Embedding Population Dynamics Models in Inference

Buckland, Stephen T.; Newman, Ken; Fernández, Carmen; Thomas, Len; Harwood, John

doi:10.1214/088342306000000673

Cited by 114 publications

(113 citation statements)

References 67 publications

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“…Simulations that contained both process and observation error were used to assess the validity of this assumption. We found that the methodology was robust to violations of the assumption of no observation error (see SI Text and Table S1 for details), thus obviating the need for a more sophisticated approach of fitting a model with both types of noise (33,34). Further studies are needed to assess the robustness of our findings to more realistic stochasticity and observation error (36).…”

Section: Methodsmentioning

confidence: 82%

Host–pathogen time series data in wildlife support a transmission function between density and frequency dependence

Smith

Telfer

Kallio

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

130

194

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A key aim in epidemiology is to understand how pathogens spread within their host populations. Central to this is an elucidation of a pathogen's transmission dynamics. Mathematical models have generally assumed that either contact rate between hosts is linearly related to host density (density-dependent) or that contact rate is independent of density (frequency-dependent), but attempts to confirm either these or alternative transmission functions have been rare. Here, we fit infection equations to 6 years of data on cowpox virus infection (a zoonotic pathogen) for 4 natural populations to investigate which of these transmission functions is best supported by the data. We utilize a simple reformulation of the traditional transmission equations that greatly aids the estimation of the relationship between density and host contact rate. Our results provide support for an infection rate that is a saturating function of host density. Moreover, we find strong support for seasonality in both the transmission coefficient and the relationship between host contact rate and host density, probably reflecting seasonal variations in social behavior and/or host susceptibility to infection. We find, too, that the identification of an appropriate loss term is a key component in inferring the transmission mechanism. Our study illustrates how time series data of the hostpathogen dynamics, especially of the number of susceptible individuals, can greatly facilitate the fitting of mechanistic disease models.cowpox ͉ disease ͉ population cycles ͉ Markov chain Monte Carlo T he seminal studies of Anderson and May (1, 2) introduced a framework for modeling the dynamics of pathogens and their hosts that has since underpinned most predictive models of host-pathogen dynamics. It has been standard practice when modeling the dynamics of host-microparasite interactions (viral and bacterial infections) to represent the rate of change of infected hosts I(t) at time t by dI͑t͒ dt ϭ transmission rate ͑infection͒ Ϫ loss rate ͑death ϩ recovery͒.[1]However, empirically based identification of appropriate functional forms for the ''transmission rate'' and ''loss rate'' terms has not generally been possible for systems with host dynamics because of a lack of sufficient data (although refs. 3 and 4 have recently done this for infectious diseases of human populations).To date, most studies have used transmission rate terms that are either density-dependent or frequency-dependent (5, 6). The underlying difference between these is the assumption about how host contact rate c, varies with host density [(N(t))/A], where N(t) is host abundance and A, the area occupied by the population, is usually assumed constant and omitted from the equations (6). For density-dependent transmission, host contact rate varies linearly with density [typically adopted for directly transmitted diseases such as measles (7) and foot and mouth disease (8)], whereas for frequencydependent transmission it is constant [typically adopted for sexually transmitted diseases such as HIV in ...

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Section: Methodsmentioning

confidence: 82%

Host–pathogen time series data in wildlife support a transmission function between density and frequency dependence

Smith

Telfer

Kallio

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

130

194

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“…Fecundity (average number of females produced per female, f ) was set at 2.6, juvenile survival (survival from birth until 1 yr old, / juv ) at 0.2 and adult survival (annual survival after 1 yr of age, / ad ) at 0.5. The expected number of individuals in the two age classes at time t þ 1 is given by the product of the population vector (containing the number of individuals) in year t and the projection matrix (Caswell 2001, Buckland et al 2007 as…”

Section: Methodsmentioning

confidence: 99%

An assessment of integrated population models: bias, accuracy, and violation of the assumption of independence

Abadi

Giménez

Arlettaz

et al. 2010

Ecology

177

182

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Abstract. Understanding population dynamics requires accurate estimates of demographic rates. Integrated population models combine demographic and survey data into a single, comprehensive analysis and provide more coherent estimates of vital rates. Integrated population models rely on the assumption that different data sets are independent, which is frequently violated in practice. Moreover, the precision that can be gained using integrated modeling compared to conventional modeling is only known from empirical studies. The present study used simulation methods to assess how the violation of the assumption of independence affects the statistical properties of the parameter estimators. Further, the gains in precision and accuracy from the model were explored under varying sample sizes. For capture-recapture, population survey, and reproductive success, we generated independent and dependent data that were analyzed with integrated and conventional models. We found only a minimal impact of the violation of the assumption of independence on the parameter estimates. Furthermore, we observed an overall gain in precision and accuracy when all three data sets were analyzed simultaneously. This was particularly pronounced when the sample size was small. These findings contribute to clearing the way for the application of integrated population models in practice.

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“…Estimation of density and habitat relationships may also be combined in a single analysis (Hedley et al 2004, Royle et al 2004, Johnson et al 2010, Niemi & Fernández 2010. Inference about population processes is improved when combined with an observation model into a single likelihood framework (Goodman 2004, Buckland et al 2007, Royle & Dorazio 2008.…”

Section: Discussionmentioning

confidence: 99%