Shape Of Density Dependence Research Articles

The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

The logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory, and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated. Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer–resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density‐regulation functions are usually non‐linear and may exhibit convex or concave curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the Schoener model. More complex consumer dynamics show similarities to a Maynard Smith–Slatkin model. We show how population‐level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. We propose simple relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer–resource systems. Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time‐series from microbial food chains to fit population growth models as a test case for our theoretical predictions. Our results show that density‐regulation functions need to be chosen carefully as their shapes will depend on the study system's biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

Evolution of population dynamics following invasion by a non-native predator.

Invasive predatory species are frequently observed to cause evolutionary responses in prey phenotypes, which in turn may lead to evolutionary shifts in the population dynamics of prey. Research has provided a link between rates of predation and the evolution of prey population growth in the lab, but studies from natural populations are rare. Here, we tested for evolutionary changes in population dynamics parameters of zooplankton Daphnia pulicaria following invasion by the predator Bythotrephes longimanus into Lake Kegonsa, Wisconsin, US. We used a resurrection ecological approach, whereby clones from pre‐ and post‐invasive periods were hatched from eggs obtained in sediment cores and were used in a 3‐month growth experiment. Based on these data, we estimated intrinsic population growth rates (r), the shape of density dependence (θ) and carrying capacities (K) using theta‐logistic models. We found that post‐invasion Daphnia maintained a higher r and K under these controlled, predation‐free laboratory conditions. Evidence for changes in θ was weaker. Whereas previous experimental evolution studies of predator–prey interactions have demonstrated that genotypes that have evolved under predation have inferior competitive ability when the predator is absent, this was not the case for the Daphnia. Given that our study was conducted in a laboratory environment and the possibility for genotype‐by‐environment interactions, extrapolating these apparent counterintuitive results to the wild should be done with caution. However, barring such complications, we discuss how selection for reduced predator exposure, either temporally or spatially, may have led to the observed changes. This scenario suggests that complexities in ecological interactions represents a challenge when predicting the evolutionary responses of population dynamics to changes in predation pressure in natural systems.

Population Density Effects on Carapace Growth in Clam Shrimp: Implications for Palaeontological Studies.

Fossil morphological data are time-averaged and generally reflect an overlap of different sources of carapace variability. To examine whether a proposed relationship between size and population density in fossil spinicaudatans is biologically meaningful, we set up rearing experiments involving two extant species: Eulimnadia texana and Eocyzicus argillaquus. Three and five days after hydration, clam shrimp were transferred into cups of various population densities that ranged between 1 and 15 inds/400 ml. Size and shape were measured 14 and 16 days after hydration, respectively. Every second day, we recorded length and sex of E. texana, which matured faster in lower-density cups. According to our growth model, population density and maximal carapace length follow a logarithmic relationship. At maturity, hermaphrodites yielded similar lengths across all population densities (~4.7 mm at 24°C), independent of age. Hence, clam shrimp can put off reproductive maturity as a response to decreased growth under higher density conditions. Growth rate generally decreases at maturity, but that effect is more pronounced in clam shrimp of high population densities, while low-density adults keep growing. For both species, multivariate analyses reveal that carapace size of low-density individuals is significantly larger than carapace size of higher-density individuals, while size values of intermediate densities cannot be distinguished. Shape distinction is strong in hermaphrodites of E. texana: 39.8% of the density-dependent shape variation is associated with relative umbo height, which is generally higher in individuals of smaller population densities. The H/L ratio, which is often used as a simple shape indicator, does not contribute to the main variation in shape, but it forms one of several ratios significant for 18.3% of the shape variability. In turn, the H/L ratio drives 30% of the shape variation in E. argillaquus. In addition, higher densities triggered shifts in ontogenetic growth trajectories in one third of the individuals, which led to aberrant morphologies. The present rearing experiment shows that some of the morphological variability on fossil bedding planes can be explained by population density. Also, it implies a considerable amount of ecophenotypic variability in Spinicaudata that affects our understanding of fossil taxonomy and palaeoecology.

Density‐dependent growth and survival in salmonids: Quantifying biological mechanisms and methodological biases

AbstractUnderstanding the complex variation in patterns of density‐dependent individual growth and survival across populations is critical to adaptive fisheries management, but the extent to which this variation is caused by biological or methodological differences is unclear. Consequently, we conducted a correlational meta‐analysis of published literature to investigate the relative importance of methodological and biological predictors on the shape and strength of density‐dependent individual growth and survival in salmonids. We obtained 160 effect sizes from 75 studies of 12 species conducted between 1977 and 2019 that differed in experimental approach (sensu Ecological Monographs, 54, 187–211; 65 laboratory experiments, 60 observational field studies, and 35 field experiments). The experimental approach was the strongest factor influencing the strength of density dependence across studies: density‐dependent survival was stronger than growth in field observational studies, whereas laboratory experiments detected stronger density‐dependent growth than survival. The difference between density‐dependent growth and survival was minimal in field experiments, and between lotic and lentic habitats. The shape of density dependence (logarithmic, linear, exponential or density‐independent) could be predicted with 66.7% accuracy based solely on the experimental approach and the density gradient (highest/lowest*100) of the study. Overall, the strength and shape of density dependence were primarily influenced by methodological predictors, while biological factors (predator presence, food abundance, and species) had predictable but modest effects. For both empirical studies and adaptive fisheries management, we recommend using field experiments with a density gradient of at least 470% to detect the proper shape of the density‐dependent response, or accounting for potential biases if observational or laboratory studies are conducted.

Application of the extended corresponding states model for prediction of the viscosity and thermal conductivity of cis-1,3,3,3-tetrafluoropropene (R1234ze(Z))

Prediction of the transport properties of low global warming potential refrigerants is a key issue for the refrigeration industry. In this work, the extended corresponding states models coupled with density-independent shape factors (empirical shape factors) or density-dependent shape factors (exact shape factors) are individually applied to predict the viscosity and thermal conductivity of 1,3,3,3-tetrafluoropropene (R1234ze(Z)). These models use 1,1,1,2-tetrafluoroethane (R134a) as a reference fluid. Empirical shape factors are obtained from the vapor pressures and saturated liquid densities of R1234ze(Z) and R134a. Exact shape factors are calculated from equations of state for these refrigerants. Predicted values with the extended corresponding states models are compared with experimental data, and the prediction capability of each model is discussed. In addition, viscosity and thermal conductivity shape factors are introduced to improve the prediction capability. With these additional shape factors, the extended corresponding states models represent the experimental data of the viscosity and thermal conductivity of R1234ze(Z) within ±2% and ±1%, respectively.

Density‐dependent life history and the dynamics of small populations

1. Small population dynamics depend importantly on the strength and shape of density dependence. Unfortunately, the lack of reliable life-history data often prevents to make accurate demographic predictions for populations regulated by density dependence. 2. We created a gradient from low to high densities in small experimental populations of common lizards (Zootoca vivipara) and investigated the shape and strength of the density dependence of life-history traits during a yearly cycle. We then analysed stochastic population dynamics using one-sex and two-sex age-structured matrix models. 3. Body growth and reproductive performances decreased with density, yearling and adult survival and body size at birth were density-independent, and juvenile survival increased with density. The density dependence of reproduction was partly explained by positive effects of body size on age at first reproduction and clutch size. 4. Parturition date decreased with density in sparse populations and then increased, providing one of the first empirical evidence of a component Allee effect in the phenology of reproduction. 5. Population growth rate (λ) was most affected by variations in juvenile and yearling survival. However, density at equilibrium was most affected by juvenile access to reproduction and yearling clutch size. 6. Stochastic simulations revealed that negative density dependence buffers the effects of initial density on extinction probability, has positive effects on the persistence of sparse populations and interacts with sex ratio fluctuations to shape extinction dynamics. 7. This study demonstrates that negative density dependence modifies the dynamics of small populations and should be investigated together with Allee effects to predict extinction risks.

Determining the Functional Form of Density Dependence: Deductive Approaches for Consumer‐Resource Systems Having a Single Resource

Consumer-resource models are used to deduce the functional form of density dependence in the consumer population. A general approach to determining the form of consumer density dependence is proposed; this involves determining the equilibrium (or average) population size for a series of different harvest rates. The relationship between a consumer's mortality and its equilibrium population size is explored for several one-consumer/one-resource models. The shape of density dependence in the resource and the shape of the numerical and functional responses all tend to be "inherited" by the consumer's density dependence. Consumer-resource models suggest that density dependence will very often have both concave and convex segments, something that is impossible under the commonly used theta-logistic model. A range of consumer-resource models predicts that consumer population size often declines at a decelerating rate with mortality at low mortality rates, is insensitive to or increases with mortality over a wide range of intermediate mortalities, and declines at a rapidly accelerating rate with increased mortality when mortality is high. This has important implications for management and conservation of natural populations.