Population Time Series Research Articles

Radial Growth Response of Douglas-fir and Grand Fir to Larval Densities of the Douglas-fir Tussock Moth and the Western Spruce Budworm

Abstract Statistical models were developed relating corrected tree-ring chronologies of grand fir (Abies grandis [Dougl. ex D. Don] Lindl.) and Douglas-fir (Pseudotsugata menziesii var. glauca [Beissn.] Franco) to population time series of Douglas-fir tussock moth (Orgyia pseudotsugata [McDunnough]) and western spruce budworm larvae (Choristoneura occidentalis Freeman) in the same stands. The study was conducted in northeastern Oregon and spanned 22 yr including 2 periods of defoliator outbreaks as well as an interval of no outbreaks. Changes in the radial increment of host trees, corrected for tree-ring age and weather, were inversely related to larval densities in the same year of growth and in each of the 4 preceding years. The strongest growth response was a delayed function of larval density with a 3 yr time delay. Regression models giving the best fit to pooled data were second-degree polynomials in which log larval density with a 3 yr delay accounted for 28.7% of the variation in rate of change in corrected tree-ring indices, and 46.4% of the variation in the absolute size of corrected indices. The results imply that reductions in radial growth are directly related to density of feeding larvae and that the cumulative maximum effect on increment in the lower bole lags defoliation by 3 yr. The models are recommended either for directly forecasting mean reductions in radial increment from monitored densities of larvae or for inversely predicting past mean densities of defoliating larvae from dendrochronology data. For. Sci. 43(2):194-205.

Explaining the colour of power spectra in chaotic ecological models

Power spectrum analysis is often used to determine whether population time series are dominated by particular frequencies. Results for chaotic time series are often reported in terms of the colour of the spectra whereby red spectra indicate a dominance of low frequency (long-term) fluctuations, white spectra indicate that all frequencies are equally dominant and blue spectra indicate a dominance of high frequency (short-term) fluctuations. Several studies have employed such analysis and much discussion has been provoked by an apparent conflict between the fact that the time series of natural populations produce reddened power spectra whereas chaotic, single species ecological models can produce blue, white or red spectra. Here, we resolve the question of which parameter values give rise to particular colour spectra by analysing simple models in terms of ‘universal’ parameters allowing direct comparisons between models to be drawn. This suggests that some models are not capable of producing reddened spectra, which would question their usefulness in describing ecological systems. The population behaviour associated with each colour spectrum is described and compared with models that incorporate simple modifications to represent delayed density dependence, spatial structure and environmental effects.

Dynamic Behavior of Douglas-Fir Tussock Moth Populations in the Pacific Northwest

Abstract Larval densities of the Douglas-fir tussock moth (Orgyia pseudotsugata [McDunnough] [Lepidoptera:Lymantriidae]) were monitored annually to construct population time series in five different forest ecosystems. The time series were generated in parts of five national forests in three geographical provinces: the northern Blue Mountains of northeastern Oregon, the southern Cascade Range of south-central Oregon, and the northern Cascade Range of north-central Washington. The five series ranged in length from 12 to 23 yr and represented the broad numerical behavior of tussock moth populations in those provinces. Time series with the most variable fluctuations were recorded in the Blue Mountains, a region with a long history of regular tussock moth outbreaks. The least variable series was in the southern Cascades, an area with no previously documented outbreaks. Characteristics of series in the Blue Mountains and the northern Cascades were significantly correlated with one another, but not with those of the series in the southern Cascades. The density-dependent structure of each time Series was examined by autocorrelation and partial autocorrelation functions, which indicated that fluctuations were quasi-periodic, even at low densities, and that the most significant autoregressive process was a second-order feedback. Each time series was fit with a linear second- order autoregressive model and a discrete nonlinear logistic model with a single time delay. The models, based on density-dependent processes associated with preceding insect generations, accounted for an average of 44.6% of the variation in the time series. The remaining 55.4% of variation was due to unknown density-independent factors related to different years in the series. The models showed that the principal dynamics of tussock moth populations are generated by direct and delayed density-dependent processes. In outbreak-prone ecosystems, like those in the Blue Mountains and the northern Cascades, the primary regulation of insect numbers is by delayed feedback processes that result in populations sometimes having extreme fluctuations in density. Conversely, in nonoutbreak ecosystems, as in the southern Cascades, feedback is more balanced between both direct and delayed processes that stabilize populations at lower densities. External factors, like weather, also may influence the numerical behavior of populations to some extent, but their specific contribution to tussock moth dynamics is largely unknown. For. Sci. 42(2):182-191.

Spline models of biological population dynamics: How to estimate mortality rates for stage structured populations with dimorphic life histories

Nonparametric spline based models of stage structured population dynamics provide an effective way of decomposing observed population dynamics into birth and death rate processes. Currently available methodology only considers simple life histories in which all individuals pass through the same sequence of stages in the same way. This paper presents techniques for obtaining birth and death rates from structured population time series of organisms with complex life histories. For example, in many species males and females develop at the same rate in early stages, but differently in late stages. The models are motivated by the need to obtain birth and death rates for a pest subject to biocontrol by a parasitoid.

The evaluation of extrapolative forecasting methods

Extrapolative forecasting methods are widely used in production and inventory decisions. Typically many hundreds of series are forecast and the cost-effectiveness of the decisions depends on the accuracy of the forecasting method(s) used. This paper examines how a forecasting method should be chosen based on analyzing alternative loss functions. It is argued that a population of time series must be evaluated by time period and by series. Of the alternative loss functions considered, only the geometric root mean squared error is well-behaved and has a straightforward interpretation. The paper concludes that exponential smoothing and ‘naive’ models, previously thought to be ‘robust’ performers, forecast poorly for the particular set of time series under analysis, whatever error measure is used. As a consequence, forecasters should carry out a detailed evaluation of the data series, as described in the paper, rather than relying on a priori analysis developed from earlier forecasting competitions.

Is Extinction Rate Related to Temporal Variability in Population Size? An Empirical Answer for Orb Spiders

This study investigates the relationship between extinction rate and temporal variability in population size for 174 populations of seven orb spider species on 106 subtropical islands. Evidence for all population time series with at least two nonzero values supports either a negative (inverse) relationship or no relationship at all; this result is robust over a wide variety of statistical treatments. This perhaps unexpected result can be interpreted mainly as reflecting the inability of populations frequently going extinct ever to achieve large enough population sizes to attain even large relative variances (such as coefficient of variation), as well as reflecting the very erratic trajectories of boom-and-bust-type populations that seldom reach resource carrying capacities. Removal of zero counts from time series is also probably involved, and skewness of population-size values may have an effect as well. One type of data preparation, however-that including zero values of the population series and using a...

Small area population forecasting: some experience with British models.

This study is concerned with the evaluation of the various models including time-series forecasts, extrapolation, and projection procedures, that have been developed to prepare population forecasts for planning purposes. These models are evaluated using data for the Netherlands. "As part of a research project at the Erasmus University, space-time population data has been assembled in a geographically consistent way for the period 1950-1979. These population time series are of sufficient length for the first 20 years to be used to build models and then evaluate the performance of the model for the next 10 years. Some 154 different forecasting models for 832 municipalities have been evaluated. It would appear that the best forecasts are likely to be provided by either a Holt-Winters model, or a ratio-correction model, or a low order exponential-smoothing model."

American, German and British antecedents to Pearl and Reed's logistic curve

Abstract This paper provides a general history of the logistic growth curve and its applications to several biological populations. Curiously, the same curve, in several disguises, was discovered at least four times by independent authors before the work of Pearl and Reed, who are usually credited with the discovery. Two aspects of the history are stressed. First, the paper discussed the apparently wide applicability of the curve to many fields of physiology, biology, and human demography. Second, it emphasizes the different reasons given as to why various populations should approach a maximum asymptotically according to the logistic curve. Biologists hypothesized that either the autocatalytic nature of some growth processes or the fixed food supply available to a single species would produce a time series of the total population of microorganisms and other species that followed the curve. Pearl and Reed's arguments concerning human populations, however, were of a different kind. They relied upon nothing more than the general idea that a fixed area imposed a ceiling to the population. This ceiling was not estimated by means of an aggregate production function or any other production theory. The error of their famous 1920 estimate of 197 million as the maximum population for the United States demonstrates the danger of seeking to apply methods which have been successful in one field to a quite different field.

American, German and British Antecedents to Pearl and Reed's Logistic Curve

Abstract This paper provides a general history of the logistic growth curve and its applications to several biological populations. Curiously, the same curve, in several disguises, was discovered at least four times by independent authors before the work of Pearl and Reed, who are usually credited with the discovery. Two aspects of the history are stressed. First, the paper discussed the apparently wide applicability of the curve to many fields of physiology, biology, and human demography. Second, it emphasizes the different reasons given as to why various populations should approach a maximum asymptotically according to the logistic curve. Biologists hypothesized that either the autocatalytic nature of some growth processes or the fixed food supply available to a single species would produce a time series of the total population of microorganisms and other species that followed the curve. Pearl and Reed's arguments concerning human populations, however, were of a different kind. They relied upon nothing ...