The theta‐logistic is unreliable for modelling most census data

Clark, Francis E.; Brook, Barry W.; Delean, Steven; Akçakaya, H. Reşi̇t; Bradshaw, Corey J. A.

doi:10.1111/j.2041-210x.2010.00029.x

Cited by 101 publications

(134 citation statements)

References 45 publications

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“…Logistic population models were developed to estimate rates of growth and density dependence and are commonly used to evaluate temporal patterns in abundance (Clark et al 2010). Our results show that, at least over the five year period that we evaluated predictive ability, neither model was clearly more accurate in predicting species abundances.…”

Section: The Prospective Applicationmentioning

confidence: 68%

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Habitat suitability through time: using time series and habitat models to understand changes in bird density

et al. 2014

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Abstract. Confronted with a rapidly changing world and limited resources for conservation, ecologists are increasingly challenged with predicting the impact of climate and land-use change on wildlife. A common approach is to use habitat-suitability models (HSMs) to explain aspects of species' occurrence, such as presence, abundance, and distribution, utilizing physical habitat characteristics. Although HSMs are useful, they are limited because they are typically created using spatial rather than temporal data, which omits temporal dynamics. We explored the value of combining spatial and temporal approaches by comparing HSMs with autoregressive population models. We investigated a 28-year period of bird community dynamics at a field site in northern California during which time the plant community has been transitioning from scrub to conifer forest. We used the two model frameworks to quantify the contribution of vegetation change, weather, and population processes (autoregressive models only) to variation in density of seven bird species over the first 23 years. Model predictive ability was then tested using the subsequent five years of population density data. HSMs explained 58% to 90% of the deviance in species' density. However, models that included density dependence in addition to vegetation covariates provided a better fit to the data for three of the seven species, Song Sparrow (Melospiza melodia), White-crowned Sparrow (Zonotrichia leucophrys), and Wrentit (Chamaea fasciata). These three species have more localized dispersal compared to the other four species, suggesting that dispersal tendency may be an important life-history trait to consider when predicting the impact of climate and land-use change on population levels. Our results suggest that HSMs can effectively explain and predict variation in species' densities through time, however for species with localized dispersal, it may be especially informative to include population processes.

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Section: The Prospective Applicationmentioning

confidence: 68%

“…We used a discrete-time stochastic logistic model, also known as a stochastic Ricker (1954) model, because it is widely used with vertebrate species and is more robust than other logistictypes models such as the theta-logistic (Clark et al 2010). The basic structure of model is…”

Section: Model Descriptionsmentioning

confidence: 99%

Habitat suitability through time: using time series and habitat models to understand changes in bird density

et al. 2014

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“…Whether or not nutrient availability is density-dependent is always a controversial topic in ecological literature [31][32][33][34][35][36]. Our experiments under controlled environments and replicated conditions suggested nutrient availability is density-dependent.…”

Section: Effect Of Fe Concentration and Initial Biomassmentioning

confidence: 77%

Effect of Fe and EDTA on Freshwater Cyanobacteria Bloom Formation

Zhang

Jian

Luo

2017

Water

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Due to the fact that not all eutrophic lakes have cyanobacteria blooms, we hypothesized Fe may be another important limiting factor which regulates cyanobacteria bloom formation. We tested the hypothesis by batch cultures of bloom-forming Cyanobacterium, Microcystis aeruginosa with different ethylenediaminetetraacetic acid (EDTA)-Fe concentrations (0.5-6.0 mg/L), three levels of initial biomass, and excessive N and P (N = 4.2 mg/L, P = 0.186 mg/L) to simulate dynamically a cyanobacteria bloom in eutrophic conditions. The effect of EDTA and Fe uptake kinetics by M. aeruginosa were also examined. Results showed M. aeruginosa growth rate positively correlated with EDTA-Fe concentration and negatively correlated with biomass. Maximal biomass of M. aeruginosa was determined by Fe availability and initial biomass. EDTA could decrease both Fe availability and toxicity. Based on experimental results, a conceptual model of how Fe availability regulates cyanobacterial biomass in eutrophic lakes was developed. This study demonstrated bioavailable Fe is a potential limiting factor in eutrophic lakes that should be included in eutrophication management strategies.

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“…Sibly et al [3] fitted theta-logistic law to model the population growth rate with density to 1780 time series of 674 species belonging to four taxonomic groups, namely, birds, mammals, bony fishes and insects from the Global Population Dynamics Database [21]. Similar studies have been carried out using other growth functions as well, e.g., theta-Ricker model and Gompertz model [22]; theta-Ricker [23]; Gompertz [24]. The theta-logistic models are often collectively used in applied ecology to estimate maximum sustainable yield targets [25], temporal abundance patterns [26], the most effective wildlife management interventions [27], extinction risk [28] and epidemiological patterns [29].…”

Section: Introductionmentioning

confidence: 88%

Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach

2014

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Scientific formalizations of the notion of growth and measurement of the rate of growth in living organisms are age-old problems. The most frequently used metric, "Average Relative Growth Rate" is invariant under the choice of the underlying growth model. Theoretically, the estimated rate parameter and relative growth rate remain constant for all mutually exclusive and exhaustive time intervals if the underlying law is exponential but not for other common growth laws (e.g., logistic, Gompertz, power, general logistic). We propose a new growth metric specific to a particular growth law and show that it is capable of identifying the underlying growth model. The metric remains constant over different time intervals if the underlying law is true, while the extent of its variation reflects the departure of the assumed model from the true one. We propose a new estimator of the relative growth rate, which is more sensitive to the true underlying model than the existing one. The advantage of using this is that it can detect crucial intervals where the growth process is erratic and unusual. It may help experimental scientists to study more closely the effect of the parameters responsible for the growth of the organism/population under study.Keywords Growth curve models · Average relative growth rate · Interval specific rate parameter · Overall rate parameter · Model selection

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The theta‐logistic is unreliable for modelling most census data

Cited by 101 publications

References 45 publications

Habitat suitability through time: using time series and habitat models to understand changes in bird density

Habitat suitability through time: using time series and habitat models to understand changes in bird density

Effect of Fe and EDTA on Freshwater Cyanobacteria Bloom Formation

Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach

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