Portrait of Dr Emily Dennis

Dr Emily Dennis

Visiting Research Associate in Statistics


Primarily supervised by Professor Byron Morgan, Emily's PhD research in statistical ecology centred upon developing methods for modelling the abundance of butterflies and other insects.

Research interests

Statistical Ecology: modelling species abundance, in particular butterflies and other insects



  • Freeman, S. et al. (2019). A generic method for estimating and smoothing multispecies biodiversity indices, robust to intermittent data. University of Kent.
    Biodiversity indicators provide a powerful and convenient way to summarise extensive, complex ecological data sets and are important in influencing government policy on biodiversity and conservation. Typically, component data consist of time-varying indices for each of a number of different species. There currently exists a wide range of different biodiversity indicators, but their derivation from these indices varies and they suffer from a range of statistical shortcomings. In this paper we describe a state-space formulation for new multispecies biodiversity indicators, based on rates of change in the abundance or occupancy11probability of the contributing individual species. Our formulation is flexible and applicable to a wide range of taxa. It possesses a number of desirable features, including:

    1) it provides a natural way to incorporate the sporadic unavailability of data;
    2) it can incorporate variation between years and species in the precision with which the individual species’ indices are estimated, and
    3) it allows the direct incorporation of smoothing over time. Furthermore, the same algorithm can be adopted for cases based on count (abundance) or ‘presence-absence’ (geographical range or distribution) data - only the subsequent interpretation differs. Model fitting is straightforward in either Bayesian or classical implementations, the latter following from efficient hidden Markov modelling. The procedure removes the need for bootstrapping, which can be prohibitive when huge volumes of data are available. We illustrate these desirable properties through the use of simulated data, and by applying our method to a suite of national-scale data sets from the UK.
  • Dennis, E. et al. (2019). Integrated modeling of insect population dynamics at two temporal scales. University of Kent.
    1. Population size of species with birth-pulse life-cycles varies both within and between seasons, but most population dynamics models ignore the former and assume that a population can be characterised adequately by a single number within a season. However, within-season dynamics can be too substantial to be ignored when modelling dynamics between seasons. Typical examples are insect populations or migratory animals. Numerous models for only between-season dynamics exist, but very few have combined dynamics at both temporal scales.
    2. We extend the models of Dennis et al. (2016b) in two directions: we adapt them for a generation time >1 year and fit them as an integrated population model for multiple data types, by maximising a joint likelihood for time-series of population counts of unmarked individuals and capture-recapture data from a smaller sample of sites with marked individuals. We analyse annual monitoring data for the endangered flightless beetle Iberodorcadion fuliginator from 17 populations in the Upper Rhine Valley for 1998–2016, with a 2-year life cycle. Standard tools of classical statistics are used for model fitting and comparison and a concentrated likelihood approach provides computational efficiency.
    3. The additional information introduced by the capture-recapture data makes the population model more robust and also enables true, rather than relative, abundance to be estimated. Fitting a dynamic stopover model provides estimates of survival and phenology parameters within a season, as well as productivity between seasons. For I. fuliginator, we demonstrate a population decline since 1998 and how this links with productivity, which is affected by temperature. A delayed mean emergence date in recent years is also shown.
    4. A main point of interest in our work is the focus on the two temporal scales at which perhaps most animal populations vary: in the short-term, a population is seldom ever truly closed even within a single season, and in the long term (between seasons) it never is. Hence models such as ours may serve as a template for a very general description of population dynamics in many species. This includes rare species with limited data sets, for which there is a general lack of population dynamic models, yet conservation actions may greatly benefit from this kind of models.


  • Dennis, E. et al. (2019). Trends and indicators for quantifying moth abundance and occupancy in Scotland. Journal of Insect Conservation [Online]. Available at: https://doi.org/10.1007/s10841-019-00135-z.
    Moths form an important part of Scotland’s biodiversity and an up-to-date assessment of their status is needed given their value as a diverse and species-rich taxon, with various ecosystem roles, and the known decline of moths within Britain. We use long-term citizen-science data to produce species-level trends and multi-species indicators for moths in Scotland, to assess population (abundance) and distribution (occupancy) changes.
    Abundance trends for moths in Scotland are produced using Rothamsted Insect Survey count data, and, for the first time, occupancy models are used to estimate occupancy trends for moths in Scotland, using opportunistic records from the National Moth Recording Scheme. Species-level trends are combined to produce abundance and occupancy indicators. The associated uncertainty is estimated using a parametric bootstrap approach, and comparisons are made with alternative published approaches.
    Overall moth abundance (based on 176 species) in Scotland decreased by 20% for 1975-2014 and by 46% for 1990-2014. The occupancy indicator, based on 230 species, showed a 16% increase for 1990-2014. Alternative methods produced similar indicators and conclusions, suggesting robustness of the results, although rare species may be under-represented in our analyses. Species abundance and occupancy trends were not clearly correlated; in particular species with negative population trends showed varied occupancy responses. Further research into the drivers of moth population changes is required, but increasing occupancy is likely to be driven by a warming summer climate facilitating range expansion, whereas population declines may be driven by reductions in habitat quality, changes in land management practices and warmer, wetter winters.
  • Dennis, E. et al. (2017). Urban indicators for UK butterflies. Ecological Indicators [Online] 76:184-193. Available at: http://dx.doi.org/10.1016/j.ecolind.2017.01.009.
    Most people live in urban environments and there is a need to produce abundance indices to assist policy and management of urban greenspaces and gardens. While regional indices are produced, with the exception of birds, studies of the differences between urban and rural areas are rare. We explore these differences for UK butterflies, with the intention to describe changes that are relevant to people living in urban areas, in order to better connect people with nature in support of conservation, provide a measure relevant to human well-being, and assess the biodiversity status of the urban environment.

    Transects walked under the UK Butterfly Monitoring Scheme are classified as urban or rural, using a classification for urban morphological zones. We use models from the Generalised Abundance Index family to produce urban and rural indices of relative abundance for UK butterfly species. Composite indices are constructed for various subsets of species. For univoltine and bivoltine species, where we are able to fit phenomenological models, we estimate measures of phenology and identify urban/rural differences. Trends in relative abundance over the period 1995–2014 are more negative in urban areas compared to rural areas for 25 out of 28 species. For the composite indices, all trends are negative, and they are significantly more negative for urban areas than for rural areas. Analysis of phenological parameters shows butterflies tend to emerge earlier in urban than in rural areas. In addition, some fly longer in urban than in rural areas, whereas in other cases the opposite is the case, and hypotheses are proposed to account for these features.

    Investigating new urban/rural indicators has revealed national declines that are stronger for urban areas. For continued monitoring, there is a need for an urban butterfly indicator, and for this to be evaluated and reported annually. We explain how this may be interpreted, and the relevance for other monitoring schemes. The results of this paper, including the phenological findings, shed new light on the potentially deleterious effects of urbanisation and climate change, which require suitable monitoring and reporting to support policy and management, for example of urban greenspaces and gardens.
  • Dennis, E. et al. (2017). Efficient occupancy model-fitting for extensive citizen-science data. PLoS ONE [Online]. Available at: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0174433.
    Appropriate large-scale citizen-science data present important new opportunities for biodiversity modelling, due in part to the wide spatial coverage of information. Recently proposed occupancy modelling approaches naturally incorporate random effects in order to account for annual variation in the composition of sites surveyed. In turn this leads to Bayesian analysis and model fitting, which are typically extremely time consuming. Motivated by presence-only records of occurrence from the UK Butterflies for the New Millennium data base, we present an alternative approach, in which site variation is described in a standard way through logistic regression on relevant environmental covariates. This allows efficient occupancy model-fitting using classical inference, which is easily achieved using standard computers. This is especially important when models need to be fitted each year, typically for many different species, as with British butterflies for example. Using both real and simulated data we demonstrate that the two approaches, with and without random effects, can result in similar conclusions regarding trends. There are many advantages to classical model-fitting, including the ability to compare a range of alternative models, identify appropriate covariates and assess model fit, using standard tools of maximum likelihood. In addition, modelling in terms of covariates provides opportunities for understanding the ecological processes that are in operation. We show that there is even greater potential; the classical approach allows us to construct regional indices simply, which indicate how changes in occupancy typically vary over a species’ range. In addition we are also able to construct dynamic occupancy maps, which provide a novel, modern tool for examining temporal changes in species distribution. These new developments may be applied to a wide range of taxa, and are valuable at a time of climate change. They also have the potential to motivate citizen scientists.
  • Dennis, E. et al. (2017). Using citizen science butterfly counts to predict species population trends. Conservation Biology [Online]. Available at: http://dx.doi.org/10.1111/cobi.12956.
    Citizen scientists are increasingly engaged in gathering biodiversity information, but trade-offs are often required between public engagement goals and reliable data collection. We compare population estimates derived from the first four years (2011-2014) of a short-duration citizen science project (Big Butterfly Count, BBC), to those from long-running, standardized monitoring data collected by experienced observers (UK Butterfly Monitoring Scheme, UKBMS), for 18 widespread butterfly species. BBC data are gathered during an annual, three-week period, whereas UKBMS sampling takes place over six months each year. An initial comparison with UKBMS data restricted to the three-week BBC period revealed that species population changes were significantly correlated between the two sources. The short-duration sampling season renders BBC counts susceptible to bias caused by inter-annual phenological variation in the timing of species’ flight periods. BBC counts were found to be described well by measures for phenology and sampling effort. Annual estimates of species abundance and population trends predicted from models including BBC data and weather covariates as a proxy for phenology correlated significantly with those derived from UKBMS data. In validating the BBC counts, we show, for the first time, that citizen science data, obtained using a simple sampling protocol, can produce comparable estimates of insect species abundance to standardized monitoring data. Although caution is urged in extrapolating from this UK study of a small number of common, conspicuous insects, we demonstrate that mass-participation citizen science can simultaneously contribute to public engagement and biodiversity monitoring. Mass-participation citizen science is not an adequate replacement for standardised biodiversity monitoring but may have a role in extending and complementing it (e.g. by sampling different land-use types), as well as serving to reconnect an increasingly urban human population with nature.
  • Dennis, E., Morgan, B. and Ridout, M. (2015). Computational aspects of N-mixture models. Biometrics [Online] 71:237-246. Available at: http://dx.doi.org/10.1111/biom.12246.
    The N-mixture model is widely used to estimate the abundance of a population in the presence of unknown
    detection probability from only a set of counts subject to spatial and temporal replication (Royle, 2004, Biometrics 60,105–115). We explain and exploit the equivalence of N-mixture and multivariate Poisson and negative-binomial models, which provides powerful new approaches for fitting these models. We show that particularly when detection probability and the number of sampling occasions are small, infinite estimates of abundance can arise. We propose a sample covariance as a diagnostic for this event, and demonstrate its good performance in the Poisson case. Infinite estimates may be missed in practice, due to numerical optimization procedures terminating at arbitrarily large values. It is shown that the use of a bound, K, for an infinite summation in the N-mixture likelihood can result in underestimation of abundance, so that default values of K in computer packages should be avoided. Instead we propose a simple automatic way to choose K. The methods are illustrated by analysis of data on Hermann’s tortoise Testudo hermanni.
  • Dennis, E. et al. (2013). Indexing butterfly abundance whilst accounting for missing counts and variability in seasonal pattern. Methods in Ecology and Evolution [Online] 4:637-645. Available at: http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12053/full.
    1. Volunteer-based ‘citizen science’ schemes now play a valuable role in deriving biodiversity indicators, both
    aiding the development of conservation policies and measuring the success of management. We provide a new
    method for analysing such data based on counts of invertebrate species characterised by highly variable numbers
    within a season combined with a substantial proportion of proposed survey visits not made.

    2. Using the UK Butterfly Monitoring Scheme (UKBMS) for illustration, we propose a two-stage model that
    makesmore efficient use of the data than previous analyses, whilst accounting for missing values. Firstly, generalised
    additive models were applied separately to data from each year to estimate the annual seasonal flight patterns.
    The estimated daily values were then normalised to estimate a seasonal pattern that is the same across sites
    but differs between years. A model was then fitted to the full set of annual counts, with seasonal values as an offset,
    to estimate annual changes in abundance accounting for the varying seasonality.

    3. The method was tested and compared against the current approach and a simple linear interpolation using
    simulated data, parameterised with values estimated from UKBMS data for three example species. The simulation
    study demonstrated accurate estimation of linear time trends and improved power for detecting trends compared with
    the current model.

    4. Comparison of indices for species covered by the UKBMS under the various model approaches showed similar
    predicted trends over time, but confidence intervals were generally narrower for the two-stage model.

    5. In addition to creating more robust trend estimates, the new method allows all volunteer records to contribute
    to the indices and thus incorporates data from more populations within the geographical range of a species. On
    average, the current model only enables data from 60% of 10 km2 grid squares with monitored sites to be
    included, whereas the two-stage model uses all available data and hence provides full coverage at least of the
    monitored area. As many invertebrate species exhibit similar patterns of emergence or voltinism, our two-stage
    method could be applied to other taxa.


  • Dennis, E. et al. (2019). Functional data analysis of multi-species abundance and occupancy data sets. University of Kent. Available at: http://www.kent.ac.uk/ims/statistics/.
    Multi-species indicators are widely used to condense large, complex amounts of information on multiple separate species by forming a single index to inform research, policy and management. Much detail is typically lost when such indices are constructed. Here we investigate the potential of Functional Data Analysis, focussing upon Functional Principal ComponentAnalysis (FPCA), which can be easily carried out using standard R programs, as a tool for displaying features of the underlying information. Illustrations are provided using data from the UK Butterflies for the New Millennium and UK Butterfly Monitoring Scheme databases. The FPCAs conducted result in a huge simplification in terms of dimensional reduction, allowing species occupancy and abundance to be reduced to two and three dimensions, respectively. We show that a functional principal component arises for both occupancy and abundance analyses that distinguishes between species that increase or decrease over time, and that it differs from percentage trend, which is a simplification of complex temporal changes. We find differences in species patterns of occupancy and abundance, providing a warning against routinely combining both types of index within multi-species indicators, for example when using occupancy as a proxy for abundance when sufficient abundance data are not available. By identifying the differences between species, figures displaying functional principal component scores are much more informative than the simple bar plots of percentages of significant trends that often accompany multi-species indicators. Informed by the outcomes of the FPCA, we make recommendations for accompanying visualisations for multi-species indicators, and discuss how these are likely to be context and audience specific. We show that, in the absence of FPCA, using mean species occupancy and total abundance can provide additional, accessible information to complement species-level trends. At the simplest level, we suggest using jitter plots to display variation in species-level trends. We recommend the routine augmentation of multi-species indicators in the future with additional statistical procedures and figures, to serve as an aid to improve communication and understanding of biodiversity metrics, as well as reveal potentially hidden patterns of behaviourand guide additional directions for investigation.
  • Dennis, E. et al. (2015). The construction of spatial distribution maps and regional occupancy indices from opportunistic records. University of Kent.
    A major advantage of opportunistic citizen-science data is the wide spatial and temporal coverage it provides, relative to long-standing monitoring data obtained from transect sampling, for example. Opportunistic schemes are used to form atlases for many taxa, but only broad trends between multi-year survey periods have typically been studied. Optimal methods for analysing opportunistic data are required, with the aim of greater understanding changes in species’ distributions. We apply occupancy models to opportunistic data in order to create spatial maps and regional indices.
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