Density dependence, population persistence, and largely futile arguments

Density dependence: an ecological Tower of Babel

The concept of density dependence represents the effect of changing population size on demographic rates and captures the demographic role of social and trophic mechanisms (e.g. competition, cooperation, parasitism or predation). Ecologists have coined more than 60 terms to denote different statistical and semantic properties of this concept, resulting in a formidable lexicon of synonymies and polysemies. We have examined the vocabulary of density dependence used in the modern ecological literature from the foundational lexicon developed by Smith, Allee, Haldane, Neave and Varley. A few simple rules suffice to abate terminological inconsistency and to enhance the biological meaning of this important concept. Correct citation of original references by ecologists and research journals could ameliorate terminological standards in our discipline and avoid linguistic confusion of mathematically and theoretically complex patterns.

Differential effects of weather and natural enemies on coexisting aphid populations

Study of mechanisms responsible for regulating populations of living organisms is essential for a better comprehension of the structure of biological communities and evolutionary forces in nature. Aphids (Hemiptera: Sternorrhyncha) comprise a large and economically important group of phytophagous insects distributed worldwide. Previous studies determined that density-dependent mechanisms play an important role in regulating their populations. However, only a few of those studies identified specific factors responsible for the observed regulation. Time series data used in this study originated from the untreated control plots that were a part of potato (Solanum tuberosum L.) insecticide trials in northern Maine from 1971 to 2004. The data set contained information on population densities of three potato-colonizing aphid species (buckthorn aphid, Aphis nasturtii; potato aphid, Macrosiphum euphorbiae; and green peach aphid, Myzus persicae) and their natural enemies. We used path analysis to explore effects of weather and natural enemies on the intrinsic growth rates of aphid populations. Weather factors considered in our analyses contributed to the regulation of aphid populations, either directly or through natural enemies. However, direct weather effects were in most cases detectable only at P ≤ 0.10. Potato aphids were negatively affected by both fungal disease and predators, although buckthorn aphids were negatively affected by predators only. Parasitoids did not have a noticeable effect on the growth of any of the three aphid species. Growth of green peach aphid populations was negatively influenced by interspecific interactions with the other two aphid species. Differential population regulation mechanisms detected in the current study might at least partially explain coexistence of three ecologically similar aphid species sharing the same host plant.

Estimating density dependence from population time series using demographic theory and life-history data

For populations with a density-dependent life history reproducing at discrete annual intervals, we analyze small or moderate fluctuations in population size around a stable equilibrium, which is applicable to many vertebrate populations. Using a life history having age at maturity alpha, with stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time lags from 1 to alpha yr. Contrary to current interpretations, the coefficients corresponding to different time lags in the autoregressive dynamics are not simply measures of delayed density dependence but also depend on life-history parameters. The theory indicates that the total density dependence in a life history, D, should be defined as the negative elasticity of population growth rate per generation with respect to change in population size, [Formula: see text], where lambda is the asymptotic multiplicative growth rate per year, T is the generation time, and N is adult population size. The total density dependence in the life history, D, can be estimated from the sum of the autoregression coefficients. We estimate D in populations of seven vertebrate species for which life-history studies and unusually long time series of complete population censuses are available. Estimates of D were statistically significant and large, on the order of 1 or higher, indicating strong density dependence in five of the seven species. We also show that life history can explain the qualitative features of population autocorrelation functions and power spectra and observations of increasing empirical variance in population size with increasing length of time series.

The demographic basis of population regulation in columbian ground squirrels

Environmental factors influence the dynamics and regulation of biological populations through their influences on demographic variables, but demographic mechanisms of population regulation have received little attention. We investigated the demographic basis of regulation of Columbian ground squirrel (Spermophilus columbianus) populations under natural and experimentally food-supplemented conditions. Food supplementation caused substantial increases in population density, and population densities returned to pretreatment levels when the supplementation ended. Control (untreated) populations remained relatively stable throughout the study period (1981-1986). Because food resources regulated the size of the ground squirrel populations, we used life-table response experiment (LTRE) analyses to examine the demographic basis of changes in population growth rate and thus also demographic influences on population regulation. LTRE analyses of two food-manipulated populations revealed that changes in age at maturity and fertility rate of females generally made the largest contributions to observed changes in population growth rate. Thus, our results suggested that abundance of food resources regulated the size of our study populations through the effects of food resources on age at maturity and fertility rates. Our results also indicated that different demographic mechanisms can underlie population regulation under different environmental conditions, because lower juvenile survival substantially contributed to population decline, but in only one of the populations. Demographic analyses of experimental data, such as those presented here, offer a rigorous and unambiguous means to elucidate the demographic basis of population regulation and to help identify environmental factors that underlie dynamics and regulation of biological populations.

Estimating density dependence in time-series of age-structured populations

For a life history with age at maturity alpha, and stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time-lags of from 1 to alpha years. Contrary to current interpretations, the coefficients for different time-lags in the autoregressive dynamics do not simply measure delayed density dependence, but also depend on life-history parameters. We define a new measure of total density dependence in a life history, D, as the negative elasticity of population growth rate per generation with respect to change in population size, D = - partial differential lnlambda(T)/partial differential lnN, where lambda is the asymptotic multiplicative growth rate per year, T is the generation time and N is adult population size. We show that D can be estimated from the sum of the autoregression coefficients. We estimated D in populations of six avian species for which life-history data and unusually long time-series of complete population censuses were available. Estimates of D were in the order of 1 or higher, indicating strong, statistically significant density dependence in four of the six species.