Preparing the Next Generation of Integrative Organismal Biologists.

Pursuing cutting edge questions in organismal biology in the future will require novel approaches for training the next generation of organismal biologists, including knowledge and use of systems-type modeling combined with integrative organismal biology. We link agendas recommending changes in science education and practice across three levels: broadening the concept of organismal biology to promote modeling organisms as systems interacting with higher and lower organizational levels; enhancing undergraduate science education to improve applications of quantitative reasoning and modeling in the scientific process; and K-12 curricula based on Next-Generation Science Standards emphasizing development and use of models in the context of explanatory science, solution design, and evaluating and communicating information. Out of each of these initiatives emerges an emphasis on routine use of models as tools for hypothesis testing and prediction. The question remains, however, what is the best approach for training the next generation of organismal biology students to facilitate their understanding and use of models? We address this question by proposing new ways of teaching and learning, including the development of interactive web-based modeling modules that lower barriers for scientists approaching this new way of imagining and conducting integrative organismal biology.

Effects of ocean-acidification-induced morphological changes on larval swimming and feeding.

Reduction in global ocean pH due to the uptake of increased atmospheric CO(2) is expected to negatively affect calcifying organisms, including the planktonic larval stages of many marine invertebrates. Planktonic larvae play crucial roles in the benthic-pelagic life cycle of marine organisms by connecting and sustaining existing populations and colonizing new habitats. Calcified larvae are typically denser than seawater and rely on swimming to navigate vertically structured water columns. Larval sand dollars Dendraster excentricus have calcified skeletal rods supporting their bodies, and propel themselves with ciliated bands looped around projections called arms. Ciliated bands are also used in food capture, and filtration rate is correlated with band length. As a result, swimming and feeding performance are highly sensitive to morphological changes. When reared at an elevated P(CO2) level (1000 ppm), larval sand dollars developed significantly narrower bodies at four and six-arm stages. Morphological changes also varied between four observed maternal lineages, suggesting within-population variation in sensitivity to changes in P(CO2) level. Despite these morphological changes, P(CO2) concentration alone had no significant effect on swimming speeds. However, acidified larvae had significantly smaller larval stomachs and bodies, suggesting reduced feeding performance. Adjustments to larval morphologies in response to ocean acidification may prioritize swimming over feeding, implying that negative consequences of ocean acidification are carried over to later developmental stages.

Estimating 3D movements from 2D observations using a continuous model of helical swimming.

Helical swimming is among the most common movement behaviors in a wide range of microorganisms, and these movements have direct impacts on distributions, aggregations, encounter rates with prey, and many other fundamental ecological processes. Microscopy and video technology enable the automated acquisition of large amounts of tracking data; however, these data are typically two-dimensional. The difficulty of quantifying the third movement component complicates understanding of the biomechanical causes and ecological consequences of helical swimming. We present a versatile continuous stochastic model-the correlated velocity helical movement (CVHM) model-that characterizes helical swimming with intrinsic randomness and autocorrelation. The model separates an organism's instantaneous velocity into a slowly varying advective component and a perpendicularly oriented rotation, with velocities, magnitude of stochasticity, and autocorrelation scales defined for both components. All but one of the parameters of the 3D model can be estimated directly from a two-dimensional projection of helical movement with no numerical fitting, making it computationally very efficient. As a case study, we estimate swimming parameters from videotaped trajectories of a toxic unicellular alga, Heterosigma akashiwo (Raphidophyceae). The algae were reared from five strains originally collected from locations in the Atlantic and Pacific Oceans, where they have caused Harmful Algal Blooms (HABs). We use the CVHM model to quantify cell-level and strain-level differences in all movement parameters, demonstrating the utility of the model for identifying strains that are difficult to distinguish by other means.

Non-linear advection-diffusion equations approximate swarming but not schooling populations.

Advection-diffusion equations (ADEs) are concise and tractable mathematical descriptions of population distributions used widely to address spatial problems in applied and theoretical ecology. We assessed the potential of non-linear ADEs to approximate over very large time and space scales the spatial distributions resulting from social behaviors such as swarming and schooling, in which populations are subdivided into many groups of variable size, velocity and directional persistence. We developed a simple numerical scheme to estimate coefficients in non-linear ADEs from individual-based model (IBM) simulations. Alignment responses between neighbors within groups quantitatively and qualitatively affected how populations moved. Asocial and swarming populations, and schooling populations with weak alignment tendencies, were well approximated by non-linear ADEs. For these behaviors, numerical estimates such as ours could enhance realism and efficiency in ecosystem models of social organisms. Schooling populations with strong alignment were poorly approximated, because (in contradiction to assumptions underlying the ADE approach) effective diffusion and advection were not uniquely defined functions of local density. PDE forms other than ADEs are apparently required to approximate strongly aligning populations.

Using collision cones to assess biological deconfliction methods.

Biological systems consistently outperform autonomous systems governed by engineered algorithms in their ability to reactively avoid collisions. To better understand this discrepancy, a collision avoidance algorithm was applied to frames of digitized video trajectory data from bats, swallows and fish (Myotis velifer, Petrochelidon pyrrhonota and Danio aequipinnatus). Information available from visual cues, specifically relative position and velocity, was provided to the algorithm which used this information to define collision cones that allowed the algorithm to find a safe velocity requiring minimal deviation from the original velocity. The subset of obstacles provided to the algorithm was determined by the animal's sensing range in terms of metric and topological distance. The algorithmic calculated velocities showed good agreement with observed biological velocities, indicating that the algorithm was an informative basis for comparison with the three species and could potentially be improved for engineered applications with further study.

Spatial memory-based behaviors for locating sources of odor plumes.

BACKGROUND: Many animals must locate odorant point sources during key behaviors such as reproduction, foraging and habitat selection. Cues from such sources are typically distributed as air- or water-borne chemical plumes, characterized by high intermittency due to environmental turbulence and episodically rapid changes in position and orientation during wind or current shifts. Well-known examples of such behaviors include male moths, which have physiological and behavioral specializations for locating the sources of pheromone plumes emitted by females. Male moths and many other plume-following organisms exhibit "counter-turning" behavior, in which they execute a pre-planned sequence of cross-stream movements spanning all or part of an odorant plume, combined with upstream movements towards the source. Despite its ubiquity and ecological importance, theoretical investigation of counter-turning has so far been limited to a small subset of plausible behavioral algorithms based largely on classical biased random walk gradient-climbing or oscillator models. RESULTS: We derive a model of plume-tracking behavior that assumes a simple spatially-explicit memory of previous encounters with odorant, an explicit statistical model of uncertainty about the plume's position and extent, and the ability to improve estimates of plume characteristics over sequential encounters using Bayesian updating. The model implements spatial memory and effective cognitive strategies with minimal neural processing. We show that laboratory flight tracks of Manduca sexta moths are consistent with predictions of our spatial memory-based model. We assess plume-following performance of the spatial memory-based algorithm in terms of success and efficiency metrics, and in the context of "contests" in which the winner is the first among multiple simulated moths to locate the source. CONCLUSIONS: Even rudimentary spatial memory can greatly enhance plume-following. In particular, spatial memory can maintain source-seeking success even when plumes are so intermittent that no pheromone is detected in most cross-wind transits. Performance metrics reflect trade-offs between "risk-averse" strategies (wide cross-wind movements, slow upwind advances) that reliably but slowly locate odor sources, and "risk-tolerant" strategies (narrow cross-wind movements, fast upwind advances) that often fail to locate a source but are fast when successful. Success in contests of risk-averse vs. risk-tolerant behaviors varies strongly with the number of competitors, suggesting empirically testable predictions for diverse plume-following taxa. More generally, spatial memory-based models provide tractable, explicit theoretical linkages between sensory biomechanics, neurophysiology and behavior, and ecological and evolutionary dynamics operating at much larger spatio-temporal scales.

Self-organized fish schools: an examination of emergent properties.

Heterogeneous, "aggregated" patterns in the spatial distributions of individuals are almost universal across living organisms, from bacteria to higher vertebrates. Whereas specific features of aggregations are often visually striking to human eyes, a heuristic analysis based on human vision is usually not sufficient to answer fundamental questions about how and why organisms aggregate. What are the individual-level behavioral traits that give rise to these features? When qualitatively similar spatial patterns arise from purely physical mechanisms, are these patterns in organisms biologically significant, or are they simply epiphenomena that are likely characteristics of any set of interacting autonomous individuals? If specific features of spatial aggregations do confer advantages or disadvantages in the fitness of group members, how has evolution operated to shape individual behavior in balancing costs and benefits at the individual and group levels? Mathematical models of social behaviors such as schooling in fishes provide a promising avenue to address some of these questions. However, the literature on schooling models has lacked a common framework to objectively and quantitatively characterize relationships between individual-level behaviors and group-level patterns. In this paper, we briefly survey similarities and differences in behavioral algorithms and aggregation statistics among existing schooling models. We present preliminary results of our efforts to develop a modeling framework that synthesizes much of this previous work, and to identify relationships between behavioral parameters and group-level statistics.

An integrated modeling approach to assessing linkages between environment, organism, and phenotypic plasticity.

Many of the most interesting questions in organismal biology, especially those involving the functional and adaptive significance of organismal characteristics, intrinsically transcend levels of biological organization. These organismal functions typically involve multiple interacting biological mechanisms. We suggest that subdisciplinary advances have led both to the opportunity and to the necessity to reintegrate knowledge into a new understanding of the whole organism. We present a conceptual framework for a modeling approach that addresses the functioning of organisms in an integrative way, incorporating elements from environments, populations, individuals, and intra-organismal dynamics such as physiology and behavior. To give substance to our conceptual framework, we provide a preliminary focal case study using phenotypic plasticity in the tooth morphology of snails in the genus Lacuna. We use this case study to illustrate ways in which questions about the evolution and ecology of organismal function intrinsically span all organizational levels. In this case, and in many others, quantitative approaches that integrate across mechanisms and scales can suggest new hypotheses about organismal function, and provide new tools to test those hypotheses. Integrative quantitative models also provide roadmaps for the large-scale collaborations among diverse disciplinary specialists that are needed to gain deeper insights into organismal function.

Behavioral and physiological changes during benthic-pelagic transition in the harmful alga, Heterosigma akashiwo: potential for rapid bloom formation.

Many species of harmful algae transition between a motile, vegetative stage in the water column and a non-motile, resting stage in the sediments. Physiological and behavioral traits expressed during benthic-pelagic transition potentially regulate the timing, location and persistence of blooms. The roles of key physiological and behavioral traits involved in resting cell emergence and bloom formation were examined in two geographically distinct strains of the harmful alga, Heterosigma akashiwo. Physiological measures of cell viability, division and population growth, and cell fatty acid content were made using flow cytometry and gas chromatography - mass spectrometry techniques as cells transitioned between the benthic resting stage and the vegetative pelagic stage. Video-based tracking was used to quantify cell-level swimming behaviors. Data show increased temperature and light triggered rapid emergence from the resting stage and initiated cell swimming. Algal strains varied in important physiological and behavioral traits, including survivorship during life-stage transitions, population growth rates and swimming velocities. Collectively, these traits function as "population growth strategies" that can influence bloom formation. Many resting cells regained the up-swimming capacity necessary to cross an environmentally relevant halocline and the ability to aggregate in near-surface waters within hours after vegetative growth supporting conditions were restored. Using a heuristic model, we illustrate how strain-specific population growth strategies can govern the timescales over which H. akashiwo blooms form. Our findings highlight the need for identification and quantification of strain-specific physiological and behavioral traits to improve mechanistic understanding of bloom formation and successful bloom prediction.

A spatially explicit Bayesian framework for cognitive schooling behaviours.

Social aggregations such as schools, swarms, flocks and herds occur across a broad diversity of animal species, strongly impacting ecological and evolutionary dynamics of these species and their predators, prey and competitors. The mechanisms through which individual-level responses to neighbours generate group-level characteristics have been extensively investigated both experimentally and using mathematical models. Models of social groups typically adopt a 'zone' approach, in which individuals' movement responses to neighbours are functions of instantaneous relative position. Empirical studies have demonstrated that most social animals such as fish exhibit well-developed spatial memory and other advanced cognitive capabilities. However, most models of social grouping do not explicitly include spatial memory, largely because a tractable framework for modelling acquisition of and response to historical spatial information has been lacking. Using fish schooling as a focal example, this study presents a framework for including cognitive responses to spatial memory in models of social aggregation. The framework utilizes Bayesian estimation parameters that are continuously distributed in time and space as proxies for animals' spatial memory. The result is a hybrid Lagrangian-Eulerian model in which the effects of cognitive state and behavioural responses to historical spatial data on individual-, group- and population-level distributions of social animals can be explicitly investigated.

The logic of ecological patchiness.

Most ecological interactions occur in environments that are spatially and temporally heterogeneous-'patchy'-across a wide range of scales. In contrast, most theoretical models of ecological interactions, especially large-scale models applied to societal issues such as climate change, resource management and human health, are based on 'mean field' approaches in which the underlying patchiness of interacting consumers and resources is intentionally averaged out. Mean field ecological models typically have the advantages of tractability, few parameters and clear interpretation; more technically complex spatially explicit models, which resolve ecological patchiness at some (or all relevant) scales, generally lack these advantages. This report presents a heuristic analysis that incorporates important elements of consumer-resource patchiness with minimal technical complexity. The analysis uses scaling arguments to establish conditions under which key mechanisms-movement, reproduction and consumption-strongly affect consumer-resource interactions in patchy environments. By very general arguments, the relative magnitudes of these three mechanisms are quantified by three non-dimensional ecological indices: the Frost, Strathmann and Lessard numbers. Qualitative analysis based on these ecological indices provides a basis for conjectures concerning the expected characteristics of organisms, species interactions and ecosystems in patchy environments.

Swimming performance in early development and the "other" consequences of egg size for ciliated planktonic larvae.

The evolutionary significance of egg size in marine invertebrates is commonly perceived in energetic terms. Embryonic size should also have direct effects upon the forces that govern swimming, a behavior common to early larval development in the plankton. If swimming is ecologically important, early larvae may need to perform to a certain "standard", or threshold of speed and/or stability. The existence of performance standards in early development could therefore act to constrain the evolution of egg size and the evolution of development. Here we present the key parameters that characterize the upward swimming speed of ciliated spheroidal larvae moving at very low Reynolds numbers. The dependence of maximum supported mass upon larval size, and the independence of neutral-weight swimming speed from size, lead to hypotheses about scaling of swimming speed with size. Experimental studies with thirteen broadcast-spawning planktotrophs demonstrate that free-living embryonic swimmers in all of these species conform to a strong negative scaling of density with size that offsets increases in mass with increasing size. This trend suggests that swimming ability is broadly under selection in early development. In experimental studies and in a hydrodynamic model of larval swimming, the performance of trochophore larvae provides support for our hypothesized scaling relationships, and also for the concept of a standard in swimming speed. Echinoid blastulae, however, show relationships between speed and size that are not predicted by our scaling arguments. Results for echinoids suggest that differences in ciliary tip speed, or possibly in spatial density of cilia over the blastula's surface, result in significant differences in species' performance. Strong phyletic differences in the initial patterning and growth of structures used for swimming thus appear to cause significant differences in the relationship of swimming ability with embryo size.

Good eaters, poor swimmers: compromises in larval form.

Compromises between swimming and feeding affect larval form and behavior. Two hypotheses, with supporting examples, illustrate these feeding-swimming trade-offs. (1) Extension of ciliated bands into long loops increases maximum clearance rates in feeding but can decrease stability of swimming in shear flows. A hydromechanical model of swimming by ciliated bands on arms indicates that morphologies with high performance in swimming speed and weight-carrying ability in still water differ from morphologies conferring high stability to external disturbances such as shear flows. Instability includes movement across flow lines from upwelling to downwelling water in vertical shear. Thus a hypothesis for the high arm elevation angles of sea urchin larvae, which reduce speed in still water, is that they reduce a downward bias imposed by the vertical shear in turbulence. Observations of sea urchin larvae in vertical shear and comparisons among brittle star larvae are consistent with the performance trade-offs predicted by the model. (2) Structures and behaviors that reduce swimming speed can enhance filtering for feeding. In the opposed-band feeding mechanisms of veligers and many trochophores, cilia push water to swim but movement of cilia relative to the water occurs when cilia overtake and capture particles. Features that may increase clearance rates at the expense of speed and weight capacity include structures that increase drag or body weight and a ciliary band that beats in opposition to the feeding-swimming current. Larval feeding mechanisms inherited from distant ancestors result in different swimming-feeding trade-offs. The different trade-offs further diversify larval form and behavior.