A population’s rate of change is central to theory and empirical studies of ecology [1–5], evolution [6–8], and disease transmission [9, 10]. Many populations will have population growth that is affected by population density , and density dependent effects on population rate of change are thus central to understanding population dynamics. Density dependence may result from resource competition [12, 13], availability of mates , social interactions , or dispersal . Resource limitation is likely the most postulated process producing density dependent effects via increasing death rates, decreasing birth rates, or decreasing individual growth rates [17, 18]. Ultimately, when these density dependent effects act on individuals the population’s per capita growth rate is influenced. Such density dependent effects, acting on individuals, ultimately influence per capita growth rate (19, 20).
Understanding density dependent effects on population growth can be especially important for investigations of disease vectors [18, 21–26]. Vectors are often targets of control efforts that may change population density, and thus may alter survival, growth, development, or fecundity. For vector mosquitoes, both field and laboratory studies indicate that density dependent effects on larvae can be strong, and can impact survival, individual growth rate (and resulting size and fecundity), and development rate (and resulting age at first reproduction) [e.g., 21, 23, 24, 27–33].
Ecological models of population per capita rate of change, such as Verhulst’s logistic or Lotka-Volterra models, postulate a linear relationship of per capita growth to intra- or inter-specific density [1, 34, 35]; however, for most organisms the relationship between density and per capita growth rate is not well known [36–38], and a linear relationship is only one possibility. Many of the relationships between density and the demographic components of population dynamics (e.g., survivorship, fecundity, reproductive age) are non-linear . Multiple studies point out the apparent flaw in the assumption of linearity, and among the few studies explicitly testing the form of the relationship between density and per capita growth rates, nonlinearity has been documented repeatedly [e.g., 11, 35, 39–41]. Additionally, individual based models of resource competition suggest that multiple aspects of species biology can produce nonlinear relationships of per capita growth to population density . Whether relationships between per capita growth and population density are linear is an important question, as nonlinearity would indicate that the effects of population density and resource use on population growth rate are not uniform across density (as they are modeled in simple logistic growth). Thus, the effects of increasing density may depress growth most strongly at low or high densities, and therefore may relate to rates of population recovery from low density [11, 42].
Determining the relationship between population density and per capita growth is likely to improve predictions and models of vector populations. Models assuming linear effects of intraspecific density on per capita rate of increase have been used to estimate logistic growth models of vector mosquitoes [34, 43], or to test theoretical predictions about responses to mortality [5, 45]. Models assuming linear effects of both intra- and interspecific densities have been used often to evaluate potential for coexistence of competing vector species [24, 45–51]. Among these investigations, only  tested explicitly alternative models for the relationship of estimated growth rate to densities; they found the best model to be one with linear relationships of estimated finite per capita rate of increase to density for A. aegypti.
To investigate the relationship between density and per capita growth we use three important vector species: Aedes aegypti, Aedes albopictus, and Aedes triseriatus. These species are an excellent model system for studies of population dynamics and density dependence for several reasons. First, these container-dwelling mosquitoes appear to be often impacted by density dependent effects in nature [e.g., 21, 28, 31–33, 52]. As container-dwelling mosquitoes they are easily reared in the laboratory in conditions that simulate natural environments in a realistic way. All three have often been the subject of population studies using Livdahl and Sugihara’s composite index of performance , which uses a life table approach to estimate per capita rate of change for large experimental cohorts . Use of this index facilitates rearing of high-density cohorts with substantial replication because it removes the necessity of following adult females for their entire lives to obtain per capita rate of increase from a full life table . Two separate laboratory studies have shown that this index is highly correlated with per capita rate of increase estimated from a full life table following reproduction of 100% of a cohort of females [41, 53]. Finally, all three species are important vectors of human diseases and have been targets of control efforts that may alter densities of larvae, thus altering density-dependent effects on population growth, production of adults, and other traits relevant to vectorial capacities .
Here, we investigate the relationship between larval density and the estimated per capita rate of increase as calculated by the index of performance, and the component variables that are used to calculate the index: survivorship to adulthood; adult female development time; and adult female size as a predictor of female fecundity. The primary objective was to determine whether the relationship of estimated per capita rate of increase to larval density is best fit by a linear logistic growth model, or alternative nonlinear models: θ logisitic; Gompertz; or polynomial. We hypothesized that the relationship between density and per capita growth is in fact non-linear. Additionally, we tested for nonlinearities in the relationships of component variables (survivorship, development time, adult size) to larval density and evaluated how those components may contribute to any nonlinear relationship observed for estimated per capita rate of increase.