@article{skalski_picha_gilliam_borski_2005, title={Variable intake, compensatory growth, and increased growth efficiency in fish: Models and mechanisms}, volume={86}, ISSN={["1939-9170"]}, DOI={10.1890/04-0896}, abstractNote={Resources fluctuate in space and time, and animals routinely experience temporally varying opportunities for resource intake, and variation in intake itself. We investigate consequences of such variation in intake on growth and growth efficiency (growth per unit intake) in juvenile hybrid striped bass. We observed, after statistically accounting for the effects of total consumption and initial body size, that individuals re- ceiving a low ration followed by a higher ration (the fluctuating ration) grew faster than individuals receiving a temporally constant ration (the normal ration). To interpret this increase in growth efficiency, we consider a set of alternative models representing different physiological hypotheses of the growth process. Using a simple growth model, an analytical result shows that the fluctuating ration as typically applied in experiments (a low ration followed by a high ration), independent of any change in physiology, increases growth efficiency relative to individuals on the normal ration. Growth efficiency increases because cumulative maintenance costs are lower for individuals that stay small initially and then grow rapidly in comparison to individuals that grow steadily. Further, a statistical analysis of alternative models inferred that fish receiving a variable ration show higher assimilation and/or conversion efficiencies of food and lower mass-specific maintenance costs. Our analysis suggests that the lower cumulative maintenance costs incurred over a time interval with low consumption followed by high consumption act in association with higher assim- ilation-conversion efficiencies, and lower overall mass-specific maintenance costs to in- crease growth efficiency in hybrid striped bass.}, number={6}, journal={ECOLOGY}, author={Skalski, GT and Picha, ME and Gilliam, JF and Borski, RJ}, year={2005}, month={Jun}, pages={1452–1462} }
 @article{skalski_2004, title={The diffusive spread of alleles in heterogeneous populations}, volume={58}, ISSN={["1558-5646"]}, DOI={10.1111/j.0014-3820.2004.tb01670.x}, abstractNote={The spread of genes and individuals through space in populations is relevant in many biological contexts. I study, via systems of reaction-diffusion equations, the spatial spread of advantageous alleles through structured populations. The results show that the temporally asymptotic rate of spread of an advantageous allele, a kind of invasion speed, can be approximated for a class of linear partial differential equations via a relatively simple formula, c = 2 square root of (rD), that is reminiscent of a classic formula attributed to R. A. Fisher. The parameters r and D represent an asymptotic growth rate and an average diffusion rate, respectively, and can be interpreted in terms of eigenvalues and eigenvectors that depend on the population's demographic structure. The results can be applied, under certain conditions, to a wide class of nonlinear partial differential equations that are relevant to a variety of ecological and evolutionary scenarios in population biology. I illustrate the approach for computing invasion speed with three examples that allow for heterogeneous dispersal rates among different classes of individuals within model populations.}, number={3}, journal={EVOLUTION}, author={Skalski, GT}, year={2004}, month={Mar}, pages={470–478} }
 @article{skalski_gilliam_2003, title={A diffusion-based theory of organism dispersal in heterogeneous populations}, volume={161}, ISSN={["1537-5323"]}, DOI={10.1086/367592}, abstractNote={We develop a general theory of organism movement in heterogeneous populations that can explain the leptokurtic movement distributions commonly measured in nature. We describe population heterogeneity in a state‐structured framework, employing advection‐diffusion as the fundamental movement process of individuals occupying different movement states. Our general analysis shows that population heterogeneity in movement behavior can be defined as the existence of different movement states and among‐individual variability in the time individuals spend in these states. A presentation of moment‐based metrics of movement illustrates the role of these attributes in general dispersal processes. We also present a special case of the general theory: a model population composed of individuals occupying one of two movement states with linear transitions, or exchange, between the two states. This two‐state “exchange model” can be viewed as a correlated random walk and provides a generalization of the telegraph equation. By exploiting the main result of our general analysis, we characterize the exchange model by deriving moment‐based metrics of its movement process and identifying an analytical representation of the model’s time‐dependent solution. Our results provide general and specific theoretical explanations for empirical patterns in organism movement; the results also provide conceptual and analytical bases for extending diffusion‐based dispersal theory in several directions, thereby facilitating mechanistic links between individual behavior and spatial population dynamics.}, number={3}, journal={AMERICAN NATURALIST}, author={Skalski, GT and Gilliam, JF}, year={2003}, month={Mar}, pages={441–458} }
 @article{skalski_gilliam_2002, title={Feeding under predation hazard: Testing models of adaptive behavior with stream fish}, volume={160}, ISSN={["1537-5323"]}, DOI={10.1086/341012}, abstractNote={Many empirical studies support the premise that animals consider both the benefits of feeding and the cost of mortality when making behavioral decisions, and many theoretical studies predict animal behavior in the presence of a feeding‐mortality trade‐off. However, empirical work is lacking in studies that quantitatively assess alternative models. Using data from two sets of behavioral experiments examining stream minnows (bluehead chubs) foraging in the presence of sunfish predators (green sunfish), we assess, via statistical model fitting, the utility of four basic optimization models of foraging behavior. Our analysis of feeding and mortality of the minnows indicates that mortality is incurred so as to feed above maintenance requirements, that feeding rate is suppressed in response to the presence of predators, and that the balance of feeding against mortality can be estimated using a life‐history parameter θ, interpreted theoretically as the marginal rate of substitution of mortality rate for growth rate. Our results indicate that both body size and age are probably involved in determining the value of θ, and we suggest that future studies should focus on estimating and understanding this parameter.}, number={2}, journal={AMERICAN NATURALIST}, author={Skalski, GT and Gilliam, JF}, year={2002}, month={Aug}, pages={158–172} }
 @article{fraser_gilliam_daley_le_skalski_2001, title={Explaining leptokurtic movement distributions: Intrapopulation variation in boldness and exploration}, volume={158}, ISSN={["1537-5323"]}, DOI={10.1086/321307}, abstractNote={Leptokurtic distributions of movement distances observed in field‐release studies, in which some individuals move long distances while most remain at or near their release point, are a common feature of mobile animals. However, because leptokurtosis is predicted to be transient in homogeneous populations, persistent leptokurtosis suggests a population heterogeneity. We found evidence for a heterogeneity that may generate persistent leptokurtosis. We tested individuals of the Trinidad killifish Rivulus hartii for boldness in a tank test and released them back into their native stream. Boldness in the tank test predicted distance moved in the field releases, even after effects of size and sex were removed. Further, data from a 19‐mo mark‐recapture study showed that individual growth correlated positively with movement in a predator‐threatened river zone where the Rivulus population is spatially fragmented and dispersal is likely to be a hazardous activity. In contrast, no such correlation existed in a predator‐absent zone where the population is unfragmented. These results show that a behavioral trait, not discernible from body size or sex, contributes to dispersal and that a component of fitness of surviving “dispersers” is elevated above that of “stayers,” a fundamental assumption or prediction of many models of the evolution of dispersal through hazardous habitat.}, number={2}, journal={AMERICAN NATURALIST}, author={Fraser, DF and Gilliam, JF and Daley, MJ and Le, AN and Skalski, GT}, year={2001}, month={Aug}, pages={124–135} }
 @article{skalski_gilliam_2001, title={Functional responses with predator interference: viable alternatives to the Holling Type II model}, volume={82}, DOI={10.2307/2679836}, abstractNote={A predator's per capita feeding rate on prey, or its functional response, provides a foundation for predator–prey theory. Since 1959, Holling's prey-dependent Type II functional response, a model that is a function of prey abundance only, has served as the basis for a large literature on predator–prey theory. We present statistical evidence from 19 predator–prey systems that three predator-dependent functional responses (Beddington-DeAngelis, Crowley-Martin, and Hassell-Varley), i.e., models that are functions of both prey and predator abundance because of predator interference, can provide better descriptions of predator feeding over a range of predator–prey abundances. No single functional response best describes all of the data sets. Given these functional forms, we suggest use of the Beddington-DeAngelis or Hassell-Varley model when predator feeding rate becomes independent of predator density at high prey density and use of the Crowley-Martin model when predator feeding rate is decreased by higher predator density even when prey density is high.}, number={11}, journal={Ecology (Brooklyn, New York, N.Y.)}, author={Skalski, G. T. and Gilliam, J. F.}, year={2001}, pages={3083–3092} }
 @article{skalski_gilliam_2000, title={Modeling diffusive spread in a heterogeneous population: A movement study with stream fish}, volume={81}, ISSN={["1939-9170"]}, DOI={10.2307/177317}, abstractNote={Using a mark–recapture technique in a small temperate stream, we described the movement of four fish species over a five-month period and developed a mathematical model that described the observed movement patterns. The movement distributions were generally leptokurtic, and two of the four species demonstrated some degree of upstream bias. There was little difference in movement among species or through time. There were no temporal correlations in probability of movement, movement direction, or distance moved. The spatial spread of the most abundant species, bluehead chubs, over a four-month period was characterized by upstream bias, diffusion-like spread, and persistent leptokurtosis. Bluehead chubs demonstrated complex relationships between probability of movement and size and growth, while creek chubs showed only an effect of size on probability of movement. Further, growth of individual bluehead chubs was correlated through time. These empirical results suggest the hypothesis that heterogeneity in phenotypic attributes, such as size and growth, is related to heterogeneity in movement behavior. A diffusion–advection model of bluehead chub movement, structured with two subgroups that dispersed at different rates (“fast fish” and “slow fish”), was parameterized and validated with the field data. This model with heterogeneity in movement rates generated the leptokurtic pattern observed in the field data, in contrast to the classic diffusion model without population heterogeneity, which produces a normal distribution. The results from this work suggest that heterogeneity in fitness-influencing attributes such as size and growth could explain heterogeneity in individual-level movement behavior and might underlie the leptokurtic patterns that have been observed at the population level in numerous field studies.}, number={6}, journal={ECOLOGY}, author={Skalski, GT and Gilliam, JF}, year={2000}, month={Jun}, pages={1685–1700} }