Evolutionary responses to harvesting in ungulates

Authors


G. Proaktor, Division of Biology and Centre for Population Biology, Imperial College, Silwood Park, Ascot, Berkshire, SL5 7PY, UK. E-mail: gil.proaktor03@imperial.ac.uk

Summary

  • 1We investigate the evolutionary responses to harvesting in ungulates using a state-dependent, stochastic, density-dependent individual-based model of red deer Cervus elaphus (L.) females subject to different harvesting regimes.
  • 2The population's mean weight at first reproduction shifts towards light weights as harvesting increases, and its distribution changes from a single peak distribution under very low or high harvest rates, to a bimodal distribution under intermediate harvest rates.
  • 3These results suggest that, consistent with previous studies on aquatic species, harvesting-induced mortality may drive adaptive responses in ungulates by reducing the fitness benefits from adult survival and growth in favour of early and lightweight reproduction.
  • 4Selective harvesting for heavy animals has no additional effect on the evolutionarily stable strategy, suggesting that harvest rate is more important than the degree of selectivity in driving adaptive responses. However, selective harvesting of light females is positively associated with maturation weights even higher than those of a nonharvested population, probably due to the reduction in the fitness value of the offspring.
  • 5The average number of weight at maturation strategies in the population declines but the total number of strategies across all simulations increases with harvest rate, suggesting that harvesting-induced selection on weight at maturity overcomes the increase in strategy diversity expected from density-dependent release.
  • 6Yield initially increases with harvesting due to enhanced productivity of light females experiencing density-dependent release. However, it crashes under intense harvesting resulting in a population skewed to light, young and, therefore, less reproductive animals.

Introduction

Harvesting has been linked to demographic changes in many wild populations, such as skewed age structure and reduced life-expectancy (Langvatn & Loison 1999), fluctuations in population size (Myers et al. 1995; Solberg et al. 1999) and skewed sex ratio (Ginsberg & Milner-Gulland 1994; Saether, Solberg & Heim 2003). Harvesting has also been implicated in evolutionary changes in heritable traits (Ricker 1981; Stockwell, Hendry & Kinnison 2003; Hutchings 2004). For example, Hutchings (2005) suggested that overexploitation of the North-west Atlantic cod Gadus morhua (L.) over the past 40 years has caused a significant reduction in age and length at maturity. The majority of studies on the evolutionary consequences of harvesting have focused on commercially important fish populations due to the financial interest in such consequences and the wealth of data on their biological, ecological and demographic characteristics (Law 2000; Ratner & Lande 2001). However, it is unclear if evolutionary responses to harvesting observed in fish also affect terrestrial species. Moreover, as fishing mortality is usually selective according to one or more phenotypic traits (Stergiou & Erzini 2002), it is yet to be established what the relative contributions are of harvest rate and the degree of selectivity to the overall harvesting-induced adaptive changes.

Ungulates are heavily harvested throughout the world for both meat and trophies (Milner-Gulland & Clayton 2002; Milner-Gulland, Coulson & Clutton-Brock 2004). While numerous studies have illuminated the demographic consequences of harvesting for many populations of ungulates (Gaillard, Festa-Bianchet & Yoccoz 1998; Coulson et al. 2004), only a few studies have focused on the evolutionary aspects of harvesting, mainly in males (Fitzsimmons, Buskirk & Smith 1995; Coltman et al. 2003). Regarding females, anecdotal evidence from other terrestrial species, for example the red kangaroo Macropus rufus (L.), suggests that selective harvesting of large individuals may drive the evolution of lighter weights at maturity and adulthood (Tenhumberg et al. 2004). The key factor that may be responsible for the evolution of lighter weights is the increase in mortality due to harvesting, resulting in a negative correlation between weight and age at maturity and successful reproduction. Whether harvesting-induced mortality drives the evolution of a lighter weight at maturity in ungulates, or prevents it due to the release from competition driven by the reduced densities of harvested populations, is yet to be established. Moreover, research on the evolutionary implications of harvesting for management and conservation of ungulates has almost exclusively focused on male traits. Therefore, the time-scale for genetic recovery of female-related traits, such as the weight at first reproduction, is unknown but important for decision makers. Evidence from fish populations suggests that genetic recovery from harvesting may take much longer than demographic recovery (Hutchings 2000).

A major difficulty in addressing these issues is the lack of detailed data sets on harvested populations that span a sufficiently long time for evolutionary changes to occur. This can be partially overcome using computer models that enable investigations over evolutionary time-scales. Another advantage is that the same model can simulate a range of different harvesting scenarios, and control factors such as immigration that may interact with harvesting-induced effects. In particular, individual-based models have been demonstrated as a useful tool for addressing demographic and evolutionary aspects of harvested populations (Witting 2002).

In this paper, we investigate the evolutionary effects of different types of harvesting on reproductive strategies in red deer females. We use a state-dependent individual-based model (IBM) that optimizes females’ reproductive strategies in a stochastic density-dependent environment. The model excludes males because the focus here is on female life-history traits, namely reproductive strategies. Initially, we test the hypothesis that the mean weight at first reproduction declines when harvest rate increases. We also test the hypothesis that selective harvesting of heavy females selects for lighter weights at maturity, and selective harvesting of light females select for heavier weights at maturity. Testing these hypotheses sheds light on whether harvesting-induced adaptive changes in ungulates are primarily driven by the rate or the degree of selectivity of harvesting. Next, we explore the effects of harvesting on the diversity of reproductive strategies. While moderate levels of harvesting, like other types of anthropogenic or natural disturbances, may increase biotic diversity (Connell 1978), it is unclear whether harvesting generates evolutionary changes in the diversity of reproductive strategies within a single population, and between different populations. Finally, we examine if these responses to harvesting change the potential harvesting yield, and discuss the implications for management and conservation.

Methods

model overview

The IBM developed here is a state-dependent model which is used to optimize weight-specific reproductive strategies of red deer females in a stochastic density-dependent environment (Fig. 1). Accumulation of weight is modelled as a proportional share of the available food resources to all nonsuckling individuals in the population (Appendix S1, see Supplementary material). Offspring up to age 6 months suckle from their mothers and therefore their weight gain is modelled as a function of the mother's body weight (Appendix S1). Each offspring inherits her reproductive strategy from her mother with a certain chance of mutation (Appendix S2). Reproduction is traded against survival (cost of reproduction) through its negative effect on the female's body weight (Appendix S2), which in turn determines the female's probability of survival to the next year (Appendix S3). The distribution of reproductive strategies evolves when females with suboptimal strategies are out-competed by females with strategies that are more suitable to the environmental conditions. Females with better strategies produce on average more viable copies of their particular strategy hence, have a greater lifetime reproductive success. Any combination of weight-specific strategy can emerge through mutation. This enables the model to evolve the set of reproductive strategies that is most suitable for the simulated conditions. The focus on body weight captures the link between density-dependent and independent environmental conditions and reproduction on the one hand, and survival and future reproduction on the other (Hancock, Milner-Gulland & Keeling 2005). This IBM provides a link between individual phenotypes (reproductive strategy and state), and population dynamic processes. It is unusual because it incorporates inheritance of reproductive strategies within a realistic model of population dynamics, a characteristic that makes this model particularly suitable for understanding evolution of reproductive behaviour in complex systems, where individual body condition is intimately linked to reproductive decisions and success (Boyd 2000).

Figure 1.

A schematic diagram of the weight-based individual-based model of red deer females.

Two aspects of harvesting are incorporated in the model: absolute offtake rate (harvest quota) and the level of selectivity towards animals according to their weight. The potential of harvesting for generating evolutionary changes in the reproductive characteristics of red deer females is initially assessed for random harvesting, and subsequently for selective harvesting.

harvesting

A given proportion, q, of the population is harvested each year. Based on q and on the population size, n, the total number of individuals harvested, h, is removed from the population at the beginning of the year before they have a chance to reproduce. Harvesting is modelled in two ways. First, by a linear function of weight whereby the probability of a given individual being harvested, ζ, is:

ζ = ψ × a × Wi,t + d(eqn 1)

where ψ is a scaling constant for weight selectivity, a and d are constants, and Wi,t is the weight of individual i at time t. When ψ = 0 harvesting is nonselective with respect to weight and therefore individuals are harvested at random. When ψ > 0 the probability of a given female being harvested increases linearly with her weight, and when ψ < 0 it declines with weight. The degree of selectivity for harvesting heavy or light animals is directly proportional to the value of ψ. Eqn 1 is applied to individuals chosen randomly from a uniform distribution, so each individual has an equal probability of being harvested. This procedure continues until the number of harvested individuals equals h.

We also model the evolutionary effects of harvesting directed exclusively at individuals whose weight falls within a specific range. We choose the mean weight at first reproduction of a population randomly harvested at a rate of 10% as a reference weight point, and calculate harvest quotas for different weight classes above and below that point. We chose this specific reference weight point in order to examine whether and to what extent harvesting-specific weight intervals may have an additional effect to random harvesting. A given female is therefore harvested only if her weight falls within the specific weight interval chosen for harvesting in the current simulation. Individuals whose weights fall within that specific weight interval are harvested at random and this process continues until the number of harvested animals is either equal to h or the total number of animals in that weight interval.

model implementation

The effects of harvesting on model predictions are assessed by comparing model results under different harvesting regimes to a base-case nonharvesting scenario. Two absolute offtake levels and a range of values for weight selectivity are simulated by modifying two parameters, ψ and d (Table 1). The second type of harvesting is implemented using a range of 5 kg weight intervals within the range of 45–90 kg. For each scenario the model is run for 500 simulations of 400 years, which is sufficient for convergence in all simulations. Values for reproductive and demographic characteristics of the population are recorded at the end of the last year of each simulation, and for each scenario a mean value of each characteristic over the 500 simulations is calculated.

Table 1.  The parameters modified under different harvesting scenarios
ParameterDescriptionValues
qHarvest rate0·1, 0·2
aSlope of weight-selective harvesting0·0125, –0·0125
dIntercept of weight-selective harvesting–0·4475, 1·6500
ψMultiplication factor for weight-selective harvesting0, 0·8, 1·0, 1·2, 1·3

sensitivity analysis

Estimation of model parameters is based on published data from studies of different red deer populations, particularly data from the Isle of Rum (Clutton-Brock 1984), and from Slowinski NP in Poland (Dzieciolowski et al. 1996). However, these data are limited in their generality because often parameter estimates are specific to the focal population of each study. Therefore it is important to assess how robust the model is to variation in parameter values. Following McCarthy, Burgman & Ferson (1995), we fit linear regressions between parameter values and model predictions to determine the sensitivity of the predictions to parameter values, after checking for linearity of response. We use uniform distributions for generating values within a range of 15% above and below the values specified in Table 1. Based on these distributions we draw 200 random sets and run 50 simulations for each set of parameters. Each of the 50 × 200 simulations is run for 200 years, sufficient for the model to converge on an equilibrium. The mean weight at first reproduction at the final year of each simulation is reported. We then calculate the mean equilibrium weight at first reproduction across simulations for each set of parameter values, and subsequently use these means as the predicted values in the regressions.

Results

weight at first reproduction

The distribution of the weight at first reproduction is strongly affected by the rate of random harvesting (Fig. 2). The distribution's mean declines from 79·12 kg in a nonharvested population to 72·3 kg and 67·6 kg in lightly (10%) and heavily (20%) harvested populations, respectively. The distribution shifts towards lighter weights and changes from near normal with a peak at 81 kg in the nonharvested population to a skewed distribution with a peak at 65 kg in the heavily harvested population. Under intermediate harvest rates, the distribution consists of both peaks. This suggests that there are two groups of strategies with different means and distributions of weight at first reproduction.

Figure 2.

The distribution of weight at first reproduction that evolves under three random harvest rates: no harvesting, 10% random harvesting, and 20% random harvesting.

A further examination of the evolutionary process reveals that the transition from a single peak to a double peak distribution occurs at harvest rates of approximately 7% (Fig. 3). As the rate of harvesting further increases, the relative frequency of the 81 kg peak declines in favour of the 65 kg peak. Overall, a bimodal distribution of the weight at first reproduction can persist at harvest rates of approximately 7–15%. Above these rates the distribution evolves back to a single peak.

Figure 3.

Changes in the number and relative frequency of peaks in the optimal distribution of weight at first reproduction with harvest rate.

We also assess the evolutionary potential of selective harvesting by comparing adaptive changes under selective harvesting with those observed under random harvesting. There is no significant difference between the means of the weight at first reproduction under random and selective harvesting, when selectivity is positively related to body weight (Table 2). However, the mean weight at first reproduction increases when the probability of being harvested declines with weight under both low and high harvest rates. These results suggest that the trade-off between the relative contribution to fitness of the mother's survival and the number of offspring is weak when mainly heavy animals that have already reproduced are harvested. In contrast, when mainly light animals are harvested, selection favours more offspring at the expense of the mother's survival.

Table 2.  The additional effect on the mean weight at first reproduction of selective harvesting over that of random harvesting, shown for 10% and 20% harvest rates. A one-way anova is used to assess significant differences between means
Type of selectivityHarvest rate% change from the mean of a randomly harvested population
  • *

    Indicates a significance level of P < 0·05.

Increase with weight10%–0·5
20%0
Decrease with weight10%+ 4·5*
20%+ 4·6*

Next, we assess how the direction and extent of the adaptive response to harvesting depend on the deviation between the mean of selectively harvested individuals and the mean weight at first reproduction of a randomly harvested population (72·3 kg). There is a strong negative effect on the weight at first reproduction, of up to 6%, when harvested animals weigh slightly above the reference point (Fig. 4). As the mean weight of harvested animals further deviates from that point, the added effect becomes increasingly negative; i.e. the mean weight at first reproduction increases beyond the reference point. The increase in the average weight at first reproduction of the selectively harvested population is more rapid when the harvested animals are lighter rather than heavier than the reference point. When the average harvest weight is only 59·5 kg the average weight at first reproduction increases beyond that of a nonharvested population. When increasingly heavy animals are harvested the resulting increase in the weight at first reproduction is asymptotic to the mean of a nonharvested population. This is because increased selectivity means that fewer animals can be harvested, hence the impact of harvesting declines.

Figure 4.

The added effects of selective harvesting to the mean weight at first reproduction of a 10% random harvested population. The effect is calculated as the percentage difference between the mean weight at first reproduction of the selective and randomly harvested populations. Negative values indicate a lighter mean weight at first reproduction relative to the mean of a randomly harvested population (67·6 kg). x-axis values show the mean weight of the selectively harvested groups of individuals. Horizontal lines indicate the corresponding averages for the nonharvested and the 10% randomly harvested populations.

diversity of strategies

An assessment of how the number of strategies varies between populations subject to different levels of harvesting may provide first, a qualitative assessment of the direction and strength of the selection operating in each population and second, an indication whether there are just few or many possible different strategies that can persist under each level of harvesting. Harvesting has a significant negative effect (one-way anova: F2,1497 = 382·41, P < 0·001) on the diversity of strategies within a given population (Fig. 5). The average number of strategies per population declines progressively from > 6 strategies in the nonharvested population to < 4 in the heavy harvested population. However, the total number of different strategies that can potentially evolve and persist in a population increases with harvest rate. Whereas, a total of 76 different strategies evolved in 500 simulations in the nonharvested population, there were 101 and 113 different strategies in the lightly and heavily harvested populations, respectively. Harvesting, by reducing population size and thus also the strength of density-dependent competition, enables different yet closely related strategies to dominate similarly harvested populations.

Figure 5.

The average number of weight-specific reproductive strategies in a population per simulation, and the total number of different strategies evolved over 500 simulations, under three harvesting scenarios: no harvesting, 10% random harvesting, and 20% random harvesting.

effects of harvesting on yield

Harvest yield (kg live meat) increases with harvest intensity at low to intermediate rates, with selective harvesting of heavy animals generating on average higher yields than random harvesting (Fig. 6). However, under high harvest rates the yield from the selectively harvested population crashes sooner and more rapidly than the randomly harvested population, indicating that harvesting the heaviest females, who are at their prime age, has a greater effect on productivity than random harvesting.

Figure 6.

Changes in yield (mean ± SD of kg live meat) shown for random harvest and selective harvest of heavy animals (> 100 kg).

model robustness

The average hind weight is dependent primarily on the maximum weight gain for suckling offspring Lmax, such that an increase in Lmax results in an increase in the average weight at first reproduction of the population (Table 3). This relationship reflects the strong impact a mother has on offspring survival through her contribution to offspring weight, which is limited by Lmax. Additional increases in Lmax give the mother greater potential, based on her weight, for enhancing her own fitness by influencing her offspring's survival. The result is a delay in the onset of reproduction to heavier weights when offspring survival is higher. These fitness benefits from a higher weight at first reproduction are ultimately limited by the cost of delaying reproduction. The model is robust to variation in the other parameters (Table 3).

Table 3.  The effect of variation in model parameters on model predictions. The sensitivities are estimated using linear regressions of model results obtained by variation in model parameters. Description of parameters is given in Table S1 (see Supplementary material)
ParameterSlope directionP-valuer2
Gmax+0·360–0·001
u+0·6450·004
y0·8560·005
Lmax+ < 0·001 0·064
b+0·1620·005
gjuvenile+0·638–0·004
gyerling+0·2540·002
gsubadult+0·502–0·002
gadult+0·380–0·001

Hind growth rates are qualitatively comparable with published rates from the Rum and Slowinski populations (Fig. 7). Model predictions for young ages approximate those on Rum and below those in Slowinski. However, at prime ages the modelled growth rates approximate the Slowinski rates, which are about 15% higher than on Rum. Different densities, harvesting regimes and weather conditions on Rum result in the considerably lower weights attained by Rum females.

Figure 7.

A comparison of model predictions against the data used for its parameterization, shown for mean age-specific weights evolved under 15% annual harvest rate. Data are from a Polish population (Slowinski; Dzieciolowski et al. 1996) and a Scottish population (Rum; Mitchell, McCowan & Nicholson 1976). Data are available for females at ages 1–10.

Discussion

Previous studies have linked observed evolutionary changes in life histories, such as a decline over a few generations in mean weight, length and age at first reproduction, to harvesting of wild populations (Heino 1998; Jennings, Reynolds & Mills 1998; Heino & Godo 2002). However, most of the long-term detailed studies on wild harvested populations were conducted on commercially important fish populations that live under fairly stable environmental conditions, and that are subject to strong phenotypic-based selective harvesting according to length or weight (Martinez-Garmendia 1998; Law 2000; Olsen et al. 2005). Using a stochastic density-dependent IBM for red deer females we have demonstrated that both random and selective harvesting can generate adaptive responses in long-lived iteroparous species. The mean weight at first reproduction of the simulated harvested population declines and its optimal distribution shifts towards lighter weights relative to a nonharvested population, and the extent of these adaptive changes increases with harvest rate.

The key factor that underpins these adaptive responses is the increase in mortality due to harvesting prior to reproduction. Under random harvesting, individuals that begin reproduction at light weights, thus at a young age, have on average a greater chance of reproducing at least once than individuals that begin reproduction at heavier weights and hence later in life. Selection for a lighter weight at first reproduction is therefore likely to increase as the relative contribution of harvesting to the overall mortality rate increases. This effect, however, is limited by the trade-off between reproduction and survival. The fitness benefits from reproduction at light weights are offset by the increasingly negative effect reproduction has on the mother's and offspring's survival because a light mother can invest fewer resources in herself and in her offspring than a heavy mother (Partridge & Harvey 1988; Lindstrom 1999).

The bimodal distribution that evolves under intermediate levels of harvesting suggests that the population consists of two groups of strategies dominated by different selection pressures. One mediates primarily the benefits of reproduction before harvesting and thus selects for a lighter weight at first reproduction. The second mediates primarily the benefits of survival and future reproduction and therefore selects for a heavier weight at first reproduction. The combined effects of harvesting-induced selection and natural stochastic density-dependent processes shift individuals from one strategy set to the other. Therefore, when harvest rate is very low or very high the population is dominated by only one of the groups, meaning the optimal distribution consists of a single peak. However, under intermediate harvest rates there are sufficient individuals in each strategy set to produce a bimodal distribution. These results reflect the distribution at equilibrium and not during the transition from a nonharvested single peak to a harvested bimodal distribution, which depends on factors such as heritability of traits.

Evidence from harvested red deer populations indicates that there is considerable variation between females of the same population in their age and weight at first reproduction (Mitchell & Lincoln 1973; Guinness, Albon & Clutton-Brock 1978; Audige, Wilson & Morris 1999). They usually conceive for the first time between age 2 and 4, and environmental factors experienced by the females (such as density-dependent competition for food, climatic conditions, and the degree of uncertainty in these factors; Clutton-Brock & Albon 1983; Langvatn et al. 1996) interact with harvesting in affecting the individual age and weight at first reproduction. The relative frequencies of red deer females that reproduce for the first time at age 2, 3 or 4 can each be over 15% in a given population, hence there is no clear-cut single optimal weight at first reproduction. This range of reproductive strategies is consistent with our results for intermediate harvest rates.

Harvesting is often selective against certain individuals according to one or more phenotypic traits, and different types of selective harvesting might be expected to generate different adaptive responses (Jennings, Greenstreet & Reynolds 1999; Law 2000). We have shown that the probability of being harvested increasing with weight has no additional effect to the adaptive changes observed under random harvesting, suggesting that the harvest rate is more important than selectivity for weight in driving evolutionary responses in female ungulates. Furthermore, harvesting only heavy females reduces the overall evolutionary effect of harvesting, because these females have already reproduced several times. In contrast, selection against females that have just matured should have the largest potential for generating adaptive responses because their reproductive potential (residual reproductive value: Williams 1966), is expected to peak at maturity (Rose & Charlesworth 1980; Clutton-Brock 1984; Caswell 2001). We demonstrate this as an additional decline in the mean maturation weight when harvest targets only recently matured females.

The evolutionary response to harvesting in this model is mitigated when harvesting is selective for light and therefore young animals. A reduction in offspring survival reduces the offspring's fitness value relative to that of an adult. Selection is therefore predicted to favour an increase in adult survival by spreading the investment in reproduction over a longer time (Bell 1980; Real & Ellner 1992), resulting in the evolution of a heavier weight at first reproduction. Moreover, when offspring survival is low, for example due to severe environmental conditions (Coulson et al. 1997), natural selection tends to favour a delay in the onset of reproduction and thus, selects for an increase in the weight at first reproduction (Hirshfield & Tinkle 1975; Stearns 1992).

The negative effect of harvesting on the variability in weight at first reproduction within the population suggests a very strong impact of the weight at first reproduction on fitness. Harvesting selects on two opposing components, the probability of reproduction before being harvested, and the survival rates of mother and offspring. Survival is determined by the mother's weight and therefore by the time she has for accumulating resources prior to reproduction. Successful reproductive strategies under these constraints exhibit minimal variation in weight at first reproduction, and it is likely that only few such strategies emerge within a single population. that the higher the harvest rate the stronger the selective pressure, and so fewer strategies persist in the population. The bimodality emerging under intermediate harvest rates reflects an increase in variability in strategy frequency, not strategy number.

Harvesting increases the number of reproductive strategies across many simulations, because when the population is well below carrying capacity, closely related strategies have very similar fitness. Harvesting reduces population size and the strength of density-dependent competition for resources between individuals. Consequently, selection on heavier females is weaker; these conditions enable different strategies to dominate on different occasions. Additionally, life span under heavy harvesting is greatly reduced, implying that reproduction late in life has on average a lower expected contribution to fitness. The evolutionary responses to harvesting also affect yield. It initially increases with harvest rate due to increased productivity attributed to lighter maturation weights and density-dependent release. Selective harvesting of heavy animals has a greater effect on density dependence and thus on productivity, because heavy individuals consume more food than light individuals. Under intense selective harvesting almost no heavy adults are left and the population becomes skewed to light, young and hence less reproductive animals.

Our model clearly demonstrates that harvesting can generate evolutionary responses. However, it does not consider the genetic level that underlies the response to selection. The exact direction and strength of the evolutionary response to harvesting is determined by gene–gene interactions, and trade-offs with multiple traits (Roff 1997). Additionally, males may affect variation in female reproductive strategies by breeding with females with different strategies, and by influencing females’ conception dates and their reproductive success (Noyes et al. 2002). As harvesting of males may generate evolutionary responses in male traits such as antler size or body weight (Coltman et al. 2003), it may influence evolutionary responses to harvesting in females.

This study highlights the need for management plans to consider the potential of harvesting to generate evolutionary change, as has been advocated in several previous studies (Kaitala & Getz 1995; Ratner & Lande 2001; Harris, Wall & Allendorf 2002). In long-lived iteroparous species such as red deer, harvesting should ideally focus on subadult and old females instead of young adults and prime-age females.

Acknowledgements

We are grateful to R. Hillary and T. Carruthers for advice on some aspects of this work. This study was supported by the British Council Lord Goodman scholarship, the UK Overseas Research Scheme, Ian Karten scholarship and Imperial College London.

Ancillary