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 These alternative methods are tested using census data, some of which are previously unpublished, from natural populations known from independent evidence to be subject to density dependent processes.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.     

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.     

Spatial scale and the detection of density dependence in spruce budworm outbreaks in eastern North America

Using two tests for direct density dependence and standard techniques of time series analysis, we identified density dependence in defoliation time series of the spruce budworm across its outbreak range in eastern North America over the years 1945–1988. We carried out analyses for the entire region and for grid cells of defoliation maps at five spatial scales created by aggregating the smallest grid cells. The rate of detection of direct density dependence, as assessed by two previously published methods, decreased with increasing spatial scale. Using both methods, density dependence was detected more frequently at the periphery of the outbreak range, where defoliation rate was lower. This result suggested that density-dependent regulation may be stronger in those areas. The first order autoregressive process was the basic model for defoliation dynamics overall and the most common model across spatial scales. Second-order processes were encountered much less frequently, and those commonly identified as resulting from delayed density dependence generally occurred across spatial scales at a rate expected by chance alone. Our results were similar to those of other published studies, which have found the detection of density dependence to decrease at larger spatial scales. The results also reinforced the importance of considering spatial scale when diagnosing population processes using time series of abundance for single species. Received: 26 December 1999 / Accepted: 17 March 2000     

新疆沙冬青种群年龄结构及数量动态特征

新疆沙冬青（Ammopiptanthus nanus (M. Pop.) Cheng f.）为第三纪古地中海沿岸的珍稀孑遗物种,是国家Ⅱ级保护植物。本研究通过种群年龄结构、静态生命表、存活曲线、生存函数曲线及时间序列模型分析,揭示新疆沙冬青种群年龄结构及数量动态趋势。结果显示,新疆沙冬青种群老年个体数量最多,占总株数的48.1%,幼苗占比最低,仅为7.0%,种群年龄结构呈衰退型;存活曲线呈Deevey-Ⅱ型,种群总体死亡率较稳定;种群数量具有前期锐减、中期稳定、后期衰退的动态趋势,表明新疆沙冬青有较高的灭绝风险。增加种群幼苗数量,提高幼龄级到成年龄级过渡阶段的存活率,是促进新疆沙冬青良性发展的关键措施。     

The effect of fluctuations in tidal inundation frequency on a salt-marsh vegetation

Over a period of 15 years recordings were made of the species cover in permanent plots on the salt marsh of one of the West Frisian Islands, Schiermonnikoog (The Netherlands). Correlations between annual changes in the cover of the major species, and fluctuations in the monthly frequency of inundation by seawater were studied. First, a spectral analysis was carried out on the inundation frequency data to look for predictable patterns. Subsequently, fluctuations were defined as deviations from these predictable patterns. In a repeated multiple regression model, the effects of the season in which the fluctuations occurred, and the elevational position of the plots on the salt marsh were studied as factors influencing the correlation patterns. The behaviour of various species is discussed in relation to their seed bank characteristics and their salt tolerance.     

Effects of delay,truncations and density dependence in reproduction schedules on stability of nonlinear Leslie matrix models

Understanding effects of hypotheses about reproductive influences, reproductive schedules and the model mechanisms that lead to a loss of stability in a structured model population might provide information about the dynamics of natural population. To demonstrate characteristics of a discrete time, nonlinear, age structured population model, the transition from stability to instability is investigated. Questions about the stability, oscillations and delay processes within the model framework are posed. The relevant processes include delay of reproduction and truncation of lifetime, reproductive classes, and density dependent effects. We find that the effects of delaying reproduction is not stabilizing, but that the reproductive delay is a mechanism that acts to simplify the system dynamics. Density dependence in the reproduction schedule tends to lead to oscillations of large period and towards more unstable dynamics. The methods allow us to establish a conjecture of Levin and Goodyear about the form of the stability in discrete Leslie matrix models.This research was supported in part by the US Environmental Protection Agency under cooperation agreement CR-816081     

Census error and the detection of density dependence

1. Studies aiming to identify the prevalence and nature of density dependence in ecological populations have often used statistical analysis of ecological time-series of population counts. Such time-series are also being used increasingly to parameterize models that may be used in population management. 2. If time-series contain measurement errors, tests that rely on detecting a negative relationship between log population change and population size are biased and prone to spuriously detecting density dependence (Type I error). This is because the measurement error in density for a given year appears in the corresponding change in population density, with equal magnitude but opposite sign. 3. This effect introduces bias that may invalidate comparisons of ecological data with density-independent time-series. Unless census error can be accounted for, time-series may appear to show strongly density-dependent dynamics, even though the density-dependent signal may in reality be weak or absent. 4. We distinguish two forms of census error, both of which have serious consequences for detecting density dependence. 5. First, estimates of population density are based rarely on exact counts, but on samples. Hence there exists sampling error, with the level of error depending on the method employed and the number of replicates on which the population estimate is based. 6. Secondly, the group of organisms measured is often not a truly self-contained population, but part of a wider ecological population, defined in terms of location or behaviour. Consequently, the subpopulation studied may effectively be a sample of the population and spurious density dependence may be detected in the dynamics of a single subpopulation. In this case, density dependence is detected erroneously, even if numbers within the subpopulation are censused without sampling error. 7. In order to illustrate how process variation and measurement error may be distinguished we review data sets (counts of numbers of birds by single observers) for which both census error and long-term variance in population density can be estimated. 8. Tests for density dependence need to obviate the problem that measured population sizes are typically estimates rather than exact counts. It is possible that in some cases it may be possible to test for density dependence in the presence of unknown levels of census error, for example by uncovering nonlinearities in the density response. However, it seems likely that these may lack power compared with analyses that are able to explicitly include census error and we review some recently developed methods.     

Factors influencing the population density of the hanuman langur (Presbytis entellus) in Sariska Tiger Reserve

We carried out a study of Hanuman langurs in Sariska Tiger Reserve, Rajasthan, India during three months in 1990. The area surveyed included habitat disturbed by human activity, with both the grazing of livestock and firewood collecting resulting in degraded forest. Langur population density was estimated to be between 19 and 36 animals/km². The density of langurs in disturbed areas was significantly lower than in undisturbed areas. Both tree cover, total tree, and shrub cover were positively correlated with langur density, suggesting that a lack of trees in disturbed areas may have caused the lower langur densities. Although bisexual groups were significantly more common in undisturbed areas the distribution of all male groups did not appear to be affected by human disturbance, suggesting that male bands are likely to inhabit more disturbed habitats than bisexual groups. We suggest that either a lack of food trees or the high density of predators in Sariska may prevent bisexual groups from inhabiting areas where tree cover is low, although the more mobile male groups can survive in these areas. Although Hanuman langurs are a relatively common species in India, these results suggest that they are not, as is commonly assumed, immune to the effects of human disturbance. In areas where langurs appear to survive in disturbed habitats the different response of bisexual and all male groups to disturbance may still result in serious disruption to the population structure.     

Sturdy cycles in the chaotic Tribolium castaneum data series

Because of the inherent discreteness of individuals, population dynamical models must be discrete variable systems. In case of strong nonlinearity, such systems interacting with noise can generate a great variety of patterns from nearly periodic behavior through complex combination of nearly periodic and chaotic patterns to noisy chaotic time series. The interaction of a population consisting of discrete individuals and demographic noise has been analyzed in laboratory population data Henson et al. (Science 294 (2001) 602; Proc. Roy. Soc. Ser. B 270 (2003) 1549). In this paper we point out that some of the cycles are fragile, i.e. they are sensitive to the discretization algorithm and to small variation of the model parameters, while others remain sturdy against the perturbations. We introduce a statistical algorithm to detect disjoint, nearly-periodic patterns in data series. We show that only the sturdy cycles of the discrete variable models appear in the data series significantly. Our analysis identified the quasiperiodic 11-cycle (emerging in the continuous model) to be present significantly only in one of the three experimental data series. Numerical simulations confirm that cycles can be detected only if noise is smaller than a certain critical level and population dynamics display the largest variety of nearly-periodic patterns if they are on the border of grey and noisy regions, defined in Domokos and Scheuring (J. Theor. Biol. 227 (2004) 535).     

Predicting fluctuations of reintroduced ibex populations: the importance of density dependence, environmental stochasticity and uncertain population estimates

1. Development of population projections requires estimates of observation error, parameters characterizing expected dynamics such as the specific population growth rate and the form of density regulation, the influence of stochastic factors on population dynamics, and quantification of the uncertainty in the parameter estimates. 2. Here we construct a Population Prediction Interval (PPI) based on Bayesian state space modelling of future population growth of 28 reintroduced ibex populations in Switzerland that have been censused for up to 68 years. Our aim is to examine whether the interpopulation variation in the precision of the population projections is related to differences in the parameters characterizing the expected dynamics, in the effects of environmental stochasticity, in the magnitude of uncertainty in the population parameters, or in the observation error. 3. The error in the population censuses was small. The median coefficient of variation in the estimates across populations was 5.1%. 4. Significant density regulation was present in 53.6% of the populations, but was in general weak. 5. The width of the PPI calculated for a period of 5 years showed large variation among populations, and was explained by differences in the impact of environmental stochasticity on population dynamics. 6. In spite of the high accuracy in population estimates, the uncertainty in the parameter estimates was still large. This uncertainty affected the precision in the population predictions, but it decreased with increasing length of study period, mainly due to higher precision in the estimates of the environmental variance in the longer time-series. 7. These analyses reveal that predictions of future population fluctuations of weakly density-regulated populations such as the ibex often become uncertain. Credible population predictions require that this uncertainty is properly quantified.     

The frequency of detection of density dependence in insect orders

Abstract.

• 1 A priori, there are no obvious reasons why patterns should exist in the frequency of density dependence across insect orders. However, orders may reflect related factors which influence population regulation (e.g. life-history patterns and ecology) and are difficult to quantify. The frequency of occurrence of density dependence is compared in 171 time series (of ten or more generations) from Lepidoptera, Hemiptera, Diptera, Odonata, Hymenoptera and Coleoptera. A posteriori attempts are made to identify the cause of observed patterns.
• 2 Buhner's (1975) test found non-delayed density dependence more frequently in Odonata than Lepidoptera and Hymenoptera, which in turn showed non-delayed density dependence more frequently than Diptera, Hemiptera and Coleoptera. Similarly, detection was greater for Odonata than other orders using Dennis & Taper's (1993) test for density dependence and Crowley's (1992) test for attraction. Varley & Gradwell's (1960) test found density dependence less frequently in Hemiptera than other orders. These differences were independent of time series length, temporal trends and numbers of generations per year.
• 3 The reasons for observed patterns in detection of density dependence (and attraction) in insect orders are not clear; however, plausible explanations are differences in: (i) intrinsic growth rate, which is correlated with body size (although evidence to support this hypothesis is weak); (ii) the sampling method used; or (iii) whether individuals come from a single population or many populations.
• 4 Using Turchin's (1990) test, delayed (lag 2) density dependence was detected most frequently in Hymenoptera, which often show delayed diapause or are parasitoids.

     

Avoiding erroneously high levels of detection in combinations of semi-independent tests

A randomization procedure is proposed which allows statistical tests to be combined into a single test to maintain specified and acceptable levels of false detection. This method was applied to the problem of detecting density dependence in 135 unpublished time-series (of 10 generations) from insect populations, and to simulated density-dependent and density-independent data, so that the correctness of observed levels of detection from the published data could be verified. To allow the application of the randomization procedure to Bulmer's (1975) tests and Varley and Gradwell's (1960) test, these were recast as randomization tests. The randomization procedure was tested with 39 combinations of tests for density dependence (and limitation/attraction); it generally producedcombined tests with levels of detection that were intermediate between detection levels of the constituent tests (and hence was limite by these). The specified rate of false detection (5%) was never exceeded (by more than 1%) when combined tests were applied to time-series from a random-walk model. Two different combinations of tests produced levels of detection from the published time-series which were slightly greater than their constituent tests when they were combined into single tests. These were the randomized form of Bulmer's (1975) first test with the tests of Pollard et al. (1987) and Reddingius and den Boer (1989) with the randomized form of Bulmer's second test. The combination of Bulmer's first and Pollard et al.'s test produced a greater level of detection (21.5%) than any other single test or combination of tests. These results were confirmed by the analysis of modelled density dependent data. Although the increase in power of combinations of tests over single tests is small with the data we used, the combined tests (listed above) had rates of detection that were less influenced by the form of data (of two forms of density-dependent data) than were their constituent tests. Hence, it appears that the combined tests are of greater generality than single test statistics. The method presented here for combining several statistical tests into a single randomization test is applicable in many other areas of ecology where we wish to apply several tests and take the most probable result of these; and if the tests being conducted are, or can be expressed as, randomization tests.     

Non-linear density dependence in time series is not evidence of non-logistic growth

Time series of population density are often used to seek deviations from logistic regulation by testing for a non-linear decline in per capita growth rate with density. Here I show that this method fails when the interval between observations is not matched by the timing of density impacts on growth. Time series overestimate instantaneous density impacts at low density and underestimate them at high density. More generally, logistic growth produces a deterministically decelerating decline in per capita growth with density if the interval between measures of population size exceeds any lag in density response. Deceleration arises independently out of stochastic density fluctuations, and under-compensating regulation. These multiple influences lead to the conclusion that sequential density estimates provide insufficient information on their own to reveal the identity of non-logistic growth processes. They can yield estimates of density compensation, however, which may suggest time lags in density dependence. Analysis of an empirical time series illustrates the issues.     

鞍山西郊水源地地下水水动态初步研究

运用时间序列分析方法,选取月抽水量及月观测静水位,建立时间序列模型。对鞍山市西郊水源地地下水水位进行了拟合,与实测数据相吻合,并进行了预报．     

Influence of density dependence on the detection of trends in unobserved life-history stages

In many species, certain life-history stages are difficult or impossible to observe directly, hampering management. Often more easily observed stages are monitored instead, but the extent to which various forms of uncertainty cloud our ability to discern trends in one critical life-history stage by observing another is poorly studied. We develop a stochastic simulation model for threatened California coho salmon Oncorhynchus kisutch to examine how well trends in one stage can be detected from observations of another. In particular, we use the model to examine the effect density dependence has on our ability to detect trends. We present a structural form for the transition between life-history stages that encompasses the common functional forms: density independence, Beverton–Holt compensatory density dependence and Ricker-type over-compensation. In small populations, such density dependence is often ignored. However, it may in fact be extremely important, for example if population decline was caused by a decrease in carrying capacity. Our results show that density dependence in any life-history transition significantly reduces the ability to detect trends in abundance; critical but inaccessible stages cannot generally be studied by monitoring more easily observed stages, especially if density dependence is present for any life-cycle transition.     

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     

Factors influencing nitrogen and phosphorus excretion rates of fish in a shallow lake

Summary 1. Fish excretion can be an important source of nutrients in aquatic ecosystems. Nitrogen (N) and phosphorus (P) excretion rates are influenced by many factors, including fish diet, fish growth rate and fish size. However, the relative influence of these and other factors on community‐level excretion rates of fish is unknown. 2. We used bioenergetics modeling to estimate excretion rates of eight fish species in a shallow, Minnesota (U.S.A.) lake over four months in both 2004 and 2005. Excretion rates of each species were summed for community‐level N and P excretion rates, as well as the N : P ratio of excretion. We then used a model‐selection approach to assess ability of independent variables to predict excretion rates, and to identify the most parsimonious model for predicting N : P excretion ratios and P and N excretion rates at the community scale. Predictive models were comprised of the independent variables water temperature and average fish density, fish size, fish growth rate, nutrient content of fish and nutrient content of fish diets at the community scale. 3. Fish density and nutrient content of fish diets (either N or P) were the most parsimonious models for predicting both N and P excretion rates, and explained 96% and 92% of the variance in N and P excretion, respectively. Moreover, fish density and nutrient models had 1400‐fold more support for predicting N and 21‐fold more support for predicting P excretion relative to models based on fish density only. Water temperature, fish size, fish growth rates and nutrient content of fish showed little influence on excretion rates, and none of our independent variables showed a strong relationship with N : P ratios of excretion. 4. Past work has focused on the importance of fish density as a driver of fish excretion rates on a volumetric basis. However, our results indicate that volumetric excretion rates at the community scale will also change substantially in response to changes in relative abundance of fish prey or shifts in relative dominance of planktivores, benthivores, or piscivores. Changes in community‐scale excretion rates will have subsequent influences on algal abundance, water clarity, and other ecosystem characteristics.