Tamsin E. Lee

Inferring extinctions from sighting records of variable reliability

A range of mathematical models has been developed to infer whether a species is extinct based on a sighting record. Although observations have variable reliability, current methods for detecting extinction do not differentiate observation qualities. A more suitable approach would consider certain and uncertain sightings throughout the sighting period. We consider a small population system, meaning we assume sighting rates are constant and the population is not declining. Based on such an assumption, we develop a Bayesian method that assumes that certain and uncertain sightings occur independently and at uniform rates. These two types of sightings are connected by a common extinction date. Several rates of false sightings can be calculated to differentiate between observation types. Prior rates of false and true sightings, as well as a prior probability that the species is extant, are included. The model is implemented in OpenBugs, which uses Markov chain Monte Carlo (MCMC). Based on records of variable reliability, we estimate the probability that the following species are extinct: Caribbean seal Monachus tropicalis, grey, black-footed ferret Mustela nigripes, Audubon & Bachman, greater stick-nest rat Leporillus conditor, Sturt, and lesser stick-nest rat Leporillus apicalis, Gould. As further examples, Birdlife International provided the sighting records for the Alaotra grebe Tachybaptus rufolavatus, Delacour, Jamaica petrel Pterodroma caribbaea, Carte, and Pohnpei mountain starling Aplonis pelzelni, Finsch, with prior probabilities for extinction. The results are compared with existing methods, which ignore uncertain sightings. We find that including uncertain sightings can considerably change the probability that the species is extant, in either direction. However, in our examples, including the quality of the uncertain sighting made little difference. When we ignore uncertain sightings, our results agree with existing methods, especially when the last sighting was near the end of the sighting period. Synthesis and applications. Estimating the probability that a species is extinct based on sighting records is important when determining conservation priorities and allocating available resources into management activities. Having a model that allows for certain and uncertain observations throughout the sighting period better accommodates the realities of sighting quality, providing a more reliable basis for decision-making.

Estimating the extent and structure of trade in horticultural orchids via social media

The wildlife trade is a lucrative industry involving thousands of animal and plant species. The increasing use of the internet for both legal and illegal wildlife trade is well documented, but there is evidence that trade may be emerging on new online technologies such as social media. Using the orchid trade as a case study, we conducted the first systematic survey of wildlife trade on an international social-media website. We focused on themed forums (groups), where people with similar interests can interact by uploading images or text (posts) that are visible to other group members. We used social-network analysis to examine the ties between 150 of these orchid-themed groups to determine the structure of the network. We found 4 communities of closely linked groups based around shared language. Most trade occurred in a community that consisted of English-speaking and Southeast Asian groups. In addition to the network analysis, we randomly sampled 30 groups from the whole network to assess the prevalence of trade in cultivated and wild plants. Of 55,805 posts recorded over 12 weeks, 8.9% contained plants for sale, and 22-46% of these posts pertained to wild-collected orchids. Although total numbers of posts about trade were relatively small, the large proportion of posts advertising wild orchids for sale supports calls for better monitoring of social media for trade in wild-collected plants.

A genetic algorithm approach for modelling low voltage network demands

Abstract Distribution network operators (DNOs) are increasingly concerned about the impact of low carbon technologies on the low voltage (LV) networks. More advanced metering infrastructures provide numerous opportunities for more accurate load flow analysis of the LV networks. However, such data may not be readily available for DNOs and in any case is likely to be expensive. Modelling tools are required which can provide realistic, yet accurate, load profiles as input for a network modelling tool, without needing access to large amounts of monitored customer data. In this paper we outline some simple methods for accurately modelling a large number of unmonitored residential customers at the LV level. We do this by a process we call buddying, which models unmonitored customers by assigning them load profiles from a limited sample of monitored customers who have smart meters. Hence the presented method requires access to only a relatively small amount of domestic customers’ data. The method is efficiently optimised using a genetic algorithm to minimise a weighted cost function between matching the substation data and the individual mean daily demands. Hence we can show the effectiveness of substation monitoring in LV network modelling. Using real LV network modelling, we show that our methods perform significantly better than a comparative Monte Carlo approach, and provide a description of the peak demand behaviour.

A simple numerical tool to infer whether a species is extinct

Summary Including uncertain sightings when inferring extinction of a species is relatively new and has proven to be significant. However, including uncertain sightings leads to non-trivial mathematical problems which are inaccessible to many ecologists. I use the Pohnpei Mountain Starling Aplonis pelzelni to describe an Excel spreadsheet which infers extinction from a sighting record. The spreadsheet implements a Bayesian model which includes uncertainty around the prior, uncertain sightings and survey effort. Survey effort has not been included in extinction models before, but clearly plays a significant role in extinction estimates, which the Pohnpei Mountain Starling example demonstrates. The spreadsheet (included as supplementary material) is user-friendly, fast and accessible on Windows.

Assessing uncertainty in sighting records: an example of the Barbary lion

As species become rare and approach extinction, purported sightings can be controversial, especially when scarce management resources are at stake. We consider the probability that each individual sighting of a series is valid. Obtaining these probabilities requires a strict framework to ensure that they are as accurately representative as possible. We used a process, which has proven to provide accurate estimates from a group of experts, to obtain probabilities for the validation of 32 sightings of the Barbary lion. We consider the scenario where experts are simply asked whether a sighting was valid, as well as asking them to score the sighting based on distinguishablity, observer competence, and verifiability. We find that asking experts to provide scores for these three aspects resulted in each sighting being considered more individually, meaning that this new questioning method provides very different estimated probabilities that a sighting is valid, which greatly affects the outcome from an extinction model. We consider linear opinion pooling and logarithm opinion pooling to combine the three scores, and also to combine opinions on each sighting. We find the two methods produce similar outcomes, allowing the user to focus on chosen features of each method, such as satisfying the marginalisation property or being externally Bayesian.

Comparison of social structures within cities of very different sizes.

People make a city, making each city as unique as the combination of its inhabitants. However, some cities are similar and some cities are inimitable. We examine the social structure of 10 different cities using Twitter data. Each city is decomposed to its communities. We show that in many cases one city can be thought of as an amalgamation of communities from another city. For example, we find the social network of Manchester is very similar to the social network of a virtual city of the same size, where the virtual city is composed of communities from the Bristol network. However, we cannot create Bristol from Manchester since Bristol contains communities with a social structure that are not present in Manchester. Some cities, such as Leeds, are outliers. That is, Leeds contains a particularly wide range of communities, meaning we cannot build a similar city from communities outside of Leeds. Comparing communities from different cities, and building virtual cities that are comparable to real cities, is a novel approach to understand social networks. This has implications when using social media to inform or advise residents of a city.

Extinct or still out there? Disentangling influences on extinction and rediscovery helps to clarify the fate of species on the edge

Each year, two or three species that had been considered to be extinct are rediscovered. Uncertainty about whether or not a species is extinct is common, because rare and highly threatened species are difficult to detect. Biological traits such as body size and range size are expected to be associated with extinction. However, these traits, together with the intensity of search effort, might influence the probability of detection and extinction differently. This makes statistical analysis of extinction and rediscovery challenging. Here, we use a variant of survival analysis known as cure rate modelling to differentiate factors that influence rediscovery from those that influence extinction. We analyse a global data set of 99 mammals that have been categorized as extinct or possibly extinct. We estimate the probability that each of these mammals is still extant and thus estimate the proportion of missing (presumed extinct) mammals that are incorrectly assigned extinction. We find that body mass and population density are predictors of extinction, and body mass and search effort predict rediscovery. In mammals, extinction rate increases with body mass and population density, and these traits act synergistically to greatly elevate extinction rate in large species that also occurred in formerly dense populations. However, when they remain extant, larger-bodied missing species are rediscovered sooner than smaller species. Greater search effort increases the probability of rediscovery in larger species of missing mammals, but has a minimal effect on small species, which take longer to be rediscovered, if extant. By separating the effects of species characteristics on extinction and detection, and using models with the assumption that a proportion of missing species will never be rediscovered, our new approach provides estimates of extinction probability in species with few observation records and scant ecological information.

On strongly connected networks with excitable-refractory dynamics and delayed coupling

We consider a directed graph model for the human brain’s neural architecture that is based on small scale, directed, strongly connected sub-graphs (SCGs) of neurons, that are connected together by a sparser mesoscopic network. We assume transmission delays within neuron-to-neuron stimulation, and that individual neurons have an excitable-refractory dynamic, with single firing ‘spikes’ occurring on a much faster time scale than that of the transmission delays. We demonstrate numerically that the SCGs typically have attractors that are equivalent to continual winding maps over relatively low-dimensional tori, thus representing a limit on the range of distinct behaviour. For a discrete formulation, we conduct a large-scale survey of SCGs of varying size, but with the same local structure. We demonstrate that there may be benefits (increased processing capacity and efficiency) in brains having evolved to have a larger number of small irreducible sub-graphs, rather than few, large irreducible sub-graphs. The network of SCGs could be thought of as an architecture that has evolved to create decisions in the light of partial or early incoming information. Hence the applicability of the proposed paradigm to underpinning human cognition.

Are extinction opinions extinct

Extinction models vary in the information they require, the simplest considering the rate of certain sightings only. More complicated methods include uncertain sightings and allow for variation in the reliability of uncertain sightings. Generally extinction models require expert opinion, either as a prior belief that a species is extinct, or to establish the quality of a sighting record, or both. Is this subjectivity necessary? We present two models to explore whether the individual quality of sightings, judged by experts, is strongly informative of the probability of extinction: the ‘quality breakpoint method’ and the ‘quality as variance method’. For the first method we use the Barbary lion as an exemplar. For the second method we use the Barbary lion, Alaotra grebe, Jamaican petrel and Pohnpei starling as exemplars. The ‘quality breakpoint method’ uses certain and uncertain sighting records, and the quality of uncertain records, to establish whether a change point in the rate of sightings can be established using a simultaneous Bayesian optimisation with a non-informative prior. For the Barbary lion, there is a change in subjective quality of sightings around 1930. Unexpectedly sighting quality increases after this date. This suggests that including quality scores from experts can lead to irregular effects and may not offer reliable results. As an alternative, we use quality as a measure of variance around the sightings, not a change in quality. This leads to predictions with larger standard deviations, however the results remain consistent across any prior belief of extinction. Nonetheless, replacing actual quality scores with random quality scores showed little difference, inferring that the quality scores from experts are superfluous. Therefore, we deem the expensive process of obtaining pooled expert estimates as unnecessary, and even when used we recommend that sighting data should have minimal input from experts in terms of assessing the sighting quality at a fine scale. Rather, sightings should be classed as certain or uncertain, using a framework that is as independent of human bias as possible.

Species distributions and area relationships

The well-known species-area relationship is one of many scaling laws, or allometries, in ecology and biology that have received much attention over the years. We present a new derivation of this relationship based on Yule׳s theory of evolution of species. Using definitions of mutation rates, our analysis yields species-area exponents that are in close agreement with previously observed values.