Edwige Bellier

Combining counts and incidence data: an efficient approach for estimating the log-normal species abundance distribution and diversity indices

Obtaining accurate estimates of diversity indices is difficult because the number of species encountered in a sample increases with sampling intensity. We introduce a novel method that requires that the presence of species in a sample to be assessed while the counts of the number of individuals per species are only required for just a small part of the sample. To account for species included as incidence data in the species abundance distribution, we modify the likelihood function of the classical Poisson log-normal distribution. Using simulated community assemblages, we contrast diversity estimates based on a community sample, a subsample randomly extracted from the community sample, and a mixture sample where incidence data are added to a subsample. We show that the mixture sampling approach provides more accurate estimates than the subsample and at little extra cost. Diversity indices estimated from a freshwater zooplankton community sampled using the mixture approach show the same pattern of results as the simulation study. Our method efficiently increases the accuracy of diversity estimates and comprehension of the left tail of the species abundance distribution. We show how to choose the scale of sample size needed for a compromise between information gained, accuracy of the estimates and cost expended when assessing biological diversity. The sample size estimates are obtained from key community characteristics, such as the expected number of species in the community, the expected number of individuals in a sample and the evenness of the community.

Geostatistical Modelling of Wildlife Populations: A Non-stationary Hierarchical Model for Count Data

We propose a hierarchical model coupled to geostatistics to deal with a non-gaussian data distribution and take explicitly into account complex spatial structures (i.e. trends, patchiness and random fluctuations). A common characteristic of animal count data is a distribution that is both zero-inflated and heavy tailed. In such cases, empirical variograms are no more robust and most structural analyses result in poor and noisy estimated spatial variogram structures. Thus kriged maps feature a broad variance of prediction. Moreover, due to the heterogeneity of wildlife population habitats, a nonstationary model is often required. To avoid these difficulties, we propose a hierarchical model that assumes that the count data follow a Poisson distribution given a theoretical sighting density which is a latent variable to be estimate. This density is modelled as the product of a positive long range trend by a positive stationary random field, characterized by a unit mean and a variogram function. A first estimate of the drift is used to obtain an estimate of the variogram of residuals including a correction term for variance coming from the Poisson distribution and weights due to the non-constant spatial mean. Then a kriging procedure similar to a modified universal kriging is implemented to directly map the latent density from raw count data. An application on fin whale data illustrates the effectiveness of the method in mapping animal density in a context that is presumably non-stationary.

Marine reserve spillover: Modelling from multiple data sources

article i nfo The functional form of spillover, measured as a gradient of abundance of fish, may provide insight about processes that control the spatial distribution of fish inside and outside the MPA. In this study, we aimed to infer on spillover mechanism of Diplodus spp. (family Sparidae) from a Mediterranean MPA (Carry-le-Rouet, France) from visual censuses and artisanal fisheries data. From the existing literature, three potential functional forms of spillover suchasalineargradient,anexponentialgradientandalogisticgradientaredefined. Each functional form is includ- ed in a spatial generalized linear mixed model allowing accounting for spatial autocorrelation of data. We select between the different forms of gradients by using a Bayesian model selection procedure. In a first step, the func- tional form of the spillover for visual census and artisanal fishing data is assessed separately. For both sets of data, our model selection favoured the negative exponential model, evidencing a decrease of the spatial abundance of fish vanishing around 1000 m from the MPA border. We combined both datasets in a joint model by including an observability parameter. This parameter captures how the different sources of data quantifytheunderlyingspa- tial distribution of the harvested species. This enabled us to demonstrate that the different sampling methods do not affect the estimation of the underlying spatial distribution of Diplodus spp. inside and outside the MPA. We show that data from different sources can be pooled through spatial generalized linear mixed model. Our findings

Estimating inter-group interaction radius for point processes with nested spatial structures

A statistical procedure is proposed in order to estimate the interaction radius between points of a non-stationary point process when the process can present local aggregated and regular patterns. The model under consideration is a hierarchical process with two levels, points and clusters of points. Points will represent individuals, clusters will represent groups of individuals. Points or clusters do not interact as soon as they are located beyond a given interaction radius, and are assumed to interact if their distance is less than this interaction radius. Interaction radius estimation is performed in the following way. For a given distance, observations are split into several clusters whose in-between distances are larger than this distance. For each cluster, a neighbourhood and an area in which this cluster is randomly located is defined under the assumption that the distance between the cluster and its neighbourhood is larger than the interaction radius. The p-value of a test of this assumption is then computed for each cluster. Modelling the expectation of this p-value as a function of the distance leads to an estimate of the interaction radius by a least-square method. This approach is shown to be robust against non-stationarity. Unlike most classical approaches, this method makes no assumption on the point spatial distribution inside the clusters. Two applications are presented in animal and plant ecology.