Diversity, extinction, and threat status in Lagomorphs

A quarter of all lagomorphs (pikas, rabbits, hares and jackrabbits) are threatened with extinction, including several genera that contain only one species. The number of species in a genus correlates with extinction risk in lagomorphs, but not in other mammal groups, and this is concerning because the non-random extinction of small clades disproportionately threatens genetic diversity and phylogenetic history. Here, we use phylogenetic analyses to explore the properties of the lagomorph phylogeny and test if variation in evolution, biogeography and ecology between taxa explains current patterns of diversity and extinction risk. Threat status was not related to body size (and, by inference, its biological correlates), and there was no phylogenetic signal in extinction risk. We show that the lagomorph phylogeny has a similar clade-size distribution to other mammals, and found that genus size was unrelated to present climate, topography, or geographic range size. Extinction risk was greater in areas of higher human population density and negatively correlated with anthropogenically modified habitat. Consistent with this, habitat generalists were less likely to be threatened. Our models did not predict threat status accurately for taxa that experience region-specific threats. We suggest that pressure from human populations is so severe and widespread that it overrides ecological, biological, and geographic variation in extant lagomorphs.

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Ecological dynamics of extinct species in empty habitat networks. 1. The role of habitat pattern and quantity, stochasticity and dispersal

We examined a remnant host plant (Primula veris L.) habitat network that was last inhabited by the rare butterfly Hamearis lucina L. in north Wales in 1943, to assess the relative contribution of several spatial parameters to its regional extinction. We first examined relationships between P. veris characteristics and H. lucina eggs in surviving H. lucina populations, and used these to predict the suitability and potential carrying capacity of the habitat network in north Wales. This resulted in an estimate of roughly 4500 eggs (ca 227 adults). We developed a discrete space, discrete time metapopulation model to evaluate the relative contribution of dispersal distance, habitat and environmental stochasticity as possible causes of extinction. We simulated the potential persistence of the butterfly in the current network as well as in three artificial (historical and present) habitat networks that differed in the quantity (current and X3) and fragmentation of the habitat (current and aggregated). We identified that reduced habitat quantity and increased isolation would have increased the probability of regional extinction, in conjunction with environmental stochasticity and H. lucina's dispersal distance. This general trend did not change in a qualitative manner when we modified the ability of dispersing females to stay in, and find suitable habitats (by changing the size of the grid cells used in the model). Contrary to most metapopulation model predictions, system persistence declined with increasing migration rate, suggesting that the mortality of migrating individuals in fragmented landscapes may pose significant risks to system-wide persistence. Based on model predictions for the present landscape we argue that a major programme of habitat restoration would be required for a re-established metapopulation to persist for > 100 years.