This paper presents some concepts and methodology essential for the analysis of population dynamics of univoltine species. Simple stochastic difference equations, comprised of endogenous and exogenous components, are introduced to provide a basic structure for density—dependent population processes. The endogenous component of a population process is modelled as a function of density in the past p generations, including the most recent. The exogenous component of the process consists of all density—independent components of the ecological factors involved, including enhance variations. The model is called a pth order density—dependent process. For a successful analysis of a population process by the above model, it is important that the process be in a state of statistical equilibrium, or stationarity. The simplest notion of stationarity is introduced, and the average behavior of the process, under this assumption, discussed. The order of density dependence in the population process of a given species depends on its interaction with other species involved in the food web. Considering certain attributes of the food web, in particular the limited number of trophic levels, the pyrmaid of numbers, the linear linkages between closely interacting species, and niche separation among competing species, it is argued that the order of density dependence is probably not much higher than three. A second—order model is perhaps adequate in many practical cases. The dynamics of some lower order density—dependent processes are compared by simulations, with a view to showing the effect of density—dependent and density—independent components at different orders. Several types of density dependence are discussed. If a given factor influencing the temporal variation in density is by itself influenced by density, it is called "causally density—dependent," which may reveal itself by some degree of correlation with density. A density—independent factor, however, may also show some sort of correlation with density in the recent past. This is called "statistically density—dependent." Such statistical density dependence may be due to: (1) spurious correlation, (2) bias in an estimator of the correlation coefficient, (3) autocorrelations in the density—independent factor, and (4) an intriguing mathematical property of the stochastic process. Particularly because of the last two reasons, it is often difficult to distinguish, by correlation method, between causal and statistical density dependence. Distinction also exists between temporal and spatial density dependence, the latter not necessarily implying the involvement of the former. The importance of the distinction between these types of density dependence is discussed in relation to the data analysis and model building. A Statistical analysis of the effect of ecological factors on population dynamics is attempted. Since it is often difficult to determine, by correlation, the causally density—dependent structure of a population process under the influence of some unknown density—independe...

This paper reformulates the notion of density dependence and shows how this notion plays an important role in constructing appropriate models for data analysis. The regulation and persistence of population processes are interpreted as a close resemblance to the behavior of a series of random variables in which the second moments are bounded. On this basis the formal criteria of persistence are deduced. General structural models of population processes are set up and translated into discrete single—variable difference equations, ranging from the simplest linear first—order process to more complex nonlinear second—order processes. The discussion includes the derivation of general conditions for the second—order limit cycles, a reanalysis of the Canadian lynx 10—yr cycle, and models for population outbreaks. Based on the results of the preceding study of models, the notion of density dependence is reformulated. First, the meaning of the word 'dependence' is discussed. In the context of 'density dependence,' the word has two meanings; the causal dependence of a factor on density, and the statistical dependence. Statistical dependence is defined as a converse of statistical independence, the latter being a process in which the rate of change in density has zero correlation with density; this is a very special class of processes and is unlikely to occur in natural population processes. Therefore, the test of density dependence against the null hypothesis of statistical independence will not provide much insight. It is also argued that a deduction from the persistence criteria shows that a negative correlation between density and its rate of change is a necessary outcome of regulation and hence that the notion of 'density—dependent regulation' in statistical dependence is an uninspiring tautology. As opposed to statistical density independence, which necessarily generates an unbounded population process, causal density independence may satisfy the persistence conditions and hence may regulate populations. However, such a causally 'density—independent regulation' tends to be 'fragile' against perturbations by random exogenous factors. It is a particular class of causally density—dependent processes that can ensure regulation more durable against such perturbations. The inference of generating mechanism from observation is discussed. Although regression analysis is an essential method of inference, simple regression analysis will not work unless the observed processes are known to be a simple Markov chain. Statistical inference of generating mechanisms in observed systems depends largely on the choice of appropriate models, and it is in the construction of such models that the notion of causal density dependence plays an important role.

I investigate the efficacy of the Moran effect as applied to natural population processes. The Moran effect, the correlated density-independent disturbances that bring independently oscillating local populations into synchrony, was originally conceived as an attribute of a linear model system. However, it applies only approximately to natural populations, as they are inherently nonlinear in their density-dependent structure, given that no animal has an unlimited reproductive capacity. The degree of approximation, as measured by the degree of correlation among populations involved, is shown to depend, given the density-dependent structure, on the variances of the random disturbances. In particular, if the unperturbed density-dependent process converges to an equilibrium density, approximation is good when the variances are equal among the populations involved and comparatively small, but it worsens as the variances and their differences increase. For those processes that do not converge, when unperturbed, but exhibit bounded oscillations, the degree of approximation tends to deteriorate considerably, or may practically collapse, even if the disturbances are not large in variance. A sample correlation coefficient is often spurious if the observed population processes to be correlated are highly autocorrelated and limited in length. To detect spuriousness, the density-independent disturbances must somehow be estimated from the data. Three methods (moving-average, linear regression, and nonlinear regression) are considered, and their merits and demerits are discussed. Results of the present investigation are summarized with respect to the interpretations (or diagnoses) of sample cross-correlation functions.

Outbreak and declining populations of spruce budworm (Choristoneura fumiferana (Clem.)) were sampled extensively at three locations in New Brunswick, Canada, between 1982 and 1992 and were examined for the prevalence of granulosis and nuclear polyhedrosis viruses (Baculoviridae). Larvae, pupae, and adults were collected using a variety of methods. Spruce budworm nuclear polyhedrosis virus (CfMNPV) genomic DNA probes and wet-mount light microscopy were used to determine CfMNPV prevalence in 50 274 juvenile spruce budworms. Spruce budworm granulosis virus (ChfuGV) genomic DNA probes were used to determine the prevalence of ChfuGV in 25 703 of these same samples. The prevalence of both viruses was low, with ChfuGV and CfMNPV not found in more than 15% and 2%, respectively, of samples in any collection in a given year. Prevalence of ChfuGV was greatest in mid-to late June in sixth-instar larvae. Each virus was detected in only two of 2177 female moths and in none of the 420 male moths examined. In the entire collection, cytoplasmic polyhedrosis virus (Reoviridae) was detected in only two budworm larvae and entomopoxvirus (Poxviridae) was not detected in any. Lucarotti CJ, Eveleigh ES, Royama T, Morin B, McCarthy P, Ebling PM, Kaupp WJ, Guertin C, Arella M. 2004. Prévalence des baculovirus dans des populations de tordeuse des bourgeons de l'épinette (Lepidoptera : Tortricidae) au Nouveau-Brunswick. The Canadian Entomologist 136 : 255-264. 255 1 Corresponding author (e-mail: clucarot@nrcan.gc.ca). mêmes échantillons. La prévalence des deux virus était faible, ne dépassant pas 15% pour ChfuGV et pas plus de 2% pour le CfMNPV, pour chaque méthode d'échantillonage, pour chaque année d'étude. La prévalence du ChfuGV atteint son maximum entre le milieu et la fin de juin, au sixième stade de développement larvaire. Chaque virus n'a été détecté que chez deux des 2177 adultes femelles et chez aucun des 420 adultes mâles examinés. Parmis tous les specimens recueillis, le virus de la polyhèdrose cytoplasmique (Reoviridae) n'a été détecté que dans deux larves de la TBE alors que l'entomopoxvirus (Poxviridae) ne l'a été dans aucun.