. Analysis of 16 years' data revealed significant temporal variation in growth, mortality, and recruitment in our study population. Flowering was strongly size dependent and, unusually for such a species, also age dependent. Individual-based models of the flowering strategy, parameterized using field data, consistently underestimated the size at flowering, when temporal variation in demographic rates was ignored. In contrast, models that incorporated temporal variation in growth, mortality, and recruitment predicted sizes at flowering not significantly different from those observed in the field. Temporal variation in mortality, which had the largest effect on the flowering strategy, selected for increased size at flowering. An analytical approximation is presented to explain this result, extending the "1-year look-ahead criterion" presented in Rees et al. (2000). A fitness landscape generated by following the fate of rare mutant invaders with a broad range of alternative flowering strategies demonstrated that the observed parameters were adaptive. However, the fitness landscape reveals that approximately equal fitness is achieved by a broad range of strategies, providing a mechanism for the maintenance of genetic variation. To understand how the different parameters that defined our models determine the fitness of rare mutants, we numerically estimated the elasticities and sensitivities of mutant fitness. This demonstrated strong selection on a number of the parameters. Elasticities and sensitivities estimated in constant and random environments were significantly positively correlated, and both were negatively related to the standard error of the parameter. This last result is surprising and, we argue, reflects the genetic and phenotypic responses to selection.

Adaptation, Physiological↗

PubMed2002

Optimization of the cell wall microenvironment allows increased production of recombinant Bacillus anthracis protective antigen from B. subtilis.

The stability of heterologous proteins secreted by gram-positive bacteria is greatly influenced by the microenvironment on the trans side of the cytoplasmic membrane, and secreted heterologous proteins are susceptible to rapid degradation by host cell proteases. In Bacillus subtilis, degradation occurs either as the proteins emerge from the presecretory translocase and prior to folding into their native conformation or after the native conformation has been reached. The former process generally involves membrane- and/or cell wall-bound proteases, while the latter involves proteases that are released into the culture medium. The identification and manipulation of factors that influence the folding of heterologous proteins has the potential to improve the yield of secreted heterologous proteins. Recombinant anthrax protective antigen (rPA) has been used as a model secreted heterologous protein because it is sensitive to proteolytic degradation both before and after folding into its native conformation. This paper describes the influence of the microenvironment on the trans side of the cytoplasmic membrane on the stability of rPA. Specifically, we have determined the influence of net cell wall charge and its modulation by the extent to which the anionic polymer teichoic acid is D-alanylated on the secretion and stability of rPA. The potential role of the dlt operon, responsible for D-alanylation, was investigated using a Bacillus subtilis strain encoding an inducible dlt operon. We show that, in the absence of D-alanylation, the yield of secreted rPA is increased 2.5-fold. The function of D-alanylation and the use of rPA as a model protein are evaluated with respect to the optimization of B. subtilis for the secretion of heterologous proteins.

Alanine↗

PubMed1999

Evolution of Size-Dependent Flowering in Onopordum illyricum: A Quantitative Assessment of the Role of Stochastic Selection Pressures.

We explore the evolution of delayed, size-dependent reproduction in the monocarpic perennial Onopordum illyricum, using a range of mathematical models, parameterized with long-term field data. Analysis of the long-term data indicated that mortality, flowering, and growth were age and size dependent. Using mixed models, we estimated the variance about each of these relationships and also individual-specific effects. For the field populations, recruitment was the main density-dependent process, although there were weak effects of local density on growth and mortality. Using parameterized growth models, which assume plants grow along a deterministic trajectory, we predict plants should flower at sizes approximately 50% smaller than observed in the field. We then develop a simple criterion, termed the "1-yr look-ahead criterion," based on equating seed production now with that of next year, allowing for mortality and growth, to determine at what size a plant should flower. This model allows the incorporation of variance about the growth function and individual-specific effects. The model predicts flowering at sizes approximately double that observed, indicating that variance about the growth curve selects for larger sizes at flowering. The 1-yr look-ahead approach is approximate because it ignores growth opportunities more than 1 yr ahead. To assess the accuracy of this approach, we develop a more complicated dynamic state variable model. Both models give similar results indicating the utility of the 1-yr look-ahead criterion. To allow for temporal variation in the model parameters, we used an individual-based model with a genetic algorithm. This gave very accurate prediction of the observed flowering strategies. Sensitivity analysis of the model suggested that temporal variation in the parameters of the growth equation made waiting to flower more risky, so selected for smaller sizes at flowering. The models clearly indicate the need to incorporate stochastic variation in life-history analyses.

delayed reproduction↗