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Stochastic processes that reinforce the traits listed above may generate positive feedback in aggressive species, permitting mass attack of healthy trees and the existence of an upper equilibrium, or outbreak density.
We fitted a bivariate Gaussian mixture model to the extracted HealthMap alerts to model a continuous surface of outbreak density (Technical Appendix).
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In population dynamics, variation in realised fecundity is important because increased fecundity is one way by which herbivorous insects escape density dependent regulation and attain outbreak densities [28], [29].
The leaf beetle Phratora vulgatissima frequently reach outbreak densities in natural willow stands [33] [35], as well as in willow plantations used for biomass production, where they are considered pests [36] [38].
In all neocolonized regions where the moth is present, C. ohridella maintains permanent outbreak densities, causing severe aesthetic damage to the horse-chestnut, a highly valued ornamental and amenity tree (Freise and Heitland 2004).
By limiting our analysis to areas contiguous with known dengue-endemic areas and smoothing outbreak alerts into an outbreak-density surface, we were able to identify a reliable signal of dengue spread.
This modeled outbreak probability density surface represents a risk map of recent DENV spread into areas of previously unknown dengue endemicity according to the 2010 Yellow Book.
Of the 19 new dengue-endemic areas reported in the 2012 Yellow Book, this threshold identified 14 (74%) as being at elevated risk of endemicity, according to the dengue outbreak probability density estimated by our model.
Four years after the 2005 2006 outbreak, wolf densities had recovered above pre-outbreak levels, and signs suggest a similar outcome following the 2010 outbreak.
To obtain a stronger and more generalized estimate of transmissibility across all of the outbreaks, probability density functions (e.g., Poisson, geometric), were fitted to these data by maximizing the log-likelihood function for the probability and frequency of individual transmission events aggregated across the datasets.
This design enabled us to compare the parental effects on offspring expression of phase-related traits between two naturally-occurring, genetically distinct populations of Locusta migratoria that differed in their historical patterns of high population density outbreak events.
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