Integrative and Comparative Biology Advance Access originally published online on October 18, 2006
Integrative and Comparative Biology 2006 46(6):1093-1109; doi:10.1093/icb/icl031
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Linking physiological effects on activity and resource use to population level phenomena
* Department of Bioscience and Biotechnology, Drexel University Philadelphia, PA 19104, USA
Department of Biology, University of Pennsylvania Philadelphia, PA 19104, USA
Correspondence: 1E-mail: mike.oconnor{at}drexel.edu
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 Synopsis IntroductionModelCanyon lizards (Sceloporus...Frogs: desiccation and activityPhysiological models as toolsSummaryREFERENCES |
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We present an approach to delineating physiological effects on population level processes by modeling the activity and resource budgets of animals. Physiology and its environmental forcing functions are assumed to affect both the total time available for activity and foraging and the resource budgets by affecting resource acquisition, costs, and handling. We extend the earlier model of Dunham and others (1989) and translate it into a computational algorithm. To satisfy conservation needs for accuracy, wide applicability, and rapid deployment, the model is relatively simple, uses as much data on the focal organism as possible, is mechanistically driven, and can be adapted to new organisms by using data for the new species, or the best available approximations to those data. We present 2 applications of the modeling approach. First, we consider a system with substantial information available, canyon lizards (Sceloporus merriami) studied by Dunham and colleagues in west Texas. In this case the focus is on integration of numerous inputs and the ability of the model to produce predictions that approximate counterintuitive empirical patterns. By using the wealth of specific data available, the model outperforms previous attempts at explanation of those patterns. Next, we consider a system with much less available information (forest-dwelling semi-fossorial frogs). The question here is how hydric conditions can become limiting. A model of evaporation from frogs buried in leaf litter was incorporated and it demonstrates how rainfall patterns can both supply water and put the frogs at risk of critical dehydration.
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Introduction |
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SynopsisIntroductionModelCanyon lizards (Sceloporus...Frogs: desiccation and activityPhysiological models as toolsSummaryREFERENCES |
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In some ways, a symposium asking how physiology can and has contributed to conservation biology should seem like posing a rhetorical question. The papers in this symposium document some of the ways in which physiology, in general, and energetics, in particular, have contributed to an understanding of conservation problems. Further, most biologists would agree that physiological challenges can constrain an animal's ecology and physiological adaptations can affect the range of habitats that an organism can occupy.
In what sense then, are the contributions of physiology and energetics to conservation not a foregone conclusion? Perhaps the most obvious procedure is to develop approaches that allow physiological theory and data to be methodically incorporated into conservation assessments and action plans. Limits on the utility of physiological data arise both from differences in the focus of the 2 fields and from differences in the approaches of applied and basic scientists. Physiology and physiological ecology focus on organism-level questions that potentially influence the population biology of the animals. Conservationists, on the other hand, tend to focus on the population and community levels of organization. In general then, physiological data must be integrated through one or more levels of ecological organization to make predictions of immediate use to conservation biology. As we will argue below, this integration is both important and difficult. Without a clear integration at the population level, physiological predictions and approaches can be difficult to incorporate into conservation plans.
Differences in research approaches between physiologists and conservationists stem both from the differences in the focal levels of organization listed above and from differing research traditions. Most comparative physiologists and physiological ecologists are trained in an academic, basic-science tradition with its emphases on detailed examination and complete explanation. Many conservation biologists must work within a much more applied tradition. Table 1 lists differences between these 2 traditions. We suspect that the first 2 differences drive the others. Conservationists, in many cases, are responding to threats to species and/or biomes which imbue the questions asked with an urgency that shortens all time scales and leaves inadequate time for testing hypotheses unless they are immediately and undeniably related to the population biology of the species of interest. Furthermore, the complicated matrix of intraspecific and interspecific influences within which all species invariably live requires that integration at the population level, discussed above, be easily performed for any factor considered. This complication and the compressed time frames for decisions can restrict attention to established approaches (Primack 1998
).
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In this setting, how can physiological data and analysis be framed so that they translate easily to conservation assessments and plans? No single approach will invariably succeed. The arguments above suggest that physiological ecologists would do well if (1) physiologically based predictions are translated as closely and concretely as possible to the population biology of the animal in question, (2) physiological models are relatively easy to use, without mounting huge research programs, (3) it is recognized that physiology dictates aspects of the focal animal's ecology, but in many cases not all aspects of that ecology, and (4) the conditions under which physiological predictions might be seriously wrong are clarified. We offer an approach that adheres as closely as possible to these conditions while remaining adaptable and, hopefully, broadly applicable.
Physiological factors will translate most directly to the population level under 3 scenarios: (1) when some environmental conditions lead to lethal, pathological, or otherwise disabling physiological conditions and one of the animal's main tasks is to avoid such conditions (for example, Grant and Dunham 1988); (2) when some resource (for example, energy, water, activity time) or combination of resources is critical to the animal's survival, growth, and/or reproduction and physiological factors alter either access to the resource (for example, foraging time), handling of the resource (for example, capture rate or digestion), or resource costs (for example, metabolism) (for example, Kingsolver 1983, 1989; Dunham and Overall 1994); or (3) when any of the conditions above dictate interactions with conspecifics, competitors, predators, prey, pathogens, or parasites (Christian and Tracy 1981).
In this paper, we offer a model-based approach to deal with the first of these scenarios. It can be extended to handle interactions with other organisms. The model attempts to integrate physiological effects over time to predict fitness and demographic correlates, using what information is available on a species of interest and allowing substitution of related data as needed. We argue that it also makes clear on which assumptions predictions depend and points out which data are needed to refine predictions when needed. We use the model to address questions of potential conservation importance, then discuss the pro's and con's of such an approach more generally.
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Model |
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SynopsisIntroductionModelCanyon lizards (Sceloporus...Frogs: desiccation and activityPhysiological models as toolsSummaryREFERENCES |
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Our conceptual model is an elaboration of the model presented by Dunham and others (1989)
to describe physiological effects on the life history and ecology of ectotherms. This model asserts that resources (for example, water, energy) needed for growth and reproduction constitute critical fitness correlates and that accumulation of those resources can be used as proxies for ecological success of individual animals and, by inference, of their parent populations (Dunham for example, 1989, Fig. 1). This approach is consistent not only with current autecological modeling practice (DeAngelis and Gross 1992; DeAngelis and others 1993; Maley and Caswell 1993; McNair and others 1998; Kooijman 2001; Grimm and Railsback 2005) but also with life history theory (Stearns 1992; McNab 2002; Sebens 2002; Dahlhoff and others 2002; Piersma 2002) and physiological ecology (Congdon and others 1982; Dunham and others 1989; Dunham 1993; Porter and Tracy 1983; Porter and others 2000, 2002; Angilletta and others 2003). Resources are accumulated by activity in an environment from which the resources can be harvested. Both the resources available and the ability of an animal to be active and forage in its habitat are key determinants of resource accumulation (Fig. 1). Physiological and physical factors affect resource accumulation by (1) facilitating or constraining time available for activity, (2) affecting resource harvest rates (for example, digestion), or (3) affecting handling of harvested resources (for example, metabolic energy costs and evaporation).
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While the conceptual model guides our consideration of physiological effects at the population and conservation levels, conceptual models alone can and have proven unreliable in predicting such effects. Witness the longstanding debate about physiological tradeoffs in life history theory, and the variety of predictions made using similar conceptual models for particular organisms (see Congdon and others 1982
; Stearns 1992). We argue that models for use in conservation must be made as explicit and quantitative as possible. Figure 2 represents a highly simplified block diagram of such an explicit model limited to one ‘resource’ (for example, water, energy, heat). For each time step, the current resource state (stored resource), the environment, and potentially other factors (for example, other resources) influence whether the animal will be active for this time step. If the animal is active, it incurs costs due to that activity (for example, increased metabolic rate and/or evaporation). Inactive animals incur different, potentially lower costs. Active animals can also forage for resources and, depending on the resource environment, ingest resources as food. Regardless of activity, animals can digest food already in the gut, body temperature permitting, and assimilate resources. Integrating costs and assimilation, we reach a new resource state at which to start the next time step. Activity and stressful thermal, hydric, and other resource states can expose animals to risks of predation and other sources of mortality (Fig. 2).
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In order to adapt the model to particular populations, one must (1) determine what resources are important in an animal's ecology, (2) expand the model to as many potentially interacting resources (for example, heat, water, energy) as necessary, (3) provide population-specific information on resource availability and handling (for example, the effect of temperature on digestive rates, tolerated body temperatures, operative environments), and (4) iterate the model over time frames appropriate to the animal's biology. It may be the case that insufficient data will be available on populations of interest to parameterize such a model and information must be substituted for other populations, species, or habitats (see below). Such substitutions are almost inevitable, and to the extent that the data used fail to accurately represent resource handling in the focal population, the predictions of the model may be inaccurate (see below).
Here we present 2 very different applications of this model framework to populations in which physiological processes affect population processes. In the first case, we examine variation in life history among populations of Sceloporus merriami in Big Bend National Park, TX where they have been studied intensively for over 25 years (Dunham 1978, 1980, 1993; Grant and Dunham 1988, 1990; Grant 1990; Dunham and Overall 1994). In this case, substantial specific information is available and must be integrated to explain variations in growth rate among populations at different elevations. For the second application, we consider forest-dwelling amphibians in eastern Missouri and ask to what extent a single resource, water, can constrain activity and foraging. Relatively few population-specific physiological data are available, and only tentative conclusions can be reached, but the overall modeling strategy remains important.
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Canyon lizards (Sceloporus merriami) |
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SynopsisIntroductionModelCanyon lizards (Sceloporus...Frogs: desiccation and activityPhysiological models as toolsSummaryREFERENCES |
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Sceloporus merriami is a small, insectivorous lizard that we treat as a model organism for examining potential effects of global warming. Global circulation models of climatic change predict large shifts (2–5.8°C) in environmental temperatures over the next 100-year time horizon. Prediction and understanding of organismal and population level responses to environmental change will require incorporation of physiological mechanisms into more complex population models (Dunham and others 1989
; Dunham 1993; Ayres 1993; Kareiva and others 1993; Dunham and Overall 1994). For terrestrial ectotherms, changes in environmental and body temperature profiles may alter individual mass–energy balance relationships by altering metabolism and digestion (Porter and Tracy 1983; Zimmerman and Tracy 1989; Beaupre and others 1993b; Henen and others 1998; Porter and others 2000; Dahlhoff and others 2002; Somero 2002). In addition, altered time-activity budgets and food availability may influence growth and reproductive potential (Grant and Dunham 1988, 1990; Dunham and others 1989; Grant 1990; Dunham 1993; Gates 1993; Dunham and Overall 1994; Piersma 2002; Sebens 2002).
Canyon lizards constitute a good test bed for predicted effects of climate change because (1) physiology and (2) population biology of the species have been well studied, (3) both climatic and microclimatic data are available for the populations examined by Dunham and others, and (4) the populations studied constitute a cline in elevation and a series of related environmental variables (Dunham and others 1989; Dunham 1993; Dunham and Overall 1994; Grant and Dunham 1988, 1990). Extant predictions from physiologically structured models suggest that (1) temperature and hydric conditions strongly and predictably affect activity, (2) effects of global warming will depend on both changes in opportunities for activity and costs of that activity, (3) increasing tolerated body temperature to extend activity time may be counterproductive because of elevated metabolic costs at higher body temperatures (Dunham 1993; Dunham and Overall 1994).
A problem with using the canyon-lizard system for such predictions, however, is that although the 3 habitats studied form a monotonic cline in a series of environmental variables (Table 2), the population dynamics (growth rates, adult body size, activity rates) for the 3 populations tend to reach extremes at the middle elevation (Grapevine Hills). Conceptual models, despite the wealth of available data, have been unsuccessful in mimicking these biotic patterns, presumably because the environmental gradients interact to affect population parameters in ways that are difficult to predict (Dunham and others 1989). The question we asked was whether a quantitative, physiological model using the physiological rates and characteristics measured by Dunham and colleagues for these populations could make more biologically accurate predictions. We use this question to illustrate our model-based approach.
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Habitat description
Both temperature and water are important to the ecology of canyon lizards (Grant and Dunham 1988
, 1990; Dunham 1993; Dunham and Overall 1994), but simple models indicate that dietary water intake rates are sufficient to maintain body-water stores (A. Dunham unpublished data), suggesting that hydric conditions primarily affect insect prey densities. To describe each of the 3 study sites thermally, we need descriptions of (1) seasonal temperature variation, (2) diel variation in microhabitat temperatures, and (3) site-specific factors that strongly affect available operative temperatures. Seasonal trends are available from meteorological stations maintained by the United States National Parks Service within 2 km of each of the sites at comparable elevations. We used data from 1976 to 1991 for which good data were available for all 3 sites. For each site we extracted precipitation and daily minimum and maximum temperatures. We constructed joint probability density distributions of minimum and maximum temperatures for each time of year for each of the field sites using a product-kernel technique (Martinez and Martinez 2002, Fig. 3). This allowed us to simulate daily environments by randomly selecting a maximum air temperature appropriate for the time of year and then selecting the minimum temperature appropriate for that maximum temperature from marginal distributions constructed for each site. This approach ignored day-to-day autocorrelations, but autocorrelations with lags greater than 1 day were negligible (data not shown). Daily air and ground temperature trajectories were estimated by fitting measured temperatures for each site (A. Dunham and W. Porter unpublished data) to a model of daily temperature variation (Parton and Logan 1981) allowing prediction of trajectories from daily maximum and minimum temperatures. The Parton and Logan model predicts trajectories of environmental temperatures based on maximum and minimum temperatures, day length and time of solar noon (
14:00 in Big Bend during the summer), and 3 parameters that vary from site to site and with height above the substrate (the time lag of maximum temperature after solar noon, the slope of exponential temperature decay at night, and the time lag of minimum temperature after sunrise). For air temperatures at each of the 3 field sites, each of these 3 Parton and Logan parameters was fit by a non-linear least-squares regression to microclimatic data recorded at the site (A. Dunham and W. Porter unpublished data). Substrate temperatures were well modeled by a regression of measured rock temperatures on air temperature and solar radiation (N. P. O'Connor and A. Dunham unpublished data). Addition of wind speeds, time-lagged temperatures, and radiation loads added no significant improvement in predictions. Solar radiation was predicted using clear day models (for example, Gates 1980) with clouds intermittently limiting radiant fluxes on a schedule estimated from microclimatic measurements made at the sites.
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A final complication to be modeled was the shading of the sites by the steep slopes and peaks that abutted each of the field sites. Peaks tended to lie to the east and/or west of the field sites and thus blocked solar warming in early morning and late afternoon (Grant and Dunham 1988
). We modeled these effects by transforming the times of local sunrise (when the sun cleared the peaks) and local sunset into solar elevation angles at which direct-beam sunshine could reach the site. When the solar elevation angle was too small to clear the peaks (and the solar azimuth was in the direction of the peaks), we set direct-beam solar radiation to zero, and used only diffuse solar radiation.
Grant and Dunham (1988, 1990) described 4 microhabitat types based on the complex topography of the rocky habitat inhabited by canyon lizards. The microhabitat types differ primarily in the exposure of both the lizard and its substrate to direct solar radiation and wind. Deep rock crevices are also used as nighttime, thermal, and antipredator refugia by the lizards and temperatures in those crevices have also been measured (A. Dunham unpublished data). Operative temperatures (Bakken and Gates 1975) measured in each microhabitat (Grant and Dunham 1988) fell within the range of temperatures predicted for the microhabitats. Temperatures for a 2-week period in late April and early May for each site and microhabitat simulated for 10 years are shown in Fig. 4.
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Prey densities at each site have been measured by a variety of techniques (Dunham 1978
, 1980; A. Dunham unpublished data). Prey densities vary among sites (Table 2), with rainfall within and between seasons, and with temperature over the course of a day (Dunham 1978, 1980). Diel variation in prey densities as temperature varies closely parallel to thermal variation in lizard activity. Feeding strikes by canyon lizards increase with prey densities, but at higher densities the increase in strike rate with increased densities falls off considerably. We estimated resource availability as prey density and alternatively as strike rate.
Physiological characteristics
We were interested in body temperatures, activity, metabolic costs, and food intake to predict (1) avoidance of lethal temperatures and (2) accumulation of energy for growth and reproduction. Canyon-lizard body temperatures are consistent with simultaneous operative temperatures in the same microhabitat (Grant and Dunham 1988, 1990). Thus, animals were considered active in a microhabitat when simulated operative temperatures in the microhabitat were within the selected thermal tolerances of the lizards; otherwise lizards could not be active in that microhabitat. When conditions in none of the microhabitats were favorable for activity, the animal was assumed to retreat to a refugium in a rocky crevice. Voluntary thermal tolerances were estimated in 2 ways. First, as in previous models, we used limits presented by Grant and Dunham (1988) corresponding to an overall 90% confidence interval for all measured active body temperatures (32.2 ± 3.3°C). Grant and Dunham (1990), however, showed that animals at the lower elevation sites (Boquillas and Grapevine Hills) use substantially higher body temperatures in the afternoon, presumably to extend activity periods. As an alternative model, we allowed the animals at Boquillas and Grapevine Hills to use those higher body temperatures.
Metabolic rates were modeled using rates measured on canyon lizards (Beaupre and others 1993b) treating the lowest-measured daytime metabolic rates as resting metabolism and assuming that active animals would have metabolic rates 2.2 times resting rates (Nagy 2005).
Food intake was treated as proportional either to prey density or to strike rates (Dunham 1980). Because individuals animals are not followed in this model and gut capacities and contents are not included, we could not incorporate thermal limits on digestion and energy assimilation into estimates of energy accumulation, but did estimate time available in each simulated day for digestive processing. We assumed that digestive processing ceased at body temperatures below 29.5°C because digestion declines precipitously at 30°C and canyon lizards at Big Bend do not eat when held at temperatures below 30°C (Beaupre and others 1993a; Beaupre and Dunham 1995; A. Dunham unpublished data).
Results—activity and energy
Using the data-based environmental and physiological parameters listed above we simulated canyon-lizard body temperatures, activity, and energy accumulation over 10 years and averaged values for 2-week periods throughout the year for each site. Predicted patterns of activity, energy intake, metabolic costs, and net energy accumulation for mid-March through October are presented in Fig. 5 for lizards at the low-elevation site (Boquillas). Important patterns include maximum activity rates, intakes, and net energy accumulation in the morning before temperatures get uncomfortably warm, shifts in activity and energy rates 15:00 h when the sun is obscured by peaks to the west, peaks in metabolic rate in the early afternoon when the animals allow temperatures to drift up (presumably to maintain activity), marginal (but slightly positive) net energy balance in afternoon during the heat of the summer, and slight seasonal changes in available activity and energy accumulation (Fig. 5). As discussed above, we examined 2 important changes in assumptions from earlier models. First, we incorporated the empirical tendency for animals at the middle and low elevations to use higher body temperatures in the afternoon when operative temperatures would otherwise preclude activity (Grant and Dunham 1990). Second, we modeled intake rates as being proportional to measured feeding rates rather than to density of invertebrate prey (Dunham 1980). Predicted net energy accumulation depended strongly on these 2 sets of assumptions (Fig. 6). Estimating intake rates from feeding strikes rather than from prey density had little effect on predicted intakes (and net energy) at the middle and low elevations where prey densities were lower and both density and feeding strikes varied proportionately. At the high elevation (Maple Canyon), however, prey densities increased to over twice the densities at Grapevine Hills, but feeding strikes increased by only 10% from Grapevine Hills to Maple Canyon. Energy intakes estimated using prey densities at Maple Canyon substantially exceeded those at the lower elevations, but those estimated using feeding strikes were more comparable (Fig. 6) consistent both with anecdotal data and measured growth rates (Table 2).
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Assuming that lizards at the low-elevation site used relatively warm microhabitats (leading to warmer body temperatures) had a very slight effect on predicted net energy accumulation (Boquillas, Fig. 6). The high metabolic rate due to the high body temperatures (Fig. 3) nearly balanced the extended foraging intakes, leading to a marginally positive energy balance in the afternoon (Fig. 5). At Grapevine Hills, where temperatures are slightly lower, the extended activities and higher temperatures increased the net energy accumulation by 10–20% during the summer (Fig. 6) and raised annual, predicted gains in energy at Grapevine Hills above those recorded at Maple Canyon.
Digestive processing of ingested prey was not included in this model because that would require thoroughly individually based models and a gut model that we cannot yet adequately parameterize. However, we used the availability of temperatures consistent with digestion to probe possible prey-processing limitations at all 3 sites (Fig. 7). As noted above, we assumed that whenever the animal could achieve a body temperature above 29.5°C, it could digest prey (Beaupre and others 1993a). Under this assumption, it appears likely that digestive constraints would vary among the 3 sites. At Boquillas, refugium temperatures in summer reached the lower end of the permissive range and significantly extended predicted time for digestion (Fig. 7). Conversely, the lower temperatures at Maple Canyon in the summer allowed only about 2/3 of the processing time predicted at Grapevine Hills (Fig. 7). Without a gut model, we cannot yet address the importance of this possible processing limitation, but it suggests that energy availability at Maple Canyon may be limited compared with that at Grapevine Hills, thereby limiting growth at Maple Canyon.
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Caveats and limitations
The model presented here matches ecological and life history patterns in canyon lizards more closely than any previous model (Dunham and Overall 1994
). As we suggested above, however, an important characteristic of physiological models meant to be used in conservation is the ability to identify critical assumptions and missing data. Figure 6 suggests that the predictions of the model are sensitive both to the body temperatures of the lizards and to estimated prey-intake rates. Although the intake rates used here are based on relatively extensive data (Dunham 1978, 1980; Ruby and Dunham 1987), annual, seasonal, and rainfall-based variations in both prey density and feeding rates are not included in the model and could substantially complicate the predictions of the model. Likewise, Figure 7 suggests that digestive performance, particularly at high elevations, may complicate estimates of energy accumulation. Finally, we assume that energy accumulation is the key fitness correlate to be measured, excluding other resources (for example, water) and biotic interactions such as predation. A variety of published and unpublished data suggest that neither of these factors are the key to canyon-lizard ecology under most conditions, but these factors will almost certainly play some role, perhaps especially in drought situations. |
Frogs: desiccation and activity |
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SynopsisIntroductionModelCanyon lizards (Sceloporus...Frogs: desiccation and activityPhysiological models as toolsSummaryREFERENCES |
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We now shift focus from a system where substantial, species-specific information is available and the purpose of the model is to integrate that information into usable predictions to a system in which much less information is currently available and the purpose of the model is to explore a much smaller part of the conceptual model in Fig. 1. Nonetheless, the approach remains the same. We focus on activity and resource budgets, how the environment can constrain those budgets, and how a mechanistic synthesis of the available information and the animal's biology can allow us to make potentially useful predictions with some idea of the limits of those predictions.
Amphibians are among the most threatened of vertebrate groups and habitat loss/modification and climatic effects are among the most important threats to amphibians (Bylmer and McGinnis 1977; Bury 1983; Dodd and Smith 2003; Stuart and others 2004). The moist skins of most amphibians and the attendant cutaneous evaporative water losses make water a major environmental and physiological concern for amphibians and hydric physiology has long been recognized as a key controller of habitat use in amphibians (Thorson and Svihla 1943; Lillywhite 1970; Pough and Wilson 1970; Spotila 1972; Tracy 1975; Preest and Pough 1989, 2003).
Here we focus on a particular aspect of the water–ecology relationship that is of conservation interest in a system currently under study. Forest-dwelling amphibians are subject to habitat modification due to logging and forestry-management techniques including clearcutting. Semlitsch and colleagues are investigating how various forest-management techniques alter habitat use and population dynamics of amphibians, including in particular wood frogs (Rana sylvatica), subjected to various forest-management techniques (Raymond and Hardy 1991; Rothermel and Semlitsch 2002; Rittenhouse and others 2004; Daszak and others 2005; Rothermel and Luhring 2005). Salient features of wood-frog ecology at a Missouri study site include (1) sequential use of different habitats over the course of a year (breeding ponds in late winter, fossorial habitats while migrating away from the ponds in the spring and summer refugia, (2) use of leaf-litter refugia for most of the time as they migrate away from the breeding ponds, emerging to move primarily during and immediately after rains, and (3) vulnerability to desiccation and mortality during droughts (Semlitsch and Rittenhouse personal communication). Because forestry-management techniques can change the hydric conditions of the forest floor and hence affect wood frogs, it becomes important to understand to what extent frogs can resist desiccation behaviorally and under what conditions they will face injurious or lethal dehydration.
Water exchanges
Evaporative exchanges of water between an amphibian and its environment are simultaneously both simple and complex, and depend critically both on the environment and the activity of the animal (Heatwole and others 1969). For most ranid frogs, the resistance to water transfer across the skin is small in comparison to resistances to transfer from the surface of the skin to the environment; hence the rates of evaporative water loss are determined primarily by diffusion and convection (Lillywhite 2006). Unfortunately convective exchanges themselves can be difficult to describe unless the animal is in a low-speed, laminar flow of air without variations in wind speed, air temperature, and humidity. Environmental surfaces (for example, the ground), refugia, and vegetation can all affect rates of convective heat and mass transfer (O'Connor 1989; Schwartzkopf and Alford 1996). In addition, evaporation cools the frog's surface, altering evaporation and buffering the animal's body temperature (Tracy 1976; Spotila and others 1992). Nonetheless, for animals active on the surface, evaporation can be estimated via standard biophysical techniques (Tracy 1976) if one knows the mass of the animal, the wind speed at the animal's height, and the environmental temperatures and humidities.
For an animal buried in leaf litter, however, we are aware of no models that predict evaporative rates. The litter creates a layer of still air around the animal, impedes diffusion by lengthening the diffusive path length and limiting the cross-sectional area through which diffusion can take place, and can absorb or contribute water vapor to the diffusing stream. We constructed a simple model of diffusion through leaf litter that treats the leaves as inert (no absorption or contribution of water vapor), interdigitated baffles (Fig. 8). Water vapor is assumed to diffuse via passive diffusion without convection along a path shown by the dotted line in Figure 8, with a cross-sectional area that depends on the total number of layers of leaves and the density with which the leaves are packed (given by the total thickness of the litter layer). We used Fick's first law of diffusion to describe the transfer rate.
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Habitat description
We used temperatures, wind speeds, humidities, and rainfall from 2003 though 2005 for several locations near the Missouri study site used by Semlitsch and colleagues. During April, when wood frogs are typically migrating from the breeding ponds toward their summer refugia, typical air temperatures were
20°C, and water vapor densities ranged from 0.0025 to 0.01 kg/m3, with wind speeds typically 1–2 m/s at 1–2 m above the ground. For small frogs on the ground in a forest, sitting on leaf litter, we assumed that wind speeds at animal height ranged from negligible to 0.2 m/s. Precipitation could be rather local at 5 weather-station locations near the study site with rain falling at one location but missing others. We focused on the interval at each site between rainfall events with a minimum of either 5 or 10 mm of rain (sufficient to wet the forest floor and recharge the litter with water) (Fig. 9).
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Time scales for activity imposed by water exchanges
For over 60 years now, it has been clear that frogs vary in their tolerance of dehydration and that dehydration tolerance plays a role in the terrestrial activity of frogs (Thorson and Svihla 1943
), the idea being that a terrestrially active frog will inevitably lose water, and that tolerance of more severe dehydration could relax limits on times that frogs could be active. In this sense, the combination of water-loss rates and the minimum tolerated hydration level impose a limit on the time that animals can be active and away from a water source (sometimes called a release time, Tracy 1976; Schwarzkopf and Alford 1996). Dehydration tolerance is usually specified as the fraction of the original, fully hydrated mass that can be lost as water, or conversely the fraction of the fully hydrated mass at which the animal becomes impaired (by any of several criteria). Here we choose 80% of fully hydrated mass (20% of mass lost as water) as the minimum hydration level tolerated by wood frogs because at that level, wood frogs start showing impaired locomotion (O'Connor 1989). Using this ‘critical’ hydration level for a 15 g wood frog in typical April conditions, we calculated rates of evaporation and release times for animals active on the surface with a variety of wind speeds and water vapor densities. We also calculated exchanges for animals buried in leaf litter with several assumptions about leaf-litter thickness and structure (Table 3). For animals active on the surface, unless wind speeds are very low (still room air often has an air speed of 0.1 m/s) or the air is nearly saturated (vapor density = 0.015 kg/m3), surface activity will be limited to 90 min or less. On the other hand, when the air is nearly saturated (for example, when it is raining or has rained in the last hour or so), activity can extend to 4–6 h. Adding solar radiation would significantly shorten the frog's release time, but wood frogs are not typically active in bright sun so we did not simulate those conditions.
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Our model suggests that leaf litter provides a significant resistance to evaporation and that, depending on assumptions about the thickness and structure of the leaf litter, it can extend release times for inactive animals to several weeks (Table 3). Assuming that frogs rehydrate with significant rains and use leaf-litter refugia between rainstorms to delay dehydration, we calculated the distribution of dehydrations that would be reached before the next rainstorm under one of the scenarios from Table 3 (4 leaf layers, overlap 0.005 m, vapor density 0.005 kg.m3, Fig. 10). In this case, 15 of 92 intervals would have resulted in minimum hydration levels of 75% or less and 2 of 92 intervals could reach hydrations <55% of fully hydrated mass. These simulations suggest that animals faced a significant risk of lethal dehydration despite using leaf-litter refugia. These simulations were for rainfall in 2005 which included extended spring droughts for much of the region. The simulations suggest that frogs face 2 kinds of dehydration risks. The frogs can be active on the surface for only a few hours except in rainstorms (Heatwole 1961
). In-between rains, the frogs could use refugia, but if extended dry periods occur, they could still dehydrate.
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Caveats and limitations
In this case, less information is available than was the case for canyon lizards, and the purpose, rather than precise prediction, is analysis of the risks frogs face. Treating leaves like inert diffusion baffles is a simplifying assumption, and further work is necessary to justify that assumption. Further, the leaf-litter parameters in a large set of simulations (not presented) were used to bracket possible environmental values because actual values for the litter frequented by the frogs are lacking and likely vary in space and time. At this point, perhaps the most important conclusion is the suggestion that frogs must balance 2 types of dehydration risk, with the balance depending on frog activity, climate, and the characteristics of the leaf-litter refugia.
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Physiological models as tools |
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SynopsisIntroductionModelCanyon lizards (Sceloporus...Frogs: desiccation and activityPhysiological models as toolsSummaryREFERENCES |
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There would be little reason to build, use, or analyze models if empirical data were already available for the hypotheses in which we were interested. Indeed, classical justifications for modeling include the ability to analyze hypotheses that would be impossible, difficult, or impractical to examine empirically, the opportunity to isolate particular factors from confounding variables that are unavoidable in nature, and the ability to strip a complicated system down to its essential features (Levins 1968
; Gotelli 1995; Keener and Sneyd 1998; Thieme 2003; Grimm and Railsback 2005). If one needs to explore the effects of conditions that do not yet exist (for example, the effects of a 5°C increase in mean air temperatures due to global warming), those abilities are clearly valuable. Alternatively, if one needs to consider processes that extend through numerous years, models can also be helpful. An impressive literature debates the utility of models; we do not propose to reproduce that debate here. We find models useful, and seek to describe how we find them helpful for linking physiology to ecology and conservation.
Advantages of models
We argue, however, that the fundamental value of models as tools to connect physiology to ecology and conservation is the ability to reveal assumptions that underlie hypotheses, explore the sensitivities of systems to perturbations and features of the biology, and map complex relationships among variables. Since Descartes, the importance and necessity of assumptions underlying our ideas has been relatively clear. In complex ecological systems, however, unrecognized assumptions can be important and have been at the center of major controversies, for example, the role of competition in structuring communities (Connell 1983) and the role of optimality in behavior and physiology (Pyke 1984; Weibel and others 1998). In our model of canyon-lizard dynamics, 2 simple (and plausible) assumptions can affect the predicted outcomes of the model, and have affected previous models. First, the assumption that animals at different elevations would tolerate and experience similar body temperatures can strongly affect predicted energy intakes, metabolic costs, and net energy accumulation (Fig. 6). The ability of animals at the warmer, lower elevation sites to tolerate and use higher afternoon body temperatures extended activity times, increased predicted energy intakes, metabolic costs, and net energy accumulation—weakly at Boquillas and more strongly at Grapevine Hills (Fig. 6)—and led to qualitatively different predictions about relative energy accumulation at Grapevine Hills and Maple Canyon (Fig. 6c and d). The virtue of the modeling process is that it both makes an assumption explicit and allows exploration of the importance of that assumption. Similarly, the assumption that energy intakes are dictated primarily by the availability of food and not by the digestive processing of ingested food could further influence predicted resource accumulation at the Grapevine Hills and Maple Canyon sites (Fig. 7). In building models connecting physiology to population level phenomena, our experience has been that assumptions often involve areas in which potential polymorphisms or adaptations on the part of the animal can affect the animal's population biology, as is the case for both of the assumptions discussed here. Hence, the role of modeling in identifying, dissecting, and evaluating such assumptions is a potentially important contribution to the conservation of the animal.
A sensitivity analysis asks how model outputs vary with changes in model inputs (Caswell 2001; Grimm and Railsback 2005). Mathematically, a sensitivity analysis estimates the derivative of a model's output with regard to some input. Biologically, sensitivity analyses reveal which inputs strongly affect system behavior, and under what circumstances they do so. Here, Figures 6 and 7 and Table 3 present the results of sensitivity analyses. We believe that such sensitivity analyses are critical in linking physiological effects to ecology and conservation.
We argue that the most important obstacle to understanding the mechanisms linking physiology to population ecology is the complexity of the mechanistic linkages. Specifically, we argue that many of the physiological processes affecting animal autecology will be characterized by non-linearities, (for example, threshold effects, saturable processes, curvilinear relationships among variables, and time lags in processes) and by competitive and synergistic effects between factors (Dreisig 1984). Further, multiple abiotic factors and physiological systems are likely to affect an animal's ecology interactively without a single dominating factor (Porter and Tracy 1983). For instance, desert reptiles must "balance" highly interrelated budgets for thermal energy (thermoregulation), water, chemical energy, and activity (Dunham and others 1989) (Fig. 1). Each of the budgets depends on the others in complicated ways (Nagy and others 1984; Adolf and Porter 1993; Dunham and Beaupre 1998).
To illustrate the complexity of such interdependences, we present sensitivity analyses (Fig. 11) from a predecessor to the canyon-lizard model presented above. In this model, we envisioned a desert-dwelling reptile that needed to avoid lethal temperatures and acquire both water and energy needed for growth and reproduction. Figure 11 presents the sensitivity of a single predicted response variable (available activity time) to changes in the environment (minimum and maximum daily air temperatures, burrow [refugium] temperature, and density and caloric and water content of food) and in the animal's physiology (maximum tolerated body temperature, metabolic rate, and cutaneous water vapor conductivity). Figures 11A and B present estimates of activity time as each of the input variables is changed in a stepwise manner from baseline values. In some cases, predicted activity time is not sensitive to the input variable (for example, minimum daily air temperature, "Tmin"; caloric content of food, "Endens"). In other cases, predicted activity time is linearly related to the input (burrow temperature, "Tburr"). In yet other cases, however, threshold effects (food density, "fddens"; metabolic rate, "Mrbase") and sigmoid responses (maximum tolerated body temperature, "Tblim") are seen. In Fig. 11C, we find the simulated activity time for a series of randomly chosen combinations of input parameters, and for the response predicted by adding together the one-at-a-time effects presented in Figs 11A and B. Although the 2 measures are correlated, the one-at-a-time predictions are poor predictors of the simulated activity time, in part because of the non-linearities in Figs 11A and B, and in part, because of interactions among the input parameter effects.
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Such non-linear, multi-causal relationships are difficult to study and document, and are poorly probed by analytic techniques that consider one factor at a time and/or depend on linear relationships among variables (Dunham and Beaupre 1998
). One of the fundamental problems of employing such techniques to probe the relationship between physiological and population data is that the non-linearity of effects and the interaction of multiple processes can produce patterns that are plausible and understandable once discovered, but are non-intuitive and difficult to predict a priori (for example, Dunham and others 1989). Thus, complicated non-linear ecological systems are likely to result in patterns that are difficult to anticipate from the physiological processes alone (Kauffman 1993; Williams 1997). Given the short time frame sometimes available in conservation assessments, we should note that models can be developed rapidly and independently of seasonal and annual activity cycles. Each of the models presented here was developed in under a year.
Disadvantages of models
We find 2 major disadvantages of models linking physiology to conservation questions. First, if model results are sensitive to input parameters or sets of parameters, then poor estimates of the parameters will lead to poor predictions. This is the equivalent of the old programming aphorism "garbage in, garbage out." The problem, for complicated models that depend on data-based parameter estimates for an animal under consideration (for example, the canyon-lizard model), is that we may not have data on the physiological or environmental characteristics for the population in which we are interested. We then tend to substitute data from nearby locations or similar species (for example, the weather data from towns near the wood-frog study sites above). While this is defensible and in many cases necessary, in so doing, we adopt the implicit assumption that the nearby population does not differ from the focal population. For example, previous models (A. Dunham unpublished data) of canyon-lizard dynamics used afternoon body temperatures drawn from the morning temperatures of the animals. For the highest elevation, Maple Canyon, this agrees with data (Grant and Dunham 1990). For the other sites, the data differ, and Fig. 6 suggests that this would affect predicted energy accumulation.
A second danger results if one forgets that a model is only a model and that all models are deliberate simplifications of complex systems. Simplifying assumptions, like adopted data, can fail to accurately reflect the ecology of the animal in which we are interested. All ecological data, empirical or model based, can be inappropriately applied, but as we noted above, applying models when their assumptions may not be satisfied has been the basis of numerous debates in ecology. Our preference is to make models as mechanistic as possible in the hopes that assumptions will be clear, and to treat all model predictions as hypotheses that are subject to empirical verification.
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SynopsisIntroductionModelCanyon lizards (Sceloporus...Frogs: desiccation and activityPhysiological models as toolsSummaryREFERENCES |
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We present resource accumulation models as a tool to link physiology to conservation questions. We give 2 very different examples—one in a well-described system in which numerous factors needed to be integrated to produce a useful population level synthesis, another in a system with less available data where the objective is to explore a system with relatively simple questions. In each case, we used an elaboration of the Dunham and colleagues (1989)
model that picks activity as a way to harvest resources useful in growth and reproduction and, hence, as a useful axis of analysis. We then seek the effects of physiological and environmental processes on activity and resource budgets. We suggest that such an approach is generalizable and easily adapted to situations where physiology may be a key factor in the population level ecology and conservation of animals. |
Acknowledgements |
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We thank Ray Semlitsch, Tracy Rittenhouse, and their colleagues for sharing their experiences and discussions of frog behavior and ecology in their ongoing study. We also thank Salvatore Agosta, Harold Heatwole, and an anonymous reviewer for thoughtful comments on an earlier draft of this manuscript.
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From the symposium "Ecophysiology and Conservation: The Contributions of Energetics" presented at the annual meeting of the Society for Integrative and Comparative Biology, January 4–8, 2006, at Orlando, Florida.
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