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PubMed2004

Geo-referenced multimedia environmental fate model (G-CIEMS): model formulation and comparison to the generic model and monitoring approaches.

A spatially resolved and geo-referenced dynamic multimedia environmental fate model, G-CIEMS (Grid-Catchment Integrated Environmental Modeling System) was developed on a geographical information system (GIS). The case study for Japan based on the air grid cells of 5 x 5 km resolution and catchments with an average area of 9.3 km2, which corresponds to about 40,000 air grid cells and 38,000 river segments/catchment polygons, were performed for dioxins, benzene, 1,3-butadiene, and di-(2-ethyhexyl)phthalate. The averaged concentration of the model and monitoring output were within a factor of 2-3 for all the media. Outputs from G-CIEMS and the generic model were essentially comparable when identical parameters were employed, whereas the G-CIEMS model gave explicit information of distribution of chemicals in the environment. Exposure-weighted averaged concentrations (EWAC) in air were calculated to estimate the exposure ofthe population, based on the results of generic, G-CIEMS, and monitoring approaches. The G-CIEMS approach showed significantly better agreement with the monitoring-derived EWAC than the generic model approach. Implication for the use of a geo-referenced modeling approach in the risk assessment scheme is discussed as a generic-spatial approach, which can be used to provide more accurate exposure estimation with distribution information, using generally available data sources for a wide range of chemicals.

Benzene↗
PubMed2006

The functional value of Caribbean coral reef, seagrass and mangrove habitats to ecosystem processes.

Caribbean coral reef habitats, seagrass beds and mangroves provide important goods and services both individually and through functional linkages. A range of anthropogenic factors are threatening the ecological and economic importance of these habitats and it is vital to understand how ecosystem processes vary across seascapes. A greater understanding of processes will facilitate further insight into the effects of disturbances and assist with assessing management options. Despite the need to study processes across whole seascapes, few spatially explicit ecosystem-scale assessments exist. We review the empirical literature to examine the role of different habitat types for a range of processes. The importance of each of 10 generic habitats to each process is defined as its "functional value" (none, low, medium or high), quantitatively derived from published data wherever possible and summarised in a single figure. This summary represents the first time the importance of habitats across an entire Caribbean seascape has been assessed for a range of processes. Furthermore, we review the susceptibility of each habitat to disturbances to investigate spatial patterns that might affect functional values. Habitat types are considered at the scale discriminated by remotely-sensed imagery and we envisage that functional values can be combined with habitat maps to provide spatially explicit information on processes across ecosystems. We provide examples of mapping the functional values of habitats for populations of three commercially important species. The resulting data layers were then used to generate seascape-scale assessments of "hot spots" of functional value that might be considered priorities for conservation. We also provide an example of how the literature reviewed here can be used to parameterise a habitat-specific model investigating reef resilience under different scenarios of herbivory. Finally, we use multidimensional scaling to provide a basic analysis of the overall functional roles of different habitats. The resulting ordination suggests that each habitat has a unique suite of functional values and, potentially, a distinct role within the ecosystem. This review shows that further data are required for many habitat types and processes, particularly forereef and escarpment habitats on reefs and for seagrass beds and mangroves. Furthermore, many data were collected prior to the regional mass mortality of Diadema and Acropora, and subsequent changes to benthic communities have, in many cases, altered a habitat's functional value, hindering the use of these data for parameterising maps and models. Similarly, few data exist on how functional values change when environmental parameters, such as water clarity, are altered by natural or anthropogenic influences or the effects of a habitat's spatial context within the seascape. Despite these limitations, sufficient data are available to construct maps and models to better understand tropical marine ecosystem processes and assist more effective mitigation of threats that alter habitats and their functional values.

Algorithms↗
PubMed2006

Discriminative analysis of lip motion features for speaker identification and speech-reading.

There have been several studies that jointly use audio, lip intensity, and lip geometry information for speaker identification and speech-reading applications. This paper proposes using explicit lip motion information, instead of or in addition to lip intensity and/or geometry information, for speaker identification and speech-reading within a unified feature selection and discrimination analysis framework, and addresses two important issues: 1) Is using explicit lip motion information useful, and, 2) if so, what are the best lip motion features for these two applications? The best lip motion features for speaker identification are considered to be those that result in the highest discrimination of individual speakers in a population, whereas for speech-reading, the best features are those providing the highest phoneme/word/phrase recognition rate. Several lip motion feature candidates have been considered including dense motion features within a bounding box about the lip, lip contour motion features, and combination of these with lip shape features. Furthermore, a novel two-stage, spatial, and temporal discrimination analysis is introduced to select the best lip motion features for speaker identification and speech-reading applications. Experimental results using an hidden-Markov-model-based recognition system indicate that using explicit lip motion information provides additional performance gains in both applications, and lip motion features prove more valuable in the case of speech-reading application.

Algorithms↗
PubMed1997

Gecko: a continuous 2D world for ecological modeling.

An individual-based simulation system, named Gecko, is presented for modeling multiple species at multiple trophic levels, on a spatially explicit, continuous two-dimensional landscape. Biologically motivated rules are specified at an individual level, and resulting behaviors are observed at an ecosystem level. Individuals are represented by circles with free range on a resource-producing plane. These circles grow allometrically with biomass of fixed resources. Resource acquisition behaviors include competition by area overlap for producers, and movement based on perception and intent. Individual-level energetics are explicitly modeled with inefficient assimilation, resource transformation, and allometrically specified metabolic costs. Individual growth and reproduction requires a history of successful resource acquisition. Terrestrial producer, herbivore, and carnivore species classes are included, extensible to further classes. A grassland food chain model of "plants," "grasshoppers," and "spiders" is used to demonstrate ecosystem-level results of given individual-level behaviors. Ecosystem-level behaviors include a trophic cascade of indirect carnivore-producer interaction effects; stable persistence of all populations; a near-realistic biomass pyramid; and spatial competition and coexistence of multiple producer species. Initial Gecko results show promise for application in both theoretical and natural ecosystem modeling.

Animals↗
PubMed2005

Modelling antibiotic- and anti-quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population.

The bacterial cell to cell signalling system known as quorum sensing (QS) is essential for the regulation of virulence in many pathogens and offers a specific biochemical target for novel antibacterial therapies. Expanding on earlier work, in which consideration was given to the primary QS system (lasR system) in a homogeneous population of the common human pathogen Pseudomonas aeruginosa, we build a simple spatial model of an early-stage P. aeruginosa biofilm subject to treatment with topically applied anti-QS drugs (of two specific kinds) and conventional antibiotics. In the case of a slowly growing biofilm we show that both kinds of anti-quorum sensing drug are effective in reducing the level of the relevant signal molecule (3-oxo-C12-homoserine lactone; henceforth AHL), in each case obtaining an explicit bound on the steady-state AHL profile in terms of a prescribed surface drug concentration. Using numerical methods, we are also able to reproduce the hysteretic phenomena exhibited by the homogeneous model, in particular showing that for each kind of anti-QS drug there is a parameter regime in which a catastrophic collapse occurs in the steady-state AHL concentration as the surface drug concentration passes some critical value; an alternative way of interpreting this result is to say that, for a prescribed surface drug concentration, there is a critical biofilm depth such that treatment is successful until this depth is reached, but fails thereafter. In the thick-biofilm limit we show that the critical concentration of each drug increases exponentially with the biofilm thickness (or, conversely, that the critical depth increases logarithmically with surface drug concentration); this is dramatically different to the behaviour observed in the corresponding homogeneous model, where the critical concentrations grow linearly with bacterial carrying capacity, and thus highlights the relative difficulty of treating a large, spatially-structured population with diffusing antibacterials.

4-Butyrolactone↗
PubMed2001

Effects of habitat destruction and resource supplementation in a predator-prey metapopulation model.

We developed a mean field, metapopulation model to study the consequences of habitat destruction on a predator-prey interaction. The model complements and extends earlier work published by Bascompte and Solé (1998, J. theor. Biol.195, 383-393) in that it also permits use of alternative prey (i.e., resource supplementation) by predators. The current model is stable whenever coexistence occurs, whereas the earlier model is not stable over the entire domain of coexistence. More importantly, the current model permits an assessment of the effect of a generalist predator on the trophic interaction. Habitat destruction negatively affects the equilibrium fraction of patches occupied by predators, but the effect is most pronounced for specialists. The effect of habitat destruction on prey coexisting with predators is dependent on the ratio of extinction risk due to predation and prey colonization rate. When this ratio is less than unity, equilibrial prey occupancy of patches declines as habitat destruction increases. When the ratio exceeds one, equilibrial prey occupancy increases even as habitat destruction increases; i.e., prey "escape" from predation is facilitated by habitat loss. Resource supplementation reduces the threshold colonization rate of predators necessary for their regional persistence, and the benefit derived from resource supplementation increases in a nonlinear fashion as habitat destruction increases. We also compared the analytical results to those from a stochastic, spatially explicit simulation model. The simulation model was a discrete time analog of our analytical model, with one exception. Colonization was restricted locally in the simulation, whereas colonization was a global process in the analytical model. After correcting for differences between nominal and effective colonization rates, most of the main conclusions of the two types of models were similar. Some important differences did emerge, however, and we discuss these in relation to the need to develop fully spatially explicit analytical models. Finally, we comment on the implications of our results for community structure and for the conservation of prey species interacting with generalist predators.

Animals↗
PubMed2006

Mechanistic home range models capture spatial patterns and dynamics of coyote territories in Yellowstone.

Patterns of space-use by individuals are fundamental to the ecology of animal populations influencing their social organization, mating systems, demography and the spatial distribution of prey and competitors. To date, the principal method used to analyse the underlying determinants of animal home range patterns has been resource selection analysis (RSA), a spatially implicit approach that examines the relative frequencies of animal relocations in relation to landscape attributes. In this analysis, we adopt an alternative approach, using a series of mechanistic home range models to analyse observed patterns of territorial space-use by coyote packs in the heterogeneous landscape of Yellowstone National Park. Unlike RSAs, mechanistic home range models are derived from underlying correlated random walk models of individual movement behaviour, and yield spatially explicit predictions for patterns of space-use by individuals. As we show here, mechanistic home range models can be used to determine the underlying determinants of animal home range patterns, incorporating both movement responses to underlying landscape heterogeneities and the effects of behavioural interactions between individuals. Our analysis indicates that the spatial arrangement of coyote territories in Yellowstone is determined by the spatial distribution of prey resources and an avoidance response to the presence of neighbouring packs. We then show how the fitted mechanistic home range model can be used to correctly predict observed shifts in the patterns of coyote space-use in response to perturbation.

Animals↗
PubMed2003

Sensitivity analysis of a spatially-explicit stochastic simulation model of the evolution of resistance in Helicoverpa zea (Lepidoptera: Noctuidae) to Bt transgenic corn and cotton.

The sensitivities of a model simulating the evolution of resistance in Helicoverpa zea to Bt toxins in transgenic crops were investigated by examining effects of each of the model parameters on the frequency of resistance alleles after 8 yr. The functional dominance of resistance alleles and the initial frequency of those alleles had a major impact on resistance evolution. The survival of susceptible insects on the transgenic crops and the population dynamics of the insect, driven by winter survival and reproductive rates, were also important. In addition, agricultural practices including the proportion of the acreage planted to corn, and the larval threshold for spraying cotton fields affected the R-allele frequency. Many of these important parameters are inherently variable or cannot be measured with accuracy, so model output cannot be interpreted as being a forecast. However, this analysis is useful in focusing empirical research on those aspects of the insects' life system that have the largest effects on resistance development, and indicates ways in which to improve products and agricultural practices to increase the expected time to resistance. The model can thus be used as a scientific basis for devising a robust resistance management strategy for Bt crops.

Agriculture↗
PubMed1987

Interdisciplinary approaches in epidemic studies--II: Four geographic models of the flow of contagious disease.

Straightforward adaptation of geographical and regional-science models to conceptual modeling of the epidemic spread of a contagious disease is achieved by: using analogies and isomorphisms, and using as a real example the observations made during a well studied epidemic of variola minor (the mild form of smallpox), a typical contagious disease. The adaptation of the Wilson model of planning for urban development includes a static view (network) of the structure and activities of the population and of organizations (diffusion agencies such as day schools), and the dynamic view (mechanism of epidemic spread) which includes the changes with time of elements of the network brough by flow of disease. Adaptation of the Brown model of spatial diffusion yields flows of disease occurring between micro-scale units (households) of social interactions but aggregations of these units do not participate explicitly in the flows. The occurrence of successive generations of affected households is specified as well as the occurrence of definite stages of the epidemic progression. Adaptation of the Alves-Morrill model of spatial diffusion yields a network of social groups and interdependencies; a simplified network of the mechanism of spread that shows flows of disease between individuals grouped into generations of infected individuals and generations of infective individuals; and a more realistic view which shows the flows of disease between real epidemiological units such as households and school classes. Adaptation of the Morrill-Manninen model of spatial diffusion concentrates on the mechanism and parameters having the epidemic spread as output. The interdependencies between the parameters and between each parameter and the epidemic spread are represented, including feedback processes. Brown's model seems to be the best for describing the epidemic spread of contagious disease while the Morrill-Manninen model is the most promising for investigating the detailed mechanism of the spread. Since these two models complement each other, their combined use is indicated.

Communicable Diseases↗
PubMed2003

Analysis of nitric oxide consumption by erythrocytes in blood vessels using a distributed multicellular model.

Multiple sets of experimental data have shown that the red blood cell (RBC) consumes nitric oxide (NO) about 600-1000-fold slower than the equivalent concentration of cell-free hemoglobin (Hb). Diffusion barriers of various sources have been suggested to explain this observation. In this work, a multicellular, spatially distributed, two-dimensional model, that describes the production, transport, and consumption of NO in blood vessels and the surrounding tissue, is developed. The model is used to assess the relative significance of NO transport barriers that reduce the rate of NO consumption in the blood. Unlike previous models of this system, the model developed here accounts explicitly for the presence of, and interactions among, a population of RBCs inside the lumen of the blood vessel and is, therefore, better suited to analyze, quantitatively, the contribution of each transport barrier as NO diffuses from its site of synthesis to the interior of the RBCs where it interacts with Hb. The model, which uses experimentally derived parameters, shows that extracellular unstirred boundary layer diffusion alone cannot account for the reduced NO consumption by RBC compared to an equivalent concentration of cell-free Hb. Since this result is reached using a two-dimensional representation of the RBCs, which overestimates the importance of the boundary layer diffusion resistance, it would be expected that in the real three-dimensional case, diffusion through the extracellular boundary layer would contribute even less to the overall mass transfer resistance. Consistent with recent experimental findings, the results of our model suggest that, under physiological conditions, transmembrane (membrane and its associated cytoskeleton layer) diffusion limitations in RBCs represent a key source of resistance for NO uptake by RBCs.

Animals↗
PubMed2006

Assessing tiger population dynamics using photographic capture-recapture sampling.

Although wide-ranging, elusive, large carnivore species, such as the tiger, are of scientific and conservation interest, rigorous inferences about their population dynamics are scarce because of methodological problems of sampling populations at the required spatial and temporal scales. We report the application of a rigorous, noninvasive method for assessing tiger population dynamics to test model-based predictions about population viability. We obtained photographic capture histories for 74 individual tigers during a nine-year study involving 5725 trap-nights of effort. These data were modeled under a likelihood-based, "robust design" capture-recapture analytic framework. We explicitly modeled and estimated ecological parameters such as time-specific abundance, density, survival, recruitment, temporary emigration, and transience, using models that incorporated effects of factors such as individual heterogeneity, trap-response, and time on probabilities of photo-capturing tigers. The model estimated a random temporary emigration parameter of gamma" = gamma' = 0.10 +/- 0.069 (values are estimated mean +/- SE). When scaled to an annual basis, tiger survival rates were estimated at S = 0.77 +/- 0.051, and the estimated probability that a newly caught animal was a transient was tau = 0.18 +/- 0.11. During the period when the sampled area was of constant size, the estimated population size N(t) varied from 17 +/- 1.7 to 31 +/- 2.1 tigers, with a geometric mean rate of annual population change estimated as lambda = 1.03 +/- 0.020, representing a 3% annual increase. The estimated recruitment of new animals, B(t), varied from 0 +/- 3.0 to 14 +/- 2.9 tigers. Population density estimates, D, ranged from 7.33 +/- 0.8 tigers/100 km2 to 21.73 +/- 1.7 tigers/100 km2 during the study. Thus, despite substantial annual losses and temporal variation in recruitment, the tiger density remained at relatively high levels in Nagarahole. Our results are consistent with the hypothesis that protected wild tiger populations can remain healthy despite heavy mortalities because of their inherently high reproductive potential. The ability to model the entire photographic capture history data set and incorporate reduced-parameter models led to estimates of mean annual population change that were sufficiently precise to be useful. This efficient, noninvasive sampling approach can be used to rigorously investigate the population dynamics of tigers and other elusive, rare, wide-ranging animal species in which individuals can be identified from photographs or other means.

Animal Identification Systems↗
PubMed2005

Scaling up from local competition to regional coexistence across two scales of spatial heterogeneity: insect larvae in the fruits of Apeiba membranacea.

Species that live in patchy and ephemeral habitats can compete strongly for resources within patches at a small scale. The ramifications of these interactions for population dynamics and coexistence at regional scales will depend on the intraspecific and interspecific distributions of individuals among patches. Spatial heterogeneity due to independent aggregation of competitors among patchy habitats is an important mechanism maintaining species diversity. I describe regional patterns of aggregation for four species of insect larvae in the fruits of Apeiba membranacea, a Neotropical rainforest tree. This aggregation results from variation in densities at a small scale (among the fruits under a single tree), compounded by significant variation among trees in both mean densities and degrees of aggregation. Both the degrees of aggregation and mean densities are statistically independent within and across species at both spatial scales. I evaluate the regional consequences of these spatial patterns by using maximum likelihood methods to parameterize a model that includes both explicit measures of the strength of competition and spatial variation at both within- and among-tree spatial scales. Despite strong competitive interactions among these species, during 2 years the observed spatial variation at both scales combined was sufficient to explain the coexistence of these species, although other coexistence mechanisms may also operate simultaneously. The observed spatial variation at small spatial scales may not be sufficient for coexistence, indicating the importance of considering multiple sources of spatial heterogeneity when scaling up from experiments that investigate local interactions to regional patterns of coexistence.

Animals↗
PubMed2005

A structured-population model of Proteus mirabilis swarm-colony development.

In this paper we present continuous age- and space-structured models and numerical computations of Proteus mirabilis swarm-colony development. We base the mathematical representation of the cell-cycle dynamics of Proteus mirabilis on those developed by Esipov and Shapiro, which are the best understood aspects of the system, and we make minimum assumptions about less-understood mechanisms, such as precise forms of the spatial diffusion. The models in this paper have explicit age-structure and, when solved numerically, display both the temporal and spatial regularity seen in experiments, whereas the Esipov and Shapiro model, when solved accurately, shows only the temporal regularity. The composite hyperbolic-parabolic partial differential equations used to model Proteus mirabilis swarm-colony development are relevant to other biological systems where the spatial dynamics depend on local physiological structure. We use computational methods designed for such systems, with known convergence properties, to obtain the numerical results presented in this paper.

Agar↗
PubMed2000

Carrying capacity and demographic stochasticity: scaling behavior of the stochastic logistic model.

The stochastic logistic model is the simplest model that combines individual-level demography with density dependence. It explicitly or implicitly underlies many models of biodiversity of competing species, as well as non-spatial or metapopulation models of persistence of individual species. The model has also been used to study persistence in simple disease models. The stochastic logistic model has direct relevance for questions of limiting similarity in ecological systems. This paper uses a biased random walk heuristic to derive a scaling relationship for the persistence of a population under this model, and discusses its implications for models of biodiversity and persistence. Time to extinction of a species under the stochastic logistic model is approximated by the exponential of the scaling quantity U=(R-1)(2) N/R(R+1), where N is the habitat size and R is the basic reproductive number.

Animals↗
PubMed2004

Empirical modelling of government health service use by children with fevers in Kenya.

An understanding of spatial patterns of health facility use allows a more informed approach to the modelling of catchment populations. In the absence of patient use data, an intuitive and commonly used approach to the delineation of facility catchment areas is Thiessen polygons. This study presents a series of methods by which the validity of these assumptions can be tested directly and hence the suitability of a Thiessen polygon catchment model explicitly assessed. These methods are applied to paediatric out-patient origin data from a sample of 81 government health facilities in four districts of Kenya. A geographical information system was used to predict the location of the catchment boundary along a transect between each pair of neighbouring facilities based on patient choice patterns. The mean location of boundaries between facilities of different type was found to be significantly displaced from the Thiessen boundary towards the lower-order facility. The affect of distance on within-catchment utilization rate was assessed by using exclusion buffers to remove the effect of neighbouring facilities. Utilization rate was found to exhibit a slight but steady decrease with distance up to 6 km from a facility. The accuracy of the future modelling of unsampled facility catchments can be increased by the incorporation of these trends.

Catchment Area, Health↗
PubMed2003

Multivariate analysis of neuronal interactions in the generalized partial least squares framework: simulations and empirical studies.

Identification of spatiotemporal interactions within/between neuron populations is critical for detection and characterization of large-scale neuronal interactions underlying perception, cognition, and behavior. Univariate analysis has been employed successfully in many neuroimaging studies. However, univariate analysis does not explicitly test for interactions between distributed areas of activity and is not sensitive to distributed responses across the brain. Multivariate analysis can explicitly test for multiple statistical models, including the designed paradigm, and allows for spatial and temporal model detection. Here, we investigate multivariate analysis approaches that take into consideration the 4D (time and space) covariance structure of the data. Principal component analysis (PCA) and independent component analysis (ICA) are two popular multivariate approaches with distinct mathematical constraints. Common difficulties in using these two different decompositions include the following: classification of the revealed components (task-related signal versus noise), overall signal-to-noise sensitivity, and the relatively low computational efficiency (multivariate analysis requires the entire raw data set and more time for model identification analysis). Using both Monte Carlo simulations and empirical data, we derived and tested the generalized partial least squares (gPLS) framework, which can incorporate both PCA and ICA decompositions with computational efficiency. The gPLS method explicitly incorporates the experimental design to simplify the identification of characteristic spatiotemporal patterns. We performed parametric modeling studies of a blocked-design experiment under various conditions, including background noise distribution, sampling rate, and hemodynamic response delay. We used a randomized grouping approach to manipulate the degrees of freedom of PCA and ICA in gPLS to characterize both paradigm coherent and transient brain responses. Simulation data suggest that in the gPLS framework, PCA mostly outperforms ICA as measured by the receiver operating curves (ROCs) in SNR from 0.01 to 100, the hemodynamic response delays from 0 to 3 TR in fMRI, background noise models of Guassian, sub-Gaussian, and super-Gaussian distributions and the number of observations from 5, 10, to 20 in each block of a six-block experiment. Further, due to selective averaging, the gPLS method performs robustly in low signal-to-noise ratio (<1) experiments. We also tested PCA and ICA using PLS in a simulated event-related fMRI data to show their similar detection. Finally, we tested our gPLS approach on empirical fMRI motor data. Using the randomized grouping method, we are able to identify both transient responses and consistent paradigm/model coherent components in the 10-epoch block design motor fMRI experiment. Overall, studies of synthetic and empirical data suggest that PLS analysis, using PCA decomposition, provides a stable and powerful tool for exploration of fMRI/behavior data.

Algorithms↗
PubMed1999

Risk-spreading and bet-hedging in insect population biology.

In evolutionary ecology, risk-spreading (i.e. bet-hedging) is the idea that unpredictably variable environments favor genotypes with lower variance in fitness at the cost of lower arithmetic mean fitness. Variance in fitness can be reduced by physiology or behavior that spreads risk of encountering an unfavorable environment over time or space. Such risk-spreading can be achieved by a single phenotype that avoids risks (conservative risk-spreading) or by phenotypic variation expressed by a single genotype (diversified risk-spreading). Across these categories, three types of risk-spreading can be usefully distinguished: temporal, metapopulation, and within-generation. Theory suggests that temporal and metapopulation risk-spreading may work under a broad range of population sizes, but within-generation risk-spreading appears to work only when populations are small. Although genetic polymorphisms have sometimes been treated as risk-spreading, the underlying mechanisms are different, and they often require different conditions for their evolution and thus are better treated separately. I review the types of evidence that could be used to test for risk-spreading and discuss evidence for risk-spreading in facultative diapause, migration polyphenism, spatial distribution of oviposition, egg size, and other miscellaneous traits. Although risk-spreading theory is voluminous and well developed in some ways, rarely has it been used to generate detailed, testable hypotheses about the evolution of risk-spreading. Furthermore, although there is evidence for risk-spreading, particularly in facultative diapause, I have been unable to find any definitive tests with unequivocal results showing that risk-spreading has been a major factor in the evolution of insect behaviors or life histories. To advance our understanding of risk-spreading in the wild, we need (a) explicit empirical models that predict levels of diversifying risk-spreading for several insect populations in several environments that vary in uncertainty, and (b) tests of these models using measurements of phenotypes and their fitnesses over several generations in each environment.

Journal Article↗