The scale transition: scaling up population dynamics with field data

Applying the recent developments of scale transition theory, we demonstrate a systematic approach to the problem of scaling up local scale interactions to regional scale dynamics with field data. Dynamics on larger spatial scales differ from the predictions of local dynamics alone because of an interaction between nonlinearity in population dynamics at the local scale and spatial variation in density and environmental factors over the regional population. Our systematic approach to scaling up involves the following five steps. First, define a model for dynamics on the local spatial scale. Second, apply scale transition theory to identify key interactions between nonlinearity and spatial variation that translate local dynamics to the regional scale. Third, measure local-scale model parameters to determine nonlinearities at local scales. Fourth, measure spatial variation. Finally, combine nonlinearity and variation measures to obtain the scale transition. Using field data for the dynamics of grazers and periphyton in a freshwater stream, we show that scale transition terms greatly reduce the growth and equilibrium density of the periphyton population at the stream scale compared to rock scale populations, confirming the importance of spatial mechanisms to stream-scale dynamics.     

Spatial selection and inheritance: applying evolutionary concepts to population dynamics in heterogeneous space

Organisms in highly suitable sites generally produce more offspring, and offspring can inherit this suitability by not dispersing far. This combination of spatial selection and spatial inheritance acts to bias the distribution of organisms toward suitable sites and thereby increase mean fitness (i.e., per capita population increase). Thus, population growth rates in heterogeneous space change over time by a process conceptually analogous to evolution by natural selection, opening avenues for theoretical cross-pollination between evolutionary biology and ecology. We operationally define spatial inheritance and spatial selective differential and then combine these two factors in a modification of the breeder's equation, derived from simple models of population growth in heterogeneous space. The modified breeder's equation yields a conservative criterion for persistence in hostile environments estimable from field measurements. We apply this framework for understanding gypsy moth population persistence amidst abundant predators and find that the predictions of the modified breeder's equation match initial changes in population growth rate in independent simulation output. The analogy between spatial dynamics and natural selection conceptually links ecology and evolution, provides a spatially implicit framework for modeling spatial population dynamics, and represents an important null model for studying habitat selection.     

Distribution patterns,abundance and population dynamics of the euphausiidsNyctiphanes capensis andEuphausia hanseni in the northern Benguela upwelling system

Distribution patterns, population structure and biomass of the euphausiidsNyctiphanes capensis andEuphausia hanseni were examined off the coast of Namibia, southwest Africa, in relation to temperature, depth and season, from data collected on nine surveys from September 1982 to March 1984. High densities ofN. capensis were found in the shallow coastal waters (<200 m), with the biomass of adults ranging from 675 to 5 706 mg dry wt m^–2. For adultE. hanseni, the biomass was an order of magnitude lower, ranging from 65 to 505 mg dry wt m^–2, with most specimens occurring over the shelf break at depths of 200 to 1000 m. These distribution patterns remained relatively constant throughout the year, despite seasonal differences in upwelling events. Both species displayed continuous breeding, with 43 to 82% of the adult femaleE. hanseni being fertilized, while a much lower proportion ofN. capensis females were reproductively active (0.5 to 26%). Different breeding strategies were adopted by these two euphausiid species, withE. hanseni producing frequent broods (14.8 broods in 6 mo) consisting of relatively large eggs which are released into the sea, andN. capensis exhibiting a lower frequency of spawning, with broods consisting of large numbers of relatively small eggs, protected by a brood pouch. These strategies enable both species to maintain high densities throughout the year in a fluctuating physical environment. Growth rate estimated from size-frequency distributions were 0.003 to 0.063 mm d^–1 forN. capensis and 0.077 to 0.083 mm d^–1 forE. hanseni, suggesting an adult lifespan of approximately 6 mo for both species. Maximum sizes were attained in September, withN. capensis reaching a total length of 21 mm (in contrast to all previous studies onN. capensis, where the maximum size recorded was only 13 mm total length) andE. hanseni a total length of 33 mm.     

Aggregation dynamics in juvenile queen conch (Strombus gigas): population structure,mortality, growth,and migration

Juvenile queen conch (Strombus gigas L.) occur in discrete aggregations within seemingly uniform seagrass beds throughout the Exuma Cays, Bahamas, suggesting that the aggregations occupy ecologically unique sectors of the habitat or that conch gain fitness by aggregated distribution. To examine the structure of a juvenile aggregation and to determine the underlying mechanisms which affect juvenile conch distribution, we axamined density, size composition, growth, survivorship, and movement patterns within a typical tidal-flow field nursery over a 14 mo period (August 1989 to September 1990). At the beginning of the study in August 1989, the conch population occupied 16.7 ha, with densities>0.2 juvenile conch m^-2. The aggregation formed an ellipse, with longitudinal axis parallel to the main axis of the tidal current. Surveys conducted every 2 mo showed that conch density in the aggregation center remained constant while all other zones had lower densities which varied with time. In areas of high population density within the aggregation, several mass migrations of juveniles (20 to 99 conch m^-2) occurred in early 1990. Tagged juveniles transplanted to zones outside the aggregation had high growth rates but suffered higher losses than individuals transplanted to the aggregation center. A tethering experiment confirmed the hypothesis that predator-induced mortality is significantly higher outside than inside the conch aggregation. Our results suggest that the queen conch aggregation occupied only a portion of the habitat that is optimal for feeding and growth. Aggregations could be maintained by differential mortality over a site; however, predation rates are probably density-dependent. Gregariousness, observed in translocation experiments, may provide an active mechanism for maintaining aggregated distribution and reducing mortality in conch nurseries. The ecological significance of aggregations should be considered in fisheries management and stock enhancement programs with queen conch.     

Spatio-temporal population dynamics of the sand snail Umbonium costatum: importance of ontogenetic migration and annual recruitment variability

The spatio-temporal population dynamics of the subtidal snail Umbonium costatum (Kiener) in Hakodate Bay, northern Japan, are described over a 9-yr period (1982 to 1988, 1992). Annual variations in recruitment success not only caused the highly variable age structure of the population, but also affected its distribution pattern. In heavy recruitment years (1982, 1984 and 1988), location of the densest population differed from the other years, and the areas with 0 yr old individuals were larger. Every year, the distribution of 0 yr olds was mostly restricted to inshore (within 320 m from shore), while the distribution of adults (>0 yr) was mostly restricted to offshore (>320 m from shore). Such patterns may be generated by ontogenetic migration of cohorts to offshore areas. Ontogenetic migration also could have buffered the large annual variation in spat distribution and maintained the small variation in the distribution of adults. (Prince et al. 1988). Density-related migration has also been reported in Acmaea digitalis (Frank 1965), Patella cochlear (Branch 1974) and Patelloida alticostata (Black 1977).Dense populations of the gastropod Umbonium costatum are found in some clean subtidal sandy-bottoms in Japan, e.g. inner part of Hakodate Bay. In the bay, the age structure of U. costatum revealed predominant year-classes. The 0 yr olds were restricted to the shallowest zone (<4 m depth) and most adult (<0 yr) cohorts were restricted to 6 to 7 m depths (Noda 1991a).This paper describes the temporal variability of population structure and distributional patterns of Umbonium costatum, and examines the distribution-regulating processes.     

Reproductive cycle,larval development,juvenile growth and population dynamics of Patiriella pseudoexigua (Echinodermata: Asteroidea) in Taiwan

A field study was conducted at Wanlitung, southern Taiwan, in 1986–1089, to determine the reproductive cycle, development mode, growth rate and population dynamics of the small seastar Patiriella pseudoexigua (Dartnall), which occurs in highly stressful and disturbed intertidal pools in this area. An inverse relationship between gonad index and pyloric-caccum index was only recorded immediately prior to spawning. A short, well-synchronized seasonal spawning occurs in October. When reared at 25 °C, lecithotrophic larvae develop directly, lack a bipinnaria stage, and metamorphose completely on the seventh day after fertilization. The growth curves of field juveniles are linear, those of laboratory-reared juveniles are sigmoid. Juveniles appear in tide pools in spring-early summer of each year. Adults spawn mainly in late fall, enabling spawning to occur in time for the larvae to benefit from the environmentally favorable winter season. Populations in high-tidal pools decrease in later summer, but remain more stable in lowtidal pools and lagoons.     

The ecological niche of Daphnia magna characterized using population growth rate

The concept of an organism's niche is central to ecological theory, but an operational definition is needed that allows both its experimental delineation and interpretation of field distributions of the species. Here we use population growth rate (hereafter, pgr) to define the niche as the set of points in niche space where pgr > 0. If there are just two axes to the niche space, their relationship to pgr can be pictured as a contour map in which pgr varies along the axes in the same way that the height of land above sea level varies with latitude and longitude. In laboratory experiments we measured the pgr of Daphnia magna over a grid of values of pH and Ca2+, and so defined its "laboratory niche" in pH-Ca2+ space. The position of the laboratory niche boundary suggests that population persistence is only possible above 0.5 mg Ca2+/L and between pH 5.75 and pH 9, though more Ca2+ is needed at lower pH values. To see how well the measured niche predicts the field distribution of D. magna, we examined relevant field data from 422 sites in England and Wales. Of the 58 colonized water bodies, 56 lay within the laboratory niche. Very few of the sites near the niche boundary were colonized, probably because pgr there is so low that populations are vulnerable to extinction by other factors. Our study shows how the niche can be quantified and used to predict field distributions successfully.     

Spatial variation in population dynamics in a colonial ascidian (Botryllus schlosseri)

Recent interest in the dynamics of marine invertebrate populations has focused largely on taxa with an open population structure. However, in many colonial taxa with limited larval dispersal, settlers may be locally derived. Consequently, dynamics may vary among sites that are separated by relatively short distances. This study explored spatial variation in temporal dynamics of colonial ascidians (Botryllus schlosseri Pallas) inhabiting five sites distributed along a ≈ 17-km temperature and phytoplankton gradient in the Damariscotta River estuary, Maine, USA. Settlement and population densities and sexual reproductive status were assayed throughout the summer seasons of 1996 and 1997. Sexual reproduction and larval settlement commenced earlier in the summer in up-river populations, which subsequently underwent a seasonal population explosion that was much smalier in down-river populations. Two peaks in settlement density up-river (in early July and early September) suggest that colonies there may have completed two sexual generations, in contrast to a single generation at down-river sites. Similar spatial variation is expected among populations of other taxa with limited larval dispersal when they are distributed across environmental gradients. Published online: 18 September 2002     

On the use of growth rate parameters for projecting population sizes: Application to aphids

This paper extends the application of the cumulative size based mechanistic model, which has previously been shown to describe diverse aphid population size data well. The mechanistic model is reviewed with a focus on the explanatory role of the birth and death rate formulation. An analysis of two data sets, one on the mustard aphid and the other on the pecan aphid, indicates that multiple linear regression equations based on the estimated birth and death rate parameters alone account for nearly all (R² > 0.95) of the variability in two key population attributes, namely the peak count and the cumulative density. This indicates that population size variables may be projected directly from the growth rate parameters using linear equations. Such linear relationships based on the birth and death rate parameters are shown to hold also for certain generalized mechanistic models for which the analytical solution is not available. The birth and death rate coefficients, therefore, constitute a new succinct set of variables that could be included in the predictive modeling of aphid populations, as well as other insect and animal populations with local collapse which follow similar growth dynamics.     

Chihuahuan Desert kangaroo rats: nonlinear effects of population dynamics, competition, and rainfall

Using long-term data on two kangaroo rats in the Chihuahuan Desert of North America, we fitted logistic models including the exogenous effects of seasonal rainfall patterns. Our aim was to test the effects of intraspecific interactions and seasonal rainfall in explaining and predicting the numerical fluctuations of these two kangaroo rats. We found that logistic models fit both data sets quite well; Dipodomys merriami showed lower maximum per capita growth rates than Dipodomys ordii, and in both cases logistic models were nonlinear. Summer rainfall appears to be the most important exogenous effect for both rodent populations; models including this variable were able to predict independent data better than models including winter rainfall. D. merriami was also negatively affected by another kangaroo rat (Dipodomys spectabilis), consistent with previous experimental evidence. We hypothesized that summer rainfall influences the carrying capacity of the environment by affecting seed availability and the intensity of intraspecific competition.     

Metabolic scaling,buoyancy, and growth in larval Atlantic menhaden,Brevoortia tyrannus

We measured growth of larval Atlantic menhaden, Brevoortia tyrannus in terms of mass, volume, and weight in water as well as the mass-specific activities of the metabolic enzymes citrate synthase, lactate dehydrogenase, and malate dehydrogenase. Weight in water, the force the fish must exert to maintain vertical position, increases by a factor of 18 in larvae growing from 10 to 15 mm. The weight increase coincides with the development of the larval swim bladder. The activities of all three enzymes per unit mass of fish tissue decline greatly over this time period, indicating that the fish does not further develop its aerobic and anaerobic metabolic capacity for swimming during this growth interval.     

Spatial structure, sampling design and abundance estimates in sandy beach macroinfauna: some warnings and new perspectives

We discuss methodological aspects directed to quantify the across-shore population structure and abundance of sandy beach macroinfauna. The reliability of estimates derived from design-based (stratified random sampling) and model-based (geostatistics, kriging) approaches is discussed. Our analysis also addresses potential biases arising from environmentally driven designs that consider a priori fixed strata for sampling macroinfauna, as opposed to species-driven sampling designs, in which the entire range of across-shore distribution is covered. Model-based approaches showed, spatially, highly autocorrelated and persistent structures in two intertidal populations of the Uruguayan coast: the isopod Excirolana armata and the yellow clam Mesodesma mactroides. Both populations presented zonation patterns that ranged from the base of the dunes to upper levels of the subtidal. The Gaussian model consistently explained the spatial distribution of species and population components (clam recruits and adults), with a minor contribution (Е%) of unresolved, small-scale variability. The consistent structure of spatial dependence in annual data strongly suggests an across-shore-structured process covering close to 35 m. Kriging predictions through cross-validation corroborated the appropriateness of the models fitted through variographic analysis, and the derived abundance estimates were very similar (maximum difference=7%) to those obtained from linear interpolation. Monthly analysis of E. armata data showed marked variations in its zonation and an unstable spatial structure according to the Gaussian model. The clear spatial structure resulting from species-driven sampling was not observed when data was truncated to simulate an environmentally driven sampling design. In this case, the linear semivariogram indicated a spatial gradient, suggesting that sampling was not performed at the appropriate spatial scale. Further, the cross-validation procedure was not significant, and both density and total abundance were underestimated. We conclude that: (1) geostatistics provides useful additional information about population structure and aids in direct abundance estimation; thus we suggest it as a powerful tool for further applications in the study of sandy beach macroinfauna; and that (2) environmentally driven sampling strategies fail to provide conclusive results about population structure and abundance, and should be avoided in studies of sandy beach populations. This is especially true for microtidal beaches, where unpredictable swash strength precludes a priori stratification through environmental reference points. The need to use adaptive sampling designs and avoid snapshot sampling is also stressed. Methodological implications for the detection of macroecological patterns in sandy beach macroinfauna are also discussed.     

Demographic heterogeneity, cohort selection, and population growth

Demographic heterogeneity--variation among individuals in survival and reproduction--is ubiquitous in natural populations. Structured population models address heterogeneity due to age, size, or major developmental stages. However, other important sources of demographic heterogeneity, such as genetic variation, spatial heterogeneity in the environment, maternal effects, and differential exposure to stressors, are often not easily measured and hence are modeled as stochasticity. Recent research has elucidated the role of demographic heterogeneity in changing the magnitude of demographic stochasticity in small populations. Here we demonstrate a previously unrecognized effect: heterogeneous survival in long-lived species can increase the long-term growth rate in populations of any size. We illustrate this result using simple models in which each individual's annual survival rate is independent of age but survival may differ among individuals within a cohort. Similar models, but with nonoverlapping generations, have been extensively studied by demographers, who showed that, because the more "frail" individuals are more likely to die at a young age, the average survival rate of the cohort increases with age. Within ecology and evolution, this phenomenon of "cohort selection" is increasingly appreciated as a confounding factor in studies of senescence. We show that, when placed in a population model with overlapping generations, this heterogeneity also causes the asymptotic population growth rate lambda to increase, relative to a homogeneous population with the same mean survival rate at birth. The increase occurs because, even integrating over all the cohorts in the population, the population becomes increasingly dominated by the more robust individuals. The growth rate increases monotonically with the variance in survival rates, and the effect can be substantial, easily doubling the growth rate of slow-growing populations. Correlations between parent and offspring phenotype change the magnitude of the increase in lambda, but the increase occurs even for negative parent-offspring correlations. The effect of heterogeneity in reproductive rate on lambda is quite different: growth rate increases with reproductive heterogeneity for positive parent-offspring correlation but decreases for negative parent-offspring correlation. These effects of demographic heterogeneity on lambda have important implications for population dynamics, population viability analysis, and evolution.     

Social dynamics of juvenile marmots: Role of kinship and individual variability

Summary A population of eight juvenile female yellow-bellied marmots (Marmota flaviventris) was introduced into a marmot locality from which all other marmots were removed. Social interactions were monitored in the field and the individual behavioral profile of each animal was determined by mirror image stimulation. Social interactions were unequally distributed among the eight juveniles. Neither body size nor kinship were significantly related to frequencies of social interactions. Social interactions were significantly related to individual differences.     

Enchytraeid population dynamics: Resource limitation and size-dependent mortality

Enchytraeids are regarded as keystone soil organisms in forest ecosystems. Their abundance and biomass fluctuate widely. Predicting the consequences of anthropogenic disturbances requires an understanding of the mechanisms underlying enchytraeid population dynamics. Here I develop a simple model, which predicts that the type of dynamics is controlled by resource input rate. If fungal resource input is a discrete event once a year, an exponential growth phase is followed by starvation and sharp decline of enchytraeid abundance. Model simulations with three different forcing functions were compared to field data. Initial parameter values were obtained from various independent sources, and parameters were estimated by minimizing the residual sum of squares. The best fitting model with resource addition once a year explained 39% of the variation in enchytraeid biomass over an 8-year study period. Further, variation in rainfall explained 59% of the variation in R² of the exponential phase models, which is also an index of the stability of population size-structure. The results emphasize the importance of resource limitation for enchytraeid population dynamics and support the hypothesis that the mortality during the decline phase is size-dependent.     

Large nonlethal effects of an invasive invertebrate predator on zooplankton population growth rate

We conducted a study to determine the contribution of lethal and nonlethal effects to a predator's net effect on a prey's population growth rate in a natural setting. We focused on the effects of an invasive invertebrate predator, Bythotrephes longimanus, on zooplankton prey populations in Lakes Michigan and Erie. Field data taken at multiple dates and locations in both systems indicated that the prey species Daphnia mendotae, Daphnia retrocurva, and Bosmina longirostris inhabited deeper portions of the water column as Bythotrephes biomass increased, possibly as an avoidance response to predation. This induced migration reduces predation risk but also can reduce birth rate due to exposure to cooler temperatures. We estimated the nonlethal (i.e., resulting from reduced birth rate) and lethal (i.e., consumptive) effects of Bythotrephes on D. mendotae and Bosmina longirostris. These estimates used diel field survey data of the vertical gradient of zooplankton prey density, Bythotrephes density, light intensity, and temperature with growth and predation rate models derived from laboratory studies. Results indicate that nonlethal effects played a substantial role in the net effect of Bythotrephes on several prey population growth rates in the field, with nonlethal effects on the same order of magnitude as or greater (up to 10-fold) than lethal effects. Our results further indicate that invasive species can have strong nonlethal, behaviorally based effects, despite short evolutionary coexistence with prey species.     

Spatial patterns of macroalgal abundance in relation to eutrophication

Based on a large monitoring data set from Danish coastal waters we tested the hypotheses: (1) The vertical pattern of algal abundance is regulated by exposure in shallow water and by light limitation towards deeper water, resulting in a bell-shaped abundance curve, with peak abundance located deeper at more exposed sites, (2) in deeper water, total algal abundance and abundance of perennial algae decrease along a eutrophication gradient while (3) abundance and relative abundance of opportunists increase. The vertical pattern of algal abundance showed a peak at intermediate water depths which was located deeper in more exposed areas and thus confirmed our first hypothesis. For algae growing from depths of peak abundance and deeper, the study demonstrated that total algal abundance and abundance of perennials and opportunists at given depths decreased significantly along a eutrophication gradient and the relationships had high explanatory power (R ² = 0.53–0.73). These results confirmed our second hypothesis. By contrast, the relative abundance of opportunists responded solely to salinity and was largest in the most brackish areas, in contradiction to hypothesis three. The lack of coupling between eutrophication and relative abundance of opportunists arises because both opportunists and the entire algal community were light limited and their ratio therefore relatively insensitive to changing water clarity. The analyses indicated that algal abundance initially responded slowly to increasing eutrophication but showed a more marked response at TN concentrations of 35–40 μM. However, the existence of possible threshold nutrient levels demands further analyses.     

Forecasting population trend from the scaling pattern of occupancy

Forecasting the temporal trend of a focal species, its range expansion or retraction, provides crucial information regarding population viability. To this end, we require the accumulation of temporal records which is evidently time consuming. Progress in spatial data capturing has enabled rapid and accurate assessment of species distribution across large scales. Therefore, it would be appealing to infer the temporal trends of populations from the spatial structure of their distributions. Based on a combination of models from the fields of range dynamics, occupancy scaling and spatial autocorrelation, here I present a model for forecasting the population trend solely from its spatial distribution. Numerical tests using cellular automata confirm a positive correlation, as inferred from the model, between the temporal change in species range sizes and the exponent of the power-law scaling pattern of occupancy. The model is thus recommended for rapid estimation of species range dynamics from a single snapshot of its current distribution. Further applications in biodiversity conservation could provide a swift risk assessment, especially, for endangered and invasive species.     

Interannual variability of growth and reproduction in Bursera simaruba: the role of allometry and resource variability

Plants are expected to differentially allocate resources to reproduction, growth, and survival in order to maximize overall fitness. Life history theory predicts that the allocation of resources to reproduction should occur at the expense of vegetative growth. Although it is known that both organism size and resource availability can influence life history traits, few studies have addressed how size dependencies of growth and reproduction and variation in resource supply jointly affect the coupling between growth and reproduction. In order to understand the relationship between growth and reproduction in the context of resource variability, we utilize a long-term observational data set consisting of 670 individual trees over a 10-year period within a local population of Bursera simaruba (L.) Sarg. We (1) quantify the functional form and variability in the growth-reproduction relationship at the population and individual-tree level and (2) develop a theoretical framework to understand the allometric dependence of growth and reproduction. Our findings suggest that the differential responses of allometric growth and reproduction to resource availability, both between years and between microsites, underlie the apparent relationship between growth and reproduction. Finally, we offer an alternative approach for quantifying the relationship between growth and reproduction that accounts for variation in allometries.     

Spatial anatomy of species survival: effects of predation and climate-driven environmental variability

The majority of survival analyses focus on temporal scales. Consequently, there is a limited understanding of how species survival varies over space and, ultimately, how spatial variability in the environment affects the temporal dynamics of species abundance. Using data from the Barents Sea, we study the spatiotemporal variability of the juvenile Atlantic cod (Gadus morhua) survival. We develop an index of spatial survival based on changes of juvenile cod distribution through their first winter of life (from age-0 to age-1) and study its variability in relation to biotic and abiotic factors. Over the 25 years analyzed (1980-2004), we found that, once the effect of passive drift due to dominant currents is accounted for, the area where age-0 cod survival was lowest coincided with the area of highest abundance of older cod. Within this critical region, the survival of age-0 cod was negatively affected by its own abundance, by that of older cod, and by bottom depth. Furthermore, during cold years, age-0 cod survival increased in the eastern and coldest portion of the examined area, which was typically avoided by older conspecifics. Based on these results we propose that within the examined area top-down mechanisms and predation-driven density dependence can strongly affect the spatial pattern of age-0 cod survival. Climate-related variables can also influence the spatial survival of age-0 cod by affecting their distribution and that of their predators. Results from these and similar studies, focusing on the spatial variability of survival rates, can be used to characterize species habitat quality of marine renewable resources.