Henrik B. Rasmussen

Effective population size dynamics reveal impacts of historic climatic events and recent anthropogenic pressure in African elephants

Two hundred years of elephant hunting for ivory, peaking in 1970–1980s, caused local extirpations and massive population declines across Africa. The resulting genetic impacts on surviving populations have not been studied, despite the importance of understanding the evolutionary repercussions of such human‐mediated events on this keystone species. Using Bayesian coalescent‐based genetic methods to evaluate time‐specific changes in effective population size, we analysed genetic variation in 20 highly polymorphic microsatellite loci from 400 elephants inhabiting the greater Samburu‐Laikipia region of northern Kenya. This area experienced a decline of between 80% and 90% in the last few decades when ivory harvesting was rampant. The most significant change in effective population size, however, occurred approximately 2500 years ago during a mid–Holocene period of climatic drying in tropical Africa. Contrary to expectations, detailed analyses of four contemporary age‐based cohorts showed that the peak poaching epidemic in the 1970s caused detectable temporary genetic impacts, with genetic diversity rebounding as juveniles surviving the poaching era became reproductively mature. This study demonstrates the importance of climatic history in shaping the distribution and genetic history of a keystone species and highlights the utility of coalescent‐based demographic approaches in unravelling ancestral demographic events despite a lack of ancient samples. Unique insights into the genetic signature of mid‐Holocene climatic change in Africa and effects of recent poaching pressure on elephants are discussed.

Where sociality and relatedness diverge: the genetic basis for hierarchical social organization in African elephants

Hierarchical properties characterize elephant fission–fusion social organization whereby stable groups of individuals coalesce into higher order groups or split in a predictable manner. This hierarchical complexity is rare among animals and, as such, an examination of the factors driving its emergence offers unique insight into the evolution of social behaviour. Investigation of the genetic basis for such social affiliation demonstrates that while the majority of core social groups (second-tier affiliates) are significantly related, this is not exclusively the case. As such, direct benefits received through membership of these groups appear to be salient to their formation and maintenance. Further analysis revealed that the majority of groups in the two higher social echelons (third and fourth tiers) are typically not significantly related. The majority of third-tier members are matrilocal, carrying the same mtDNA control region haplotype, while matrilocality among fourth-tier groups was slightly less than expected at random. Comparison of results to those from a less disturbed population suggests that human depredation, leading to social disruption, altered the genetic underpinning of social relations in the study population. These results suggest that inclusive fitness benefits may crystallize elephant hierarchical social structuring along genetic lines when populations are undisturbed. However, indirect benefits are not critical to the formation and maintenance of second-, third- or fourth-tier level bonds, indicating the importance of direct benefits in the emergence of complex, hierarchical social relations among elephants. Future directions and conservation implications are discussed.

Population Genetic Structure of Savannah Elephants in Kenya: Conservation and Management Implications

We investigated population genetic structure and regional differentiation among African savannah elephants in Kenya using mitochondrial and microsatellite markers. We observed mitochondrial DNA (mtDNA) nucleotide diversity of 1.68% and microsatellite variation in terms of average number of alleles, expected and observed heterozygosities in the total study population of 10.20, 0.75, and 0.69, respectively. Hierarchical analysis of molecular variance of mtDNA variation revealed significant differentiation among the 3 geographical regions studied (F(CT) = 0.264; P < 0.05) and a relatively lower differentiation among populations within regions (F(SC) = 0.218; P < 0.0001). Microsatellite variation significantly differentiated among populations within regions (F(SC) = 0.019; P < 0.0001) but not at the regional levels (F(CT) = 0.000; P > 0.500). We attribute the high differentiation at the mitochondrial genome to the matrilineal social structure of elephant populations, female natal philopatry, and probably ancient vicariance. Lack of significant regional differentiation at the nuclear loci vis-a-vis strong differences at mtDNA loci between regions is likely the effect of subsequent homogenization through male-mediated gene flow. Our results depicting 3 broad regional mtDNA groups and the observed population genetic differentiation as well as connectivity patterns should be incorporated in the planning of future management activities such as translocations.

An option pricing formula for the GARCH diffusion model

The first four conditional moments of the integrated variance implied by the GARCH diffusionprocess are derived analytically. Based on these moments and on a power series method an analytical approximation formula to price European options under the GARCH diffusion model is obtained. Monte Carlo simulations show that this approximation formula up to order three is accurate for a large set of reasonable parameters and highlight potential instabilities of the fourth term. Finally, the closed-form approximation formula is used to shed light on the qualitative properties of implied volatility surfaces induced by GARCH diffusion models.

Controlling for behavioural state reveals social dynamics among male African elephants, Loxodonta africana

The drivers of social affiliation may vary over time as individuals change their goals with respect to changing environments or physical condition. Studies of companion preference rarely consider shifts in motivational state, despite the potential importance of such shifts in structuring association and population processes. Ignoring state dependence in social behaviour may weaken the ability to recognize social properties and identify their underlying drivers. Modifying established approaches, we apply a state-specific analysis to investigate social properties in male African elephants, which are thought to be weakly social. Specifically, we delineate associations during distinct sexually active and inactive periods and quantify common social metrics (network size, density, betweenness and the number and age of preferred companions) to examine how sexual states may relate to male elephant social relationships. We found that state-dependent association index values were higher and quantitative definitions of preferred companions were more conservative than those derived when sexual state was not taken into account. Preferred companions tended to be closer in age among sexually inactive dyads relative to sexually active dyads, indicating that bulls seek out age-mates when sexually inactive. Networks were larger and denser when sexually inactive. By accounting for dynamic behaviour in social systems, this study demonstrates that male African elephants show more social preference than had been previously thought.