Parameter estimation in a generalized discrete-time model of density dependence

Flexible discrete-time per-capita-growth-rate models accommodating a variety of density-dependent relationships offer parsimonious explanations for the variation of population abundance through time. However, the accuracy of standard approaches to parameter estimation and confidence interval construction for such models has not been explored in a generalized setting or with consideration of limited sample sizes typical for ecology. Here, we use simulated data to quantify the relative effects of sample size, population perturbations, and environmental stochasticity on statistical inference. We focus on the key parameters that inform population dynamic predictions in a generalized Beverton–Holt model. We find that reliable parameter estimation requires data spanning ranges where both low and high density dependence act. However, the asymptotic distribution of the likelihood ratio test statistic can be fairly accurate for constructing confidence regions even when point estimation is poor. Consideration of the joint profile likelihood surface is shown to be useful for assessing reliability of point estimates and dynamical population predictions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Cross‐scale effects of spruce budworm outbreaks on boreal warblers in eastern Canada

Insect outbreaks are major natural disturbance events that affect communities of forest birds, either directly by affecting the food supply or indirectly by changing the vegetation composition of forest canopies. An examination of correlations between measures of bird and insect abundance across different spatial scales and over varying time lag effects may provide insight into underlying mechanisms. We developed a hierarchical Bayesian model to assess correlations between counts of eight warbler species from the Breeding Bird Survey in eastern Canada, 1966 to 2009, with the presence of spruce budworm (Choristoneura fumiferana Clem.) at immediate local scales and time‐lagged regional scales, as measured by extent of defoliation on host tree species. Budworm‐associated species Cape May warbler (Setophaga tigrina), bay‐breasted warbler (Setophaga castanea), and Tennessee warbler (Oreothlypis peregrina) responded strongly and positively to both local and regional effects. In contrast, non‐budworm‐associated species, Blackburnian warbler (Setophaga fusca), magnolia warbler (Setophaga magnolia), Canada warbler (Cardellina canadensis), black‐throated blue warbler (Setophaga caerulescens), and black‐throated green warbler (Setophaga virens), only responded to regional effects in a manner that varied across eastern Canada. The complex responses by forest birds to insect outbreaks involve both increased numerical responses to food supply and to longer term responses to changes in forest structure and composition. These effects can vary across spatial scales and be captured in hierarchical population models, which can serve to disentangle common trends from data when examining drivers of population dynamics like forest management or climate change.     

Stochastic density dependence in population size of a benthic clonal invertebrate: the regulating role of fission

The influence of environmental variation on the demography of clonal organisms has been poorly studied. I utilise a matrix model of the population dynamics of the intertidal zoanthid Palythoa caesia to examine how density dependence and temporal variation in demographic rates interact in regulating population size. The model produces realistic simulations of population size, with erratic fluctuations between soft lower and upper boundaries of approximately 55 and 90% cover. Cover never exceeds the maximum possible of 100%, and the population never goes to extinction. A sensitivity analysis indicates that the model’s behaviour is driven by density dependence in the fission of large colonies to produce intermediate sized colonies. Importantly, there is no density-dependent mortality in the model, and density dependence in recruitment, while present, is unimportant. Thus it appears that the main demographic processes which are considered to regulate population size in aclonal organisms may not be important for clonal species. Received: 18 August 1999 / Accepted: 29 October 1999     

Spatial scale of aggregation in three acarine predator species with different degrees of polyphagy

Aggregative responses by the predatory mites, Phytoseiulus persimilis, Typhlodromus occidentalis, and Amblyseius andersoni (Acari: Phytoseiidae), to spatial variation in the density of mobile stages of Tetranychus urticae (Acari: Tetranychidae) were studied over different spatial scales on greenhouse roses. Significant spatial variations in prey numbers per leaflet, per leaf, per branch or per plant were present in all experimental plots. None of the predator species responded to prey numbers per plant, and all searched randomly among plants. Within a plant, the oligophagous P. persimilis searched randomly among branches, but aggregated strongly among leaves within a branch and among leaflets within a leaf. The narrowly polyphagous T. occidentalis searched randomly among leaflets within a leaf and amond leaves within a branch, but aggregated strongly among leaflets or leaves within a plant. The boradly polyphagous A. andersoni searched randomly among leaflets within a leaf, a branch or a plant, and among leaves within a branch or a plant, but distributed themselves more often on branches with lower prey densities. Thus, specialist predators aggregate strongly at lower spatial levels but show random search at higher spatial levels, whereas generalist predators show random search at lower spatial levels but aggregate at higher spatial levels. This is the first empirical evidence demonstrating the relation between the degree of polyphagy and the spatial scale of aggregation. It is also concluded that both the prey patch size (i.e. grain) and predator foraging range (i.e. extent) are important for analyzing spatial scales of predator aggregation. The importance of studying spatial scale of aggregation is also discussed in relation to predator-prey metapopulation dynamics.     

A test of statistical techniques for detecting density dependence in sequential censuses of animal populations

Summary Principal and reduced major axes, and Bulmer's (1975) tests have been suggested as methods for detecting the presence of density dependence in a series of population censuses that are unsuitable for analysis by alternative means e.g. by k-factor analysis. These alternative methods are tested using census data, some of which are previously unpublished, from natural populations known from independent evidence to be subject to density dependent processes. All the methods fail to detect density dependence reliably, irrespective of sample size and the dynamics of the population. We conclude that none of the methods tested is sufficiently reliable to be useful as a test of density dependence in sequential censues of animal populations.     

Atmospheric mold spore counts in relation to meteorological parameters

 Fungal spore counts of Cladosporium, Alternaria, and Epicoccum were studied during 8 years in Denver, Colorado. Fungal spore counts were obtained daily during the pollinating season by a Rotorod sampler. Weather data were obtained from the National Climatic Data Center. Daily averages of temperature, relative humidity, daily precipitation, barometric pressure, and wind speed were studied. A time series analysis was performed on the data to mathematically model the spore counts in relation to weather parameters. Using SAS PROC ARIMA software, a regression analysis was performed, regressing the spore counts on the weather variables assuming an autoregressive moving average (ARMA) error structure. Cladosporium was found to be positively correlated (P<0.02) with average daily temperature, relative humidity, and negatively correlated with precipitation. Alternaria and Epicoccum did not show increased predictability with weather variables. A mathematical model was derived for Cladosporium spore counts using the annual seasonal cycle and significant weather variables. The model for Alternaria and Epicoccum incorporated the annual seasonal cycle. Fungal spore counts can be modeled by time series analysis and related to meteorological parameters controlling for seasonallity; this modeling can provide estimates of exposure to fungal aeroallergens. Received: 14 October 1996 / Revised: 17 February 1997 / Accepted: 28 February 1997     

Factors influencing detection of density dependence in British birds

If censuses are taken at less than generation intervals, the number of successive censuses in which a given individual is recorded will depend on longevity. Repeatedly recording the same individuals could produce under-estimates of population variability and influence detection of density dependence. We investigated this possibility in 60 time series of abundances of British birds compiled from the Common Birds Census data and then used simple population models to illustrate the proposed mechanism. Species had average lifespans of 2–10 years and were censused annually. Density dependence was detected (at P<0.05) much more frequently in bird species with long lifespans than in those with short lifespans; 75% of the 12 longest-lived species showed density dependence compared to 46% of all species. Population variability measured in annual censuses (termed annual variability) was lower in bird species with longer lifespans. We used discrete time models based on difference equations to demonstrate how longevity influences population variability and detection of density dependence in series of annual censuses. A model in which only first-year birds experienced density dependence was rejected because annual variability was greater and detection of density dependence was less likely when longevity was greater, the opposite of the observed effects of longevity in birds. A model in which all age classes experienced density dependence gave time series with lower annual variability and in which density dependence was detected more frequently when longevity was greater, which is the pattern observed in British birds. Analysis of data from this model showed that the amount of density dependence actually present caused only small changes in annual variability, whereas detection of density dependence from simulated series was strongly influenced by annual variability. The high annual variability of series from short-lived bird species could mask any density dependence that was present. Correcting for trends lead us to detect density dependence in 75% of the 12 longest lived bird species. There is no reason to believe that this rate is not also representative of short-lived species.     

Spatial patterns of goldenrod aphids and the response of enemies to patch density

Summary The two aphid species feeding on goldenrod (Solidago altissima) in northern Florida (U.S.A.) exhibited behavioral differences that resulted in characteristic spatial patterns. Uroleucon nigrotuberculatum alates (winged forms) aggregated when colonizing stems and subsequent non-winged generations were relatively sedentary, resulting in a clumped spatial pattern. U. tissoti colonized stems singly and was more mobile; these behaviors resulted in its more random spatial pattern within fields of goldenrod.Manipulations of aphid density in the field revealed that although patches with high densities of aphids accumulated more predators than patches with few aphids, predation pressure (measured as number of predators per aphid) was lower in dense patches. As a result, aphids in dense patches had a higher per capita change in density than aphids in sparse patches. However, when the fungal pathogen, Neozygites fresenii, became the dominant mortality agent, the influence of aphid density on mortality was reversed; aphids in dense patches were then more vulnerable than aphids in sparse patches. Thus the spatial patterns exhibited by the U. nigrotuberculatum and U. tissoti resulted in differences in their relative vulnerability to different natural enemies.     

Predation on reef-building corals: multiscale variation in the density of three corallivorous gastropods, Drupella spp.

 Feeding aggregations of three corallivorous gastropods, Drupella cornus, D. fragum and D. rugosa, have caused considerable coral damage on reefs across the Indo-West Pacific. Distribution and abundance of these three species were explored at Lizard Island, Great Barrier Reef, to determine within-reef variations in density, and spatial relationships between Drupella and their prey corals. The scales of greatest variation were between reef habitats (combinations of exposure and depth) and individual coral colonies. Density varied 12-fold among four habitats: exposed crests (2.55/m²), exposed slopes (0.22/m²), sheltered crests (0.34/m²) and sheltered slopes (2.07/m²). Species composition also varied markedly between habitats. Individuals were highly aggregated, usually forming small clusters (<10 individuals) on live coral colonies and other substrata, and occasional large aggregations of=200 to>2000. Five basic tenets for sampling Drupella are established, based on patterns of variation in density and species composition, and small-scale habitat use. Accepted: 8 February 1999     

Interaction between Cry9Ca and two Cry1A delta-endotoxins from Bacillus thuringiensis in larval toxicity and binding to brush border membrane vesicles of the spruce budworm,Choristoneura fumiferana Clemens

A genetically altered variant of Cry9Ca from Bacillus thuringiensis shows high potency against the spruce budworm, Choristoneura fumiferana Clemens. Its activity, as measured by feeding inhibition in frass-failure assays, is estimated to be four to seven times greater than B. thuringiensis subsp. kurstaki HD-1, the strain currently used in commercial products to control this insect. Bioassays against budworm of mixtures of the modified Cry9Ca and two of the Cry1A endotoxin proteins produced by HD-1 show neither synergism nor antagonism. Experiments with brush border membrane vesicles from budworm midgut revealed that Cry9Ca and the Cry1A toxins share a common binding site and that bound Cry9Ca can be displaced from the membrane to some extent by the Cry1A toxins. However, it is uncertain whether the binding site is actually the receptor molecule or a membrane protein associated with pore formation.     

Time series analysis supporting the hypothesis that enhanced cosmic radiation during germ cell formation can increase breast cancer mortality in germ cell cohorts

 Techniques from cancer epidemiology and time series analysis were used to explore the hypothesis that cosmic radiation can induce germ cell changes leading to increases in future breast cancer mortality. A birth cohort time series for female breast cancer mortality was obtained using a model-independent, age-period-cohort analysis on age-specific mortality data for 1940–1990. The birth cohort series contained several oscillatory components, which were isolated and compared to the corresponding frequency components of a cosmic ray surrogate time series – Greenland ice-core ¹⁰Be concentrations. A technique, referred to as component wave-train alignment, was used to show that the breast cancer and cosmic ray oscillations were phase-locked approx. 25 years before the time of birth. This is consistent with the time of germ cell formation, which occurs during the fetal development stage of the preceding generation. Evidence is presented that the observable oscillations in the birth cohort series were residues of oscillations of much larger amplitude in the germ cell cohort, which were attenuated by the effect of the broad maternal age distribution. It is predicted that a minimum of 50% of breast cancer risk is associated with germ cell damage by cosmic radiation (priming event), which leads to the development of individuals with a higher risk of breast cancer. It is proposed that the priming event, by preceding other steps of carcinogenesis, works in concert with risk factor exposure during life. The priming event is consistent with epigenetic changes such as imprinting. Received: 10 June 1996 / Revised: 4 December 1996 / Accepted: 19 December 1996     

Impacts of climate and density on the duration of the tadpole stage of the common toad Bufo bufo

In an ongoing long-term study of a breeding population of common toads Bufo bufo at a pond in southern England, the dates of first spawning have been recorded since 1980, the dates of toadlet emergence since 1984, and the numbers of emergent toadlets estimated since 1988. The dates when spawn was first laid varied considerably between years from the earliest on 2 February 1993 (day 33) to the latest on 19 March 1996 (day 79). The duration of the tadpole stage was negatively correlated with the date of appearance of first spawn and was up to 30 days longer in early spawning years than in late ones. Despite this, toadlets still emerged from the natal pond up to 36 days earlier in early spawning years than in late ones. Significant positive correlations were found between the duration of the tadpole stage and both the proportion of days during the tadpole stage when the minimum ground temperature was at or below 0°C and the proportion of days when 10 mm or more rain fell. Tadpole mortality was positively correlated with the proportion of days during the tadpole stage when the minimum ground temperature was at or below 1.5°C. Evidence was also found to suggest that tadpole mortality was density-dependent, being proportionately higher when initial tadpole numbers were high than when they were low. Received: 7 May 1999 / Accepted: 19 July 1999     

Sexual segregation in North American elk: the role of density dependence

We investigated how density‐dependent processes and subsequent variation in nutritional condition of individuals influenced both timing and duration of sexual segregation and selection of resources. During 1999–2001, we experimentally created two population densities of North American elk (Cervus elaphus), a high‐density population at 20 elk/km², and a low‐density population at 4 elk/km² to test hypotheses relative to timing and duration of sexual segregation and variation in selection of resources. We used multi‐response permutation procedures to investigate patterns of sexual segregation, and resource selection functions to document differences in selection of resources by individuals in high‐ and low‐density populations during sexual segregation and aggregation. The duration of sexual segregation was 2 months longer in the high‐density population and likely was influenced by individuals in poorer nutritional condition, which corresponded with later conception and parturition, than at low density. Males and females in the high‐density population overlapped in selection of resources to a greater extent than in the low‐density population, probably resulting from density‐dependent effects of increased intraspecific competition and lower availability of resources.     

Variation in plant quality and the population dynamics of herbivores: there is nothing average about aphids

In the attempt to use results from small-scale studies to make large-scale predictions, it is critical that we take into account the greater spatial heterogeneity encountered at larger spatial scales. An important component of this heterogeneity is variation in plant quality, which can have a profound influence on herbivore population dynamics. This influence is particularly relevant when we consider that the strength of density dependence can vary among host plants and that the strength of density dependence determines the difference between exponential and density- dependent growth. Here, we present some simple models and analyses designed to examine the impact of variable plant quality on the dynamics of insect herbivore populations, and specifically the consequences of variation in the strength of density dependence among host plants. We show that average values of herbivore population growth parameters, calculated from plants that vary in quality, do not predict overall population growth. Furthermore, we illustrate that the quality of a few individual plants within a larger plant population can dominate herbivore population growth. Our results demonstrate that ignoring spatial heterogeneity that exists in herbivore population growth on plants that differ in quality can lead to a misunderstanding of the mechanisms that underlie population dynamics.     

Temporal and spatial variation of larval parasitism in non-outbreaking populations of a folivorous moth

In order to assess the role of parasitoids in the regulation of non-outbreaking populations of Epirrita autumnata, a geometrid lepidopteran with outbreaking populations in northern Europe, we examined the temporal and spatial variation of larval parasitism in southwestern Finland during 6 successive years. The study was carried out on two spatial scales, among trees within sites of about 1 ha and among sites separated by distances of 2–10 km, using experimental and observational approaches respectively. The overall percent parasitism was independent of host density on both spatial scales, while temporally it fluctuated only little. Of the two main parasitoids, the commoner one, Protapanteles immunis, showed a variable response to host density on the larger spatial scale and negative density dependence on the smaller scale. Temporally, parasitism caused by this species was independent of host density. Another parasitoid, Phobocampe bicingulata, showed positive density dependence on the smaller spatial scale and had a variable response on the larger scale, but exhibited negative density dependence over time. The results of this study caution against drawing conclusions concerning population regulation on the grounds of spatial density dependence alone. Larval parasitoids apparently do not maintain low densities in the E. autumnata populations studied. However, they may suppress E. autumnata densities to a level low enough for density-dependent mortality factor(s) to become regulating. Among other mortality factors of E. autumnata, pupal predation has been found to be temporally positively density-dependent. Received: 19 October 1999 / Accepted: 10 January 2000     

Influence of prey availability and conspecifics on patch quality for a cannibalistic forager: laboratory experiments with the wolf spider Schizocosa

 Because cannibals are potentially both predator and prey, the presence of conspecifics and alternative prey may act together to influence the rate at which cannibals prey upon each other or emigrate from a habitat patch. Wolf spiders (Lycosidae) are cannibalistic-generalist predators that hunt for prey with a sit-and-wait strategy characterized by changes in foraging site. Little information is available on how both prey abundance and the presence of conspecifics influence patch quality for these cursorial, non-web-building spiders. To address this question, laboratory experiments were conducted with spiderlings and older juveniles of the lycosid genus Schizocosa. The presence of insect prey consistently reduced rates of spider emigration when spiders were housed either alone or in groups. Solitary juvenile Schizocosa that had been recently collected from the field exhibited a median giving-up time (GUT) of 10 h in the absence of prey (Collembola); providing Collembola increased the median GUT to 64 h. For solitary spiders, the absence of prey increased by about fourfold the rate of emigration during the first 24 h. In contrast, for spiders in patches with a high density of conspecifics, the absence of prey increased the 24-h emigration rate by only 1.6-fold. For successful cannibals in the no-prey patches, the presence of conspecifics improved patch quality by providing a source of food. Mortality by cannibalism was affected by both prey availability and openness of the patch to net emigration. In patches with no net emigration, the presence of prey reduced rates of cannibalism from 79% to 57%. Spiders in patches open to emigration but not immigration experienced a rate of cannibalism (16%) that was independent of prey availability. The results of these experiments indicate that for a cannibalistic forager such as the wolf spider Schizocosa, (1) the presence of conspecifics can improve average patch quality when prey are absent, and (2) cannibalism has the potential to be a significant mortality factor under natural field conditions because cannibalism persisted in prey patches that were open to emigration. Received: 12 April 1996 / Accepted: 14 August 1996     

Climatic and intertrophic effects detected in 10-year population dynamics of biological control of the arrowhead scale by two parasitoids in southwestern Japan

Relative effects of weather and three-trophic interactions were studied for a classical biological control system consisting of the arrowhead scale Unaspis yanonensis, known formerly as a serious pest of the Satsuma mandarin orange Citrus unshiu, and its two introduced parasitoids, Coccobius fulvus and Aphytis yanonensis. Yearly population responses of the three insect species on a per-tree basis for up to 10 years at two orange groves were analyzed by general linear models, with a backward stepwise procedure, to select among abiotic (summer/winter temperature and rainfall) and biotic (densities of the three insect species and orange bearing in the previous years) independent variables. Temperature positively affected the arrowhead scale and the two parasitoids. A negative correlation of rainfall was detected for all three insect species. Mandarin fruiting showed negative delayed density dependence, thereby supporting the observed alternate bearing phenomenon in mandarins, presumably due to physiological imbalance triggered by climatic factors. The arrowhead scale was negatively correlated with fruit production in the preceding years, possibly due to reduced resistance in subsequent years of mast fruiting. We found a negative correlation of the arrowhead scale with Coccobius only in a single grove and none with Aphytis. Thus, it appears that bottom-up forces may be more important than top-down control by the parasitoids in the post-transient phase of this system.     

The effects of plant dispersion and prey density on parasitism rates in a naturally patchy habitat

Despite extensive research on parasitoid-prey interactions and especially the effects of heterogeneity in parasitism on stability, sources of heterogeneity other than prey density have been little investigated. This research examines parasitism rates by three parasitoid species in relationship to prey density and habitat spatial pattern. The herbivore Itame andersoni (Geometridae) inhabits a subdivided habitat created by patches of its host plant, Dryas drummondii, in the Wrangell Mountains of Alaska. Dryas colonizes glacial moraines and spreads clonally to form distinct patches. Habitat subdivision occurs both on the patch scale and on the larger spatial scale of sites due to patchy successional patterns. Itame is attacked by three parasitoids: an ichneumonid wasp (Campoletis sp.), a braconid wasp (Aleiodes n. sp.), and the tachinid fly (Phyrxe pecosensis). I performed a large survey study at five distinct sites and censused Itame density and parasitism rates in 206 plant patches for 1–3 years. Parasitism rates varied with both plant patch size and isolation and also between sites, and the highest rates of overall parasitism were in the smallest patches. However, the effects of both small- and large-scale heterogeneity on parasitism differed for the three parasitoid species. There was weak evidence that Itame density was positively correlated with parasitism for the braconid and tachinid at the patch scale, but density effects differed for different patch sizes, patch isolations, and sites. At the site scale, there was no evidence of positive, but some indication of negative density-dependent parasitism. These patterns do not appear to be driven by negative interactions between the three parasitoid species, but reflect, rather, individual differences in habitat use and response to prey density. Finally, there was no evidence that parasitism strongly impacted the population dynamics of Itame. These results demonstrate the importance of considering habitat pattern when examining spatial heterogeneity of parasitism and the impacts of parasitoids. Received: 3 June 1999 / Accepted: 4 October 1999