I Philip Smith

Douglas J Booker

Neil C Wells

Bioenergetic modelling of the marine phase of Atlantic salmon (Salmo salar L.)

Keywords: Atlantic salmon, post-smolt, marine phase, growth, temperature, climate change, marine ecology, mathematical models

A bioenergetic model of marine-phase, wild Atlantic salmon was constructed to investigate the potential effects on post-smolt growth of predicted changes in oceanic conditions. Short-term estimates of growth in weight were similar to measurements in captivity and simulated growth varied with water temperature and swimming speed as expected. Longer-term estimates of growth in length were less than that achieved by wild salmon, particularly with constant swimming assumed. The model was sensitive to parameters relating to maximum daily food consumption, respiration and the relationships between body energy content, length and weight. Some of the sensitive parameters were based on substantive information on Atlantic salmon and their realistic ranges are likely to be much narrower than those tested. However, other parameter values were based on scant data, farmed Atlantic salmon or other salmonid species, and are therefore less certain and indicate where future empirical research should be focussed.

Introduction

Populations of Atlantic salmon (Salmo salar L.) have declined considerably across the species' range on both sides of the North Atlantic Ocean since the 1970s [START_REF] Jonsson | Factors affecting marine production of Atlantic salmon (Salmo salar)[END_REF].

While in some populations, there may be causal factors during the freshwater phase of the life cycle, there are indications of a widespread increase in mortality during the marine phase not attributable to directed fishing [START_REF] Hawkins | Problems facing salmon in the sea -summing up[END_REF]. In most of the well-studied stocks, there has been a 30-year trend of increasing marine mortality in salmon that mature after two or more winters in the sea. Among salmon that mature after only one winter at sea ('grilse'), there appears to have been a sudden increase in marine mortality in the late 1980s, which has persisted subsequently [START_REF] Potter | A perspective on the marine survival of Atlantic salmon[END_REF]. Assuming that marine predation on salmon is highest when post-smolts are small [START_REF] Peterson | Mortality rate of fishes in the pelagic ecosystem[END_REF][START_REF] Griffiths | Natural mortality, growth parameters, and environmental temperature in fishes revisited[END_REF], it seems likely that such significant variation in survival is linked to changes in the nature or intensity of processes operating in the first few weeks after emigration from rivers to the sea.

There is mounting evidence that marine mortality of salmon is inversely related to growth rate during the early marine phase and that growth is strongly related to sea temperatures experienced by the fish in that period [START_REF] Friedland | The emerging role of climate in post-smolt growth of Atlantic salmon[END_REF][START_REF] Peyronnet | Links between patterns of marine growth and survival of Atlantic salmon Salmo salar[END_REF][START_REF] Mccarthy | Monthly indices of the post-smolt growth of Atlantic salmon from the Drammen River, Norway[END_REF][START_REF] Todd | Detrimental effects of recent ocean surface warming on growth conditions of Atlantic salmon[END_REF].

It is not clear whether the influence of temperature on historical variation in post-smolt growth rate is predominantly a direct effect on salmon physiology or an indirect effect related to ocean currents or prey availability [START_REF] Hawkins | Problems facing salmon in the sea -summing up[END_REF]. Temperature certainly has a direct effect on metabolic processes [START_REF] Brett | Physiological energetics[END_REF], but [START_REF] Beaugrand | Long-term changes in phytoplankton, zooplankton and salmon related to climate[END_REF] have detected significant correlations among indices of climate variability, zooplankton abundance and an index of salmon abundance.

An understanding of how salmon survival may be affected by future changes in oceanic conditions is required to inform management decisions on how best to conserve Atlantic salmon stocks [START_REF] Solomon | An integrated approach to salmonid management[END_REF]. One approach to this is bioenergetic modelling, in which the energy available for somatic growth is estimated from the balance of energy gained from feeding against that lost through egestion, excretion, standard and active metabolism, and reproduction [START_REF] Brett | Physiological energetics[END_REF]. Combined with a model of how the oceanic ecosystem may respond to climatic changes, this provides a tool for investigating the consequences of future climate scenarios for salmon stocks, as has been done for sockeye salmon (Oncorhynchus nerka) in the north Pacific Ocean [START_REF] Rand | NerkaSim: a research and educational tool to simulate the marine life history of Pacific salmon in a dynamic environment[END_REF]. There have been numerous published bioenergetic models of salmonids, including wild juvenile Atlantic salmon in fresh water (Broekhusien et al., 1994;[START_REF] Elliott | A functional model for maximum growth of Atlantic Salmon parr, Salmo salar, from two populations in northwest England[END_REF][START_REF] Forseth | Functional models for growth and food consumption of Atlantic salmon parr, Salmo salar, from a Norwegian river[END_REF][START_REF] Jones | Seasonal patterns of growth, expenditure and assimilation in juvenile Atlantic salmon[END_REF][START_REF] Gurney | Resource allocation, hyperphagia, and compensatory growth in juveniles[END_REF].

Empirical models of growth in relation to temperature, ration and body size have been constructed for marine-phase Atlantic salmon in aquaculture [START_REF] Austreng | Growth rate estimates for cultured Atlantic salmon and rainbow trout[END_REF][START_REF] Cho | Development of bioenergetic models and the Fish-PrFEQ software to estimate production, feeding ration and waste output in aquaculture[END_REF], but there are no published bioenergetic models of the marine phase of wild S.

salar.

The aim of the present study was to construct and test an individual-based model [START_REF] Grimm | Individual-based modelling and ecological theory: synthesis of a workshop[END_REF] of growth in marine-phase Atlantic salmon, using existing information on temperature and body size dependencies of consumption and energy losses. Owing to the limited information on some aspects of the energy metabolism of marine-phase Atlantic salmon, it has been necessary to use parameters estimated for closely-related species or freshwater stages of S. salar for some functions. The sensitivity of the model to variation in uncertain parameters has therefore been investigated to indicate where future empirical research effort should be directed. The present model is not spatially explicit (i.e. does not include a representation of varying geographical location), but we have previously reported a model for simulating trajectories of migrating Atlantic salmon [START_REF] Booker | Modelling the trajectories of migrating Atlantic salmon, Salmo salar L[END_REF]. Coupling these approaches with a climate-driven ecosystem model of the North Atlantic Ocean (e.g. [START_REF] Palmer | Production and export in a global ocean ecosystem model[END_REF] will allow spatially explicit modelling of marine-phase growth.

Methods

Model description

The model consisted of a system of equations, described below, for calculating daily energy gain and loss from food consumption, egestion, excretion and respiratory losses under different conditions of body size, water temperature, day length, swimming speed and prey availability.

Growth was then calculated from the net energy gain. Since the model was not spatially explicit, spatial aspects, such as water temperature, day length and prey density were held constant for each run of the model. The initial salmon body length was taken as 0.125 m as a typical value for wild smolts [START_REF] Shearer | The Atlantic salmon. Natural history, exploitation and future management[END_REF]; although variation in this value was investigated) and initial weight was calculated from a weight-length relationship derived from unpublished data on smolts from British rivers (I. Russell, G. W. Smith, pers. comm.).

Prey encounter and capture

Analysis of stomach contents indicates that salmon prey on a wide variety of invertebrates and fish during their marine phase [START_REF] Jacobsen | Feeding habits of Atlantic salmon at different life stages at sea[END_REF]. In estuarine and nearshore waters, post-smolts take terrestrial insects and other arthropods, such as intertidal amphipods [START_REF] Hansen | The marine phase of the Atlantic salmon (Salmo salar) life cycle, with comparisons to Pacific salmon[END_REF][START_REF] Sturlaugsson | The food and feeding of Atlantic salmon (Salmo salar L.) during feeding and spawning migrations in Icelandic coastal waters[END_REF]. As post-smolts move further offshore, marine prey species become more prevalent and mainly comprise planktonic crustaceans, such as decapod larvae, copepods, amphipods and euphausiids, and larval fish [START_REF] Sturlaugsson | The food and feeding of Atlantic salmon (Salmo salar L.) during feeding and spawning migrations in Icelandic coastal waters[END_REF][START_REF] Andreassen | Feeding and prey-selection of wild Atlantic salmon post-smolts[END_REF][START_REF] Haugland | Feeding of Atlantic salmon (Salmo salar L.) post-smolts in the Northeast Atlantic[END_REF]. At oceanic feeding grounds and during the spawning migration, small pelagic fish, such as capelin, sandeels, myctophids and clupeoids, dominate the diet by weight, although in the north-east Atlantic, planktonic crustaceans also constitute a considerable proportion of the diet [START_REF] Hislop | Marine predators and prey of Atlantic salmon (Salmo salar L.)[END_REF][START_REF] Holst | Observations of the biology and parasites of postsmolt Atlantic salmon, Salmo salar, from the Norwegian sea[END_REF]Jacobsen andHansen, 2000, 2001). Prey items span a wide range of sizes and energy densities. It has been suggested that salmon are opportunistic feeders, implying a lack of selectivity, although there is some evidence of preference with respect to prey species [START_REF] Andreassen | Feeding and prey-selection of wild Atlantic salmon post-smolts[END_REF][START_REF] Jacobsen | Feeding habits of wild and escaped farmed Atlantic salmon, Salmo salar L., in the Northeast Atlantic[END_REF] and prey size [START_REF] Holst | Observations of abundance, stock composition, body size and food of postsmolts of Atlantic salmon in the NE Atlantic during summer[END_REF][START_REF] Jacobsen | Feeding habits of wild and escaped farmed Atlantic salmon, Salmo salar L., in the Northeast Atlantic[END_REF].

Available prey was modelled as a uniformly distributed constant total biomass per unit volume of sea water, divided proportionally into seven categories for simplicity (Table 1). Average individual mass of prey obtained from published weight-length relationships were used to calculate numerical abundance of each prey category from its biomass. Published values of energy density were used to calculate the energy content of prey items in each category (Table 1).

Salmon were assumed to encounter each category of prey, i, within a cylindrical volume of water, V i (m 3 ), defined by swimming speed, u (m s -1 ), the duration of the model time step (1 d) and the salmon's reaction distance -the distance within which they may attack encountered prey items, which can vary by prey category:

2 4 10 64 . 8 i i d u V π × =
The reaction distance, d i (m), of salmon of length L s (m) to prey of length L i (m, Table 1) was calculated using a function given by [START_REF] Hughes | Position choice by drift-feeding salmonids: model and test for Arctic grayling (Thymallus arcticus) in subarctic mountain streams, Interior Alaska[END_REF]:

( ) ( ) s L i i e L d 20 1 120 - - =
This function indicates that for a given prey length, salmon length has little influence on detection distance when salmon length is >0.1 m, as is the case for most post-smolts [START_REF] Shearer | The Atlantic salmon. Natural history, exploitation and future management[END_REF].

Following [START_REF] Keeley | Prey size of salmonid fishes in streams, lakes, and oceans[END_REF], after [START_REF] Wankowski | Morphological limitations, prey size selectivity, and growth response of juvenile atlantic salmon, Salmo salar[END_REF], the range of prey sizes that could be taken was set to 0.012 L s to 0.105 L s . It was assumed that prey width was the limiting dimension and width-length ratios were set for each prey category. The range of prey sizes acceptable to salmon of particular sizes was used to calculate the proportion of each prey category available.

To calculate the number of prey items potentially eaten within a model time step, a form of the Holling type 2 disc equation [START_REF] Holling | Some characteristics of simple types of predation and parasitism[END_REF] was applied, assuming that no more than one prey item can be consumed at a time, salmon can not search for prey while capturing and ingesting ('handling') a prey item and the salmon may not consume every prey item that it encounters. The time spent searching for prey, t s (s), was given by:

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = ∑ = i i i i i i f s h a V t t max 1 1 ρ
where t f is the time available for feeding (set to 12 h per day in seconds), i max is the number of prey classes, ρ i is the density of prey class i (m -3 ), a i is the attack rate on prey class i (proportion of encountered prey items taken) and h i is the handling time for prey class i (s). The potential number of prey items of class i eaten per time step, n i , was given by:

i i i s i V a t n ρ =
and the total weight of prey class i potentially consumed per time step, W i (g), given unlimited stomach size was:

i i i w n W =
where i w is the average individual weight in prey class i (g). The mean energy density of prey consumed, E (J g -1 ), was given by:

( ) ∑ ∑ = = = max max 1 1 i i i i i i i W E W E
where E i is the energy density of prey class i (J g -1 ).

Maximum daily consumption

Maximum daily consumption, C max (g g -1 d -1 ), was calculated as dry mass of prey per unit dry mass of salmon by a Thornton-Lessem function [START_REF] Thornton | A temperature algorithm for modifying biological rates[END_REF], using the weight exponent of [START_REF] Beauchamp | Corroboration of a bioenergetics model for sockeye salmon[END_REF] and fitted to C max estimates for post-smolt S. salar at different temperatures [START_REF] Handeland | Seawater adaptation and growth of post-smolt Atlantic salmon (Salmo salar) of wild and farmed strains[END_REF][START_REF] Jørgensen | Feeding and growth of exercised and unexercised juvenile Atlantic salmon in freshwater, and performance after transfer to seawater[END_REF][START_REF] Damsgård | Feeding, growth and social interactions during smolting and seawater acclimation in Atlantic salmon, Salmo salar[END_REF][START_REF] Toften | Feed intake, growth and ionoregulation in Atlantic salmon (Salmo salar L.) smolts in relation to dietary addition of a feeding stimulant and time of seawater transfer[END_REF][START_REF] Stead | Effect of ration and seawater transfer on food consumption and growth of Atlantic salmon (Salmo salar) smolts[END_REF][START_REF] Koskela | Feed intake, growth rate and body composition of juvenile Baltic salmon exposed to different constant temperatures[END_REF]. Iterative non-linear fitting procedures [START_REF] Wilkinson | Systat for Windows: Statistics, Version 5 Edition[END_REF] failed to converge, so the function was fitted by eye (Table 2).

C max was converted to maximum wet weight of prey that could be consumed daily, W cmax , using published values of prey species water content (Table 1), water content of salmon from the formula of [START_REF] Johansen | Weight gain and lipid deposition in Atlantic salmon, Salmo salar, during compensatory growth: evidence for lipostatic regulation?[END_REF], and the body weight of the salmon. Achieved daily consumption, W c (g), was taken as the lesser of W cmax and ∑ = max 1 i i i W . Daily ingested energy, I (J), was the product of W c and E . Where W c was constrained to be W cmax , the number of prey items eaten was recalculated.

Egestion, excretion and specific dynamic action

The proportion of ingested energy lost in the faeces, P f , was calculated in relation to water temperature, T (°C), and consumption as a proportion of maximum consumption from:

max 2 1 Wc Wc Fb Fb a f e T F P =
where F a , F b1 and F b2 are the constant, temperature coefficient and consumption coefficient, respectively, derived for brown trout, Salmo trutta (Elliott, 1976b; Table 3). The proportion of energy lost by excretion was calculated with the same form of relationship using the parameters U a , U b1 and U b2 , respectively (Table 3). Specific dynamic action, the additional heat liberated after feeding, can be represented as a constant proportion (P SDA ) of metabolizable energy (i.e. energy ingested minus energy lost through egestion and excretion) independent of temperature or ration size [START_REF] Brett | Physiological energetics[END_REF]. A value of 17% of metabolizable energy was adopted (Nimi and Beamish, 1974).

Respiration

A function relating rate of oxygen consumption (M O2 ) to body weight, swimming speed and temperature derived from measurements of farmed adult Atlantic salmon by [START_REF] Grøttum | A model for oxygen consumption of Atlantic salmon (Salmo salar) based on measurements of individual fish in a tunnel respirometer[END_REF] was found to produce unrealistic values for small fish and higher swimming speeds.

Another function was derived from relationships given by [START_REF] Brett | Metabolic rates and critical swimming speeds of sockeye salmon (Oncorhynchus nerka) in relation to size and temperature[END_REF] for standard and active rates of oxygen consumption in sockeye salmon (Oncorhynchus nerka) as functions of body weight at different temperatures. 'Active' measurements were made at the maximum swimming speed sustained for 1 h (termed the 'critical' swimming speed, U crit ). [START_REF] Brett | Metabolic rates and critical swimming speeds of sockeye salmon (Oncorhynchus nerka) in relation to size and temperature[END_REF] also gave temperature-specific relationships between U crit and body length. Values of M O2 at intermediate swimming speeds were obtained by interpolating between the standard and active values for the appropriate body weight, temperature and U crit [START_REF] Brett | Metabolic rates and critical swimming speeds of sockeye salmon (Oncorhynchus nerka) in relation to size and temperature[END_REF]. In this way, an array of predicted oxygen consumption rates was generated for a range of weights (10, 50, 100, 700 and 2000 g), temperatures (5, 15, 20 °C) and swimming speeds (body lengths per second, bl s -1 ) as a proportion (0.2, 0.4, 0.6, 0.8, 1.0) of U crit . The weight and temperature increments chosen reflected the conditions under which the relationships of [START_REF] Brett | Metabolic rates and critical swimming speeds of sockeye salmon (Oncorhynchus nerka) in relation to size and temperature[END_REF] had been obtained. Length was calculated from the weight-length relationship given by [START_REF] Brett | Metabolic rates and critical swimming speeds of sockeye salmon (Oncorhynchus nerka) in relation to size and temperature[END_REF]. A relationship between rate of oxygen consumption and the independent variables was estimated by multiple regression and found to be of the form:

× =

where, M O2 is rate of oxygen consumption (mg O 2 g -1 h -1 ), W is weight (g), T is temperature (°C), and U is swimming speed (bl s -1 ). The multiple regression was highly significant (F 5,69 =429.89, p<0.0001, r 2 =0.967), with significant interactions between the effects of weight and temperature, weight and swimming speed, and temperature and swimming speed. The [START_REF] Grøttum | A model for oxygen consumption of Atlantic salmon (Salmo salar) based on measurements of individual fish in a tunnel respirometer[END_REF] model assumed the effects of these variables were independent.

Comparison of oxygen consumption rates predicted by this function with literature values is not straightfoward, owing to the considerable variation in methodology and conditions in published studies and, in some cases, a lack of information on swimming speed. Nevertheless, oxygen consumption rates predicted by this function were strongly correlated with values reported for S. salar at a range of life stages, body sizes, water temperatures and swimming speeds [START_REF] Withey | Effect of a reciprocal photoperiod regime on standard rate of oxygen consumption of postsmolt Atlantic salmon (Salmo salar)[END_REF][START_REF] Higgins | Metabolic differences between Atlantic salmon (Salmo salar) parr and smolts[END_REF][START_REF] Lucas | An annular respirometer for measuring aerobic metabolic rates of large, schooling fishes[END_REF][START_REF] Lucas | Heart rate as an indicator of metabolic rate and activity in adult Atlantic salmon, Salmo salar[END_REF][START_REF] Maxime | Effects of transfer to sea water on standard and routine metabolic rates in smolting Atlantic salmon at different stages of seawater adaptability[END_REF].

The mass of oxygen consumed (mg) was converted to an energy equivalent (J) with an oxycalorific coefficient of 13.563 J mg -1 [START_REF] Elliott | Energy equivalents of oxygen consumption in animal energetics[END_REF].

Modelled salmon were assumed to swim at a constant relative speed while migrating ('cruising'), but swam at maximum speed to capture specified prey items ('burst' swimming).

Respiration was calculated separately for the proportion of the time that salmon were burst swimming and cruising. Each time a mobile prey item of type i was attacked (determined by prey encounter and attack rates), the salmon was assumed to travel at burst speed for a distance equating to the radius of half of the capture area, (0.5 d i 2 ) ½ . It was assumed that burst swimming was required to capture prey in the 'small fish', 'large fish' and 'squid' categories.

Burst swimming speed (u burst , m s -1 ) of salmon was calculated in relation to temperature (T, °C)

and body length (L s , m) from:

( ) ( ) 7009 . 0 0074 . 0 4525 . 5 121 . 0 + - + = T s burst L T u
which was derived from equations fitted by [START_REF] Turnpenny | Literature review swimming speeds in fish[END_REF] to values reported by [START_REF] Wardle | Limit of fish swimming speed[END_REF].

Growth

Assimilated energy (A, J) that was not lost in respiration was assumed to be partitioned into reserves (Y), such as lipids, which may be mobilized to meet metabolic requirements during starvation, and structure (S), which determines body length and can not be mobilized. Following Broekhusien et al. (1994) and [START_REF] Jones | Seasonal patterns of growth, expenditure and assimilation in juvenile Atlantic salmon[END_REF], the rate of change in reserves was equal to net assimilation rate (A) minus losses in respiration (R) and the rate of energy commitment to structural tissues:

dt dS R A dt dY - - =
The rate of commitment to structure was a variable proportion (κ) of the rate of assimilation:

A dt dS κ =
κ was scaled to ensure that (so far as was possible) the ratio (λ) of reserves to structure did not fall below a 'defended level' (λ def ) (Jones et al., 2002). κ was interpolated between zero (since structural energy should not be lost) and a specified maximum value (κ max ) when the reserve/structure ratio lay within a specified range (λ switch ) above the defended level:

( ) ( ) switch def def switch def λ λ λ λ λ λ λ κ κ + < ≤ - = , max
When λ was below λ def , all assimilated energy was allocated to reserves (κ = 1). When λ was above λ def + λ switch , the proportion 1 -κ max of assimilated energy was allocated to reserves.

Parameter values for the calculation of κ are given in Table 4.

Structural and reserve energy content at the start of the next time step were calculated from:

( ) dt dS S S t t + = +1 ( ) dt dY Y Y t t + = +1
Salmon length in the next time step, L s(t+1) , was given by:

( ) α S L L t s 0 1 = +
where L 0 and α are parameters derived from a re-arrangement of a function relating body energy content to length and weight (Elliott, 1976a; Table 4), applying an estimate of the proportion of body energy content that can not be mobilized during starvation (28.8%, [START_REF] Jonsson | Changes in proximate composition and estimates of energetic costs during upstream migration and spawning in Atlantic salmon Salmo salar[END_REF] and substituting for weight with a rearranged weight-length relationship [START_REF] Broekhuizen | Modeling compensatory growth[END_REF].

Body weight in the next time step, W s(t+1) , was given by:

( ) ( ) ( ) ( ) γ β 1 1 ) 1 ( 0 1 + + + + + = t t t s t s S Y L W W
where W 0 , β and γ are parameters derived from a rearrangement of Elliott's (1976a) empirical relationship for total energy as a function of length and wet weight of brown trout, S. trutta (Table 4). Thus, body length depended only on structural energy content, whereas body weight depended on length and total energy content [START_REF] Jones | Seasonal patterns of growth, expenditure and assimilation in juvenile Atlantic salmon[END_REF]. Body weight could reduce, but length could not.

Simulations

To test the sensitivity of the bioenergetic algorithms to variation in their parameters, the model was run with each parameter varied individually between -50% and +50% of the default values (in 25% increments), with combinations of a range of constant sea surface temperatures (2-18°C, by 2°C) and constant swimming speeds (0.5-2.5 bl s -1 , by 0.25 bl s -1 ). [START_REF] Cotterell | Endurance swimming of diploid and triploid Atlantic salmon[END_REF] measured a maximum sustainable swimming speed of 2.99 bl s -1 for 0.3-m post-smolt Atlantic salmon at 10°C. Within simulations, available prey density and feeding time were held constant, but variation in these parameters was also investigated between simulations. Other spatial aspects of the model, such as directionality of migration, ocean currents and migratory responses to ocean currents were disregarded. The effects of simple behavioural options in the model were also tested: 'burst' swimming to capture prey, optimising cruising speed (using a constant swimming speed that maximised daily energy gain) and optimising daily cruising duration (salmon swam at a defined speed until maximum daily consumption had been achieved and at a defined minimum speed, 0.05 m s -1 , for the rest of that day). Simulated growth under these constant conditions was represented by the length attained after 15.5 months: the average duration of the marine phase for a one-sea-winter salmon emigrating from its home river in early May and returning in mid-August typical of British rivers (unpublished data: FRS, CEFAS). The effect of changes in parameter values has been summarised by the difference in final salmon length between that obtained with a 25% increase in the default parameter value and that obtained with a 25% decrease, expressed as a percentage of the final length obtained with the default parameter value.

To compare growth in weight indicated by the model with published measurements of post-smolt growth rate in captivity (progeny of wild parents), simulations were run with fish of the same size and at the same temperature as the empirical studies, with prey attributes set to resemble an excess of the commercially available feed pellets used (moisture content 5%, energy density 24 MJ kg -1 , density 1.59 × 10 3 kg m -3 ). The conditions in two empirical studies were modelled: fish length 0.18 m and weight 61 g simulated over a period of 30 d at 4.3°C, 9.4°C or 14.3°C (Handeland et al., 1999); and fish length 0.37 m and weight 528 g simulated over a period of 84 d at 9°C [START_REF] Thodesen | Feed intake, growth and feed utilization of offspring from wild and selected Altantic salmon (Salmo salar)[END_REF]. Swimming speeds in the published studies were not reported, so simulations were run with speeds of 0.5 bl s -1 and 1.0 bl s -1 , which were thought likely to encompass the average values. Specific growth rate (SGR) was calculated as (ln W 2 -ln W 1 )/∆t, where W 1 and W 2 are the simulated body weights (g) at the start and end of a period of ∆t days (Handeland et al., 1999). Thermal-unit growth coefficient (TGC) was calculated as (W 2 1/3 -W 1 1/3 )/T∆t [START_REF] Thodesen | Feed intake, growth and feed utilization of offspring from wild and selected Altantic salmon (Salmo salar)[END_REF], where T is the temperature (°C).

Results

With the default bioenergetic parameter values, growth varied with sea surface temperature and swimming speed (Fig. 1). At any given temperature, final length was greater at lower swimming speeds, but the effect of swimming speed was less at lower temperatures. At any given swimming speed, final length increased with temperature to a maximum at 14-16°C and declined slightly at 18°C. The effect of temperature on growth was less at higher swimming speeds. The maximum final length with default parameter values was 0.44 m (at a temperature of 14°C and a swimming speed of 0.5 bl s -1 ).

Simulated growth was most sensitive to certain of the parameters directly affecting energy intake (parameters of the function for maximum daily consumption, prey energy density, relative dry weight proportions of salmon and prey), energy expenditure (some of the respiration parameters, burst speed parameters) and the parameters of the length-structure relationship (Table 5,6).

Certain parameters, mostly powers, led to zero energy reserves ('bioenergetic death') with a 25% change from the default value: these were the initial weight-length power, maximum consumption parameter C TL , respiration-temperature coefficient, respiration-temperature-speed coefficient, length-structure power and weight-energy power.

Changes in certain other parameters had a marked effect (>10%) on final length without causing simulated energy reserves to fall to zero (Table 5,6). In relation to energy intake, for example, growth was positively related to the maximum consumption scale, C A (Fig. 2a), consumptionweight power, C B (Fig. 2b), the prey energy density (Fig. 2c) and the salmon dry weight constant, DW a (Fig. 2d), and was negatively related to the prey dry weight ratio (Fig. 2e). These effects increased with temperature and decreased with swimming speed. Sensitivity to some other parameters was negatively correlated with temperature and swimming speed (e.g. consumption parameter C Q , Fig. 2f). Parameters associated with prey encounter rate and ingestion, such as minimum edible prey size, prey density and reaction distance had less influence on growth (Table 5,6). At higher temperatures (Table 5) and slower swimming speeds (Table 6), simulated growth was greater with larger maximum edible prey sizes. Available feeding time and prey item handling time had no effect within the range of values tested.

In relation to energy loss, growth was sensitive to parameters of the respiration function (Fig. 3a), with the effects being greater at higher temperatures and swimming speeds. Growth was also sensitive to the burst speed constant (negatively, Fig. 3b) and the burst speed-length-temperature constant (positively, Fig. 3c). Growth was moderately sensitive to parameters of the egestion (Fig. 3d) and excretion functions (Table 5,6).

In relation to the functions for determining length and weight from assimilated energy, in addition to the high sensitivity to changes in the length-structure power and the weight-energy power mentioned above, growth was sensitive to the length-structure scale (Fig. 4a) and, to a lesser extent, to the maximum proportion of assimilated energy committed to structure (κ max , Fig. 4b), these effects being positively related to temperature and negatively related to swimming speed. Growth was comparatively insensitive to the defended reserve ratio (λ def ) and, at a swimming speed of 1 bl s -1 , the weight-length-energy scale (W 0 ) and the weight-length power (β, except at low temperatures). At 10 °C, the influence of the last two parameters varied negatively and positively, respectively, with swimming speed (Table 6). The allocation switch width (λ switch ) had no effect within the range of values tested.

For most parameters to which growth showed marked sensitivity, the differences in final length varied monotonically with temperature and swimming speed over the range of values tested.

However, with certain parameters, there was an inflection in sensitivity within the tested range of temperatures, including the maximum consumption parameter C TO , (Fig. 5), the burst speedlength-temperature constant, κ max and the length-structure scale.

The implementation of burst swimming to catch nektonic prey items caused a slight reduction in growth, particularly at combinations of high temperatures and low cruising speed (i.e. conditions of maximum growth; Fig. 6). Optimising daily cruising duration resulted in growth being higher and largely independent of cruising speed, particularly when compared with higher continuous cruising speeds (Fig. 7). The percentage improvement in growth over that at given continuous cruising speeds was almost constant across the temperature range, except at higher speeds, when the improvement in growth increased over the lowest temperatures (Fig. 8). Optimising cruising speed produced almost identical results, since salmon encountered sufficient prey items to achieve their maximum daily consumption even at the minimum speed.

With prey attributes set to resemble commercial pelleted feed and initial body weight of 61 g [START_REF] Handeland | Seawater adaptation and growth of post-smolt Atlantic salmon (Salmo salar) of wild and farmed strains[END_REF], modelled values of SGR at swimming speeds of 0.5 bl s -1 and 1.0 bl s -1 bracketed the published empirical value for 4.3 °C, but was slightly less than the published values at higher temperatures (Table 7). The modelled TGC for a fish of 528 g at 9.0 °C swimming at 0.5 bl s -1 was close to the published value (Table 7).

Discussion

The maximum salmon length attained over a simulated 15.5-month period with the default parameters (0.44 m) was somewhat smaller than the typical size of one-sea-winter salmon in UK rivers (e.g. mean length of 0.66 m in the Chester Dee, CEFAS, unpublished data). The constancy of temperature, prey density, swimming speed and available feeding time in the non-spatial simulation was not intended to represent the seasonally varying conditions experienced by real salmon (although some of the simulated values may reflect annual averages in the ocean), so the absolute values of the final lengths attained can not be expected to be realistic. In particular, salmon are unlikely to swim continuously at a constant speed for 24 hours per day over prolonged periods, but there is, as yet, little information on swimming speeds during marine migration and at oceanic feeding grounds. Ultrasonic tracking of post-smolts in the early stages of marine migration has indicated rapid movement during both day and night, with speeds over the ground of 0.1 to >0.5 m s -1 and a strong tidal component to speed and direction [START_REF] Holm | Migration and distribution of Atlantic salmon post-smolts in the North Sea and North-East Atlantic[END_REF]. However, tagged post-smolts recaptured in the Faroe-Shetland Channel 38-56 days after release from their home rivers in Ireland had been displaced at speeds of 0.2-0.3 m s -1 -slower than the Slope Current in which they were found [START_REF] Holst | Distribution and possible migration routes of post-smolt Atlantic salmon in the north-east Atlantic[END_REF]. Observations of farmed salmon in sea cages have shown a variety of sustained swimming speeds and diel patterns of speed, ranging from minimum speeds of <0.5 bl s -1 to maximum daily values of 1.0-1.5 bl s -1 [START_REF] Sutterlin | Swimming behavior of salmonid fishes in ocean pens[END_REF][START_REF] Kadri | Daily feeding rhythms in Atlantic salmon in sea cages[END_REF][START_REF] Juell | An ultrasonic telemetry system for automatic positioning of individual fish used to track Atlantic salmon (Salmo salar L.) in a sea cage[END_REF][START_REF] Smith | Daily and seasonal patterns in the feeding behaviour of Atlantic salmon (Salmo salar L.) in a sea cage[END_REF][START_REF] Andrew | The effect of demand feeding on swimming speed and feeding responses in Atlantic salmon Salmo salar L., gilthead sea bream Sparus aurata L. and European sea bass Dicentrarchus labrax L. in sea cages[END_REF]. In the present model, modifying the behaviour of simulated salmon to optimise swimming speed, or to swim at minimum speed after the maximum daily consumption had been achieved, led to more realistic growth rates, particularly when higher swimming speeds would otherwise have applied. Comparison of modelled rates of growth in weight over shorter periods with available published values for progeny of wild parents indicated good agreement under some conditions and underestimates in others [START_REF] Thodesen | Feed intake, growth and feed utilization of offspring from wild and selected Altantic salmon (Salmo salar)[END_REF][START_REF] Handeland | Seawater adaptation and growth of post-smolt Atlantic salmon (Salmo salar) of wild and farmed strains[END_REF].

Without knowing the swimming speeds in the empirical studies it is not possible to account for the differences.

Under the default bioenergetic parameters, the optimal temperature for growth was 14-16 °C.

This optimum arises from the different temperature dependencies of maximum daily consumption, which peaks at 17-18 °C, and respiration, which increases exponentially with temperature. From rather sparse data on Norwegian farmed strains of Atlantic salmon postsmolts, [START_REF] Handeland | Seawater adaptation and growth of post-smolt Atlantic salmon (Salmo salar) of wild and farmed strains[END_REF] estimated that the optimum temperature for growth was 13 °C. A wild strain grew faster at 14 °C (the maximum temperature tested) than at 9 °C or 4 °C [START_REF] Handeland | Seawater adaptation and growth of post-smolt Atlantic salmon (Salmo salar) of wild and farmed strains[END_REF]. [START_REF] Koskela | Feed intake, growth rate and body composition of juvenile Baltic salmon exposed to different constant temperatures[END_REF] estimated an optimum temperature for growth in large juvenile Baltic salmon (Salmo salar, 16-29 cm total length) of 16 °C.

Simulated growth declined with increasing swimming speed, due to the additional energy used in active metabolism. Empirical studies have produced mixed results about the effects of exercise on growth rate in Atlantic salmon [START_REF] Davison | The effects of exercise training on teleost fish, a review of recent literature[END_REF]. In some studies, growth rate was higher under moderate exercise regimes [START_REF] Totland | Growth and composition of the swimming muscle of adult Atlantic salmon (Salmo salar L.) during long-term sustained swimming[END_REF][START_REF] Jørgensen | The effects of exercise on growth, food utilisation and osmoregulatory capacity of juvenile Atlantic salmon, Salmo salar[END_REF], owing to greater appetite, utilisation of feed [START_REF] Jørgensen | The effects of exercise on growth, food utilisation and osmoregulatory capacity of juvenile Atlantic salmon, Salmo salar[END_REF] and perhaps release of growth hormones [START_REF] Barrett | Sustained exercise increases plasma growth hormone concentrations in two anadromous salmonids[END_REF]. However, these results are difficult to interpret in the present context, because the low swimming speeds in these studies involved holding salmon together in still or slow-flowing water, leading to greater stress from agonistic activity, which may have depressed appetite and increased the metabolic rate.

Output from the model was very sensitive to the values of certain parameters, so it is important to consider their likely range of values. For some of these parameters, a 25% change may have resulted in unrealistic values. For example, the initial weight-length power was varied to extremes of 2.3 and 3.8, whereas the 95% confidence limit of this parameter derived from over 6500 measurements of Atlantic salmon from the British Isles (CEFAS and FRS, unpublished data) was 3.02 to 3.03 (analysis in present study). Over a range of 2.8 to 3.2 (i.e. -7% to +7%), there was little effect on final length.

The length-structure power, weight-energy power and weight-length power were derived from a combination of information from Atlantic salmon (weight-length relationship and maximum energy loss during starvation) and brown trout (Salmo trutta; a function relating body energy density to length and weight). There may therefore be greater uncertainty about the value of these parameters and, given their importance to the model, an energy-length-weight relationship derived for post-smolt Atlantic salmon would be helpful, but difficult to obtain for wild fish.

Output from the present model was also very sensitive to maximum consumption parameter C TL , which contributes to defining the temperature dependence of daily food consumption at higher temperatures. In the Thonton-Lessem function for maximum daily consumption, four of the parameters define temperatures at which consumption is certain proportions of the maximum (Table 2). Paradoxical results may be obtained if these temperatures are out of sequence, as may have occurred by varying one of them independently of the others. Other parameters of the maximum daily consumption function also had a strong influence on the output. The parameters were fit to data on Atlantic salmon fed on fish meal pellets under controlled conditions, but there are few data for post-smolts below 8 °C and above 14 °C. There is therefore scope for studying food consumption of wild post-smolts fed on natural prey over a range of temperatures, although it is not easy to keep wild fish healthy in captivity or to supply natural prey.

Not surprisingly, simulated growth was sensitive to certain other parameters directly affecting energy intake: prey energy density and the relative dry weight proportions of salmon and prey.

The relative dry matter contents of salmon and prey are important because maximum consumption is calculated first on the basis of dry weight of prey per unit dry weight of salmon.

The wet weight of prey is then calculated from the ratio of the proportions of dry weight in prey and salmon. Water content of salmon and prey species is variable, but the values chosen are thought to represent average conditions. Prey energy density varies seasonally and spatially among and within species, but again, the values chosen were considered to be representative.

Parameters associated with prey encounter rate and ingestion, such as minimum edible prey size, prey density, reaction distance, available feeding time and prey item handling time had little influence on growth within the range of values tested. Under most conditions tested, simulated salmon were able to achieve their maximum daily consumption. However, in the North Atlantic Ocean, prey density and available feeding time will vary by more than the plus or minus 50% differences tested here. The influence of prey abundance and distribution can be investigated by coupling bioenergetic, migration and ecosystem models.

Values of the parameters in the respiration function had a strong negative influence on simulated growth, particularly the respiration-temperature coefficient and the respiration-temperaturespeed coefficient, which both led to bioenergetic death when increased by 25%. However, all of the respiration parameters had important effects on simulated growth, which is not surprising, given that respiration is the major energy loss. The respiration function was derived from relationships given by [START_REF] Brett | Metabolic rates and critical swimming speeds of sockeye salmon (Oncorhynchus nerka) in relation to size and temperature[END_REF] for standard and active rates of oxygen consumption in sockeye salmon (Oncorhynchus nerka). Although the predictions from this function compared reasonably well with the limited available measurements of Atlantic salmon, it would be worthwhile to conduct a detailed study of metabolic rate in marine-phase Atlantic salmon in relation to body size, temperature and swimming speed, so that respiratory losses can be modelled more reliably.

Level of activity is one of the most uncertain aspects of bioenergetic modelling of salmon during the marine phase. There is a pressing need to extend empirical studies of swimming activity from estuarine and coastal waters to offshore areas during both migration and non-migratory periods in oceanic feeding grounds. In the meantime, spatially explicit modelling provides insights into the consequences of different migratory behaviours [START_REF] Booker | Modelling the trajectories of migrating Atlantic salmon, Salmo salar L[END_REF].

Conclusions

An individual-based bioenergetic model has been developed to estimate variation in marine growth, and indirectly survival, of Atlantic salmon in relation to smolt body size, sea water temperature, prey availability and swimming activity. Short-term estimates of growth in weight were similar to empirical measurements made in captivity; longer-term estimates of growth in length were more difficult to assess, owing to uncertainty about the oceanic conditions experienced by wild salmon and their patterns of swimming activity. The non-spatial model is sensitive to certain physiological parameters for which there is limited information available for wild, marine-phase Salmo salar and this highlights areas for future empirical research. When coupled with an ecosystem model of the North Atlantic Ocean, the present bioenergetic model will allow the effects of future changes in oceanic conditions on the growth and survival of Atlantic salmon to be investigated. a defined proportion (default 0.25) of the value at the optimum temperature [START_REF] Hewett | A generalized bioenergetics model of fish growth for microcomputers[END_REF]. Swimming speed 1 bl s -1 in all cases. of the value at the optimum [START_REF] Hewett | A generalized bioenergetics model of fish growth for microcomputers[END_REF].

Figure legends

Figure 6 Final salmon length (m) as a function of sea surface temperature and swimming speed with (black contours) or without (grey contours) burst swimming to capture nektonic prey items.

Figure 7 Final salmon length (m) as a function of sea surface temperature and swimming speed with (black contours) or without (grey contours) optimising the duration of cruise swimming by swimming at a specified minimum speed after maximum daily consumption had been achieved.

Figure 8 Contours of the percentage increase in final length achieved by optimising the duration of cruise swimming, as a function of sea surface temperature and the swimming speed.

Table legends

Table 1. Attributes of prey categories.

Table 2. Parameter values for the Thornton-Lessem function fitted to maximum daily consumption estimates for post-smolt Salmo salar (symbols after [START_REF] Hewett | A generalized bioenergetics model of fish growth for microcomputers[END_REF].

Table 3. Parameter values for the function relating the proportion of ingested energy lost through egestion or nitrogenous excretion as a function of water temperature and consumption as a proportion of the maximum daily consumption.

Table 4. Parameter values of functions for allocation of assimilated energy to reserves or structure, calculation of length from structure and calculation of weight from length and reserves.

Table 5. Sensitivity of simulation results to variation in the model parameters at different sea surface temperatures and a swimming speed of 1 bl s -1 . Difference in final salmon length between that obtained with a 25% increase in the default parameter value and that obtained with a 25% decrease, expressed as a percentage of the final length obtained with the default parameter value. Asterisks indicate cases in which the simulated salmon reached zero energy reserves (bioenergetic 'death') during simulations with altered parameter values.

Table 6. Sensitivity of simulation results to variation in the model parameters at different swimming speeds and a sea surface temperature of 10°C. Difference in final salmon length between that obtained with a 25% increase in the default parameter value and that obtained with a 25% decrease, expressed as a percentage of the final length obtained with the default parameter value. Asterisks indicate cases in which the simulated salmon reached zero energy reserves (bioenergetic 'death') during simulations with altered parameter values. Minimum size (m) 2 × 10 -4 a 5 × 10 -4 b 1 × 10 -3 b 2 × 10 -3 c 2 × 10 -2 e 6 × 10 -2 e 2 × 10 -2 f Maximium size (m) 5 × 10 -4 a 1 × 10 -3 3.5 × 10 -3 4 × 10 -2 c 6 × 10 -2 e 3 × 10 -1 e 2 × 10 -1 f Shape (L:W) 1.75 g 3.24 h 3.24 h 5.88 c 6.00 e 6.00 e 2.63 [START_REF] Holland | Lipid reserves and energy metabolism in the larvae of benthic marine invertebrates[END_REF]; b. [START_REF] Båmstedt | Chemical composition and energy content[END_REF]; c. [START_REF] Mauchline | The biology of euphausiids[END_REF]d. Van Pelt et al. (1997); e. [START_REF] Wheeler | Key to the fishes of Northern Europe. A guide to the identification of more than 350 species[END_REF]; f. [START_REF] Clarke | A review of the systematics and ecology of oceanic squids[END_REF]; g. [START_REF] Newell | Marine plankton: a practical guide[END_REF]; h. [START_REF] Marshall | The biology of a marine copepod Calanus finmarchicus (Gunnerus)[END_REF]i. Hayward and Ryland (1995); j. [START_REF] Mauchline | The biology of calanoid copepods[END_REF]; k. [START_REF] Arkhipkin | Ontogenetic changes in morphometric and reproductive indices of the squid Gonatus fabricii (Oegopsida, Gonatidae) in the Norwegian Sea[END_REF]; l. [START_REF] Payne | Proximate composition of some north-eastern Pacific forage fish species[END_REF]; m. [START_REF] Logerwell | New data on proximate composition and energy density of Steller sea lion (Eumetopias jubatus) prey fills seasonal and geographic gaps in existing information[END_REF]; n. [START_REF] Head | A comparative study of size-fractioned mesozooplankton biomass and grazing in the North East Atlantic[END_REF] 1.0 bl s -1 528 9.0 1.41 × 10 -3 9.57 × 10 -4 1.39 × 10 -3 [START_REF] Thodesen | Feed intake, growth and feed utilization of offspring from wild and selected Altantic salmon (Salmo salar)[END_REF]

Figure 1

 1 Figure 1 Contours of final salmon length (m) as a function of sea surface temperature and swimming speed with default bioenergetic parameter values.

Figure 2

 2 Figure 2 Contours of final salmon length (m) as a function of sea surface temperature and the value of certain parameters of the growth model: (a) maximum consumption scale (constant), C A ; (b) maximum consumption-weight exponent, C B ; (c) prey energy density; (d) salmon dry weight proportion scale, DW a ; (e) proportional dry matter content of prey; (f) maximum consumption parameter C Q -the low temperature (°C) at which maximum daily consumption is

Figure 3

 3 Figure 3 Contours of final salmon length (m) as a function of sea surface temperature and the value of certain parameters of the growth model: (a) respiration scale; (b) burst speed constant; (c) burst speed-length-temperature constant; (d) egestion scale (a proportion). Swimming speed 1 bl s -1 in all cases. Crosses indicate combinations of parameters under which energy reserves reached zero during the simulation.

Figure 4

 4 Figure 4 Contours of final salmon length (m) as a function of sea surface temperature and the value of certain parameters of the growth model: (a) length-structure scale; (b) maximum proportion of assimilated energy commited to structure, κ max . Swimming speed 1 bl s -1 in all cases. Crosses indicate combinations of parameters under which energy reserves reached zero during the simulation.

Figure 5

 5 Figure 5 Contours of final salmon length (m) as a function of sea surface temperature and value of the maximum consumption parameter C TO , at a swimming speed of 1 bl s -1 . C TO is the temperature (°C) below the optimum temperature at which maximum daily consumption is 0.98

803

  Fig 1 806

Table 7 .

 7 Comparison of simulated and published values of specific growth rate (SGR) and

	thermal-unit growth coefficient (TGC) under different conditions of initial body weight,
	temperature and swimming speed.

Table 3 .

 3 Parameter values for the function relating the proportion of ingested energy lost through egestion or nitrogenous excretion as a function of water temperature and consumption as a proportion of the maximum daily consumption.

	Parameter	Egestion	Excretion
	Constant	F a	0.212	U a	0.026
	Temperature	F b1	-0.222	U b1	0.580
	Proportion of max. consumption	F b2	0.631	U b2	-0.299

Table 4 .

 4 Parameter values of functions for allocation of assimilated energy to reserves or structure, calculation of length from structure and calculation of weight from length and reserves.

	Parameter	Value
	Defended reserve ratio, λ def Allocation switch width, λ switch Maximum proportion to structure, κ max Length-structure scale, L 0 (m)	2.44 0.362 0.232 3.621 × 10 -3
	Length-structure power, α Weight-length-energy scale, W 0 (g)	0.341 2.0072 × 10 -2
	Weight-length power, β Weight-energy power, γ	0.692 0.719

Table 5 .

 5 Sensitivity of simulation results to variation in the model parameters at different sea surface temperatures and a swimming speed of 1 bl s -1 . Difference in final salmon length between that obtained with a 25% increase in the default parameter value and that obtained with a 25% decrease, expressed as a percentage of the final length obtained with the default parameter value. Asterisks indicate cases in which the simulated salmon reached zero energy reserves (bioenergetic 'death') during simulations with altered parameter values.

	Sea surface temperature (°C)

Table 6 .

 6 Sensitivity of simulation results to variation in the model parameters at different swimming speeds and a sea surface temperature of 10°C. Difference in final salmon length between that obtained with a 25% increase in the default parameter value and that obtained with a 25% decrease, expressed as a percentage of the final length obtained with the default parameter value. Asterisks indicate cases in which the simulated salmon reached zero energy reserves (bioenergetic 'death') during simulations with altered parameter values.

	Swimming speed (body lengths s -1 )

Table 7 .

 7 Comparison of simulated and published values of specific growth rate (SGR) and thermal-unit growth coefficient (TGC) under different conditions of initial body weight, temperature and swimming speed.

	Initial weight (g)	(°C) Temperature	SGR at speed 0.5 bl s -1 1.0 bl s -1	value Published	Reference
	61	4.3	0.342	0.225	0.274	Handeland et al. (2003)
		9.4	1.196	1.072	0.723
		14.3	1.515	1.384	0.989
			TGC at speed
			0.5 bl s -1

Acknowledgements

This study was funded by the UK Department for Environment, Food and Rural Affairs (contract no. SF0237). P. Ward helped to gather information on salmon prey and A. Moore (Cefas) provided helpful advice. The following are thanked for making unpublished data available: G.W.

Smith (Fisheries

Research Services), I. Davidson and R. Cove (Environment Agency), I. Russel (Cefas), A. Ibbotson (Centre for Ecology and Hydrology), N. Jonsson (Norwegian Institute for Nature Research), W. Roy (University of Stirling).


M James

C Crabbe

Scleractinian coral population size structures and growth rates indicate coral resilience on the fringing reefs of North Jamaica

Keywords: demographics, tropical storms, hurricanes, cyclones, bleaching, climate change, global warming, coral growth, recruitment, Discovery Bay

Scleractinian coral population size structures and growth rates indicate coral resilience on the fringing reefs of North Jamaica

M. James C.

Introduction

Coral reefs throughout the world are under severe challenges from a variety of environmental factors including overfishing, destructive fishing practices, coral bleaching, ocean acidification, sea-level rise, algal blooms, agricultural run-off, coastal and resort development, marine pollution, increasing coral diseases, invasive species, and hurricane/cyclone damage, (Gardner et al., 2003;[START_REF] Bellwood | Confronting the coral reef crisis[END_REF]Crabbe et al., 2009). The fringing reefs around Discovery Bay in Jamaica constitute one of the best documented areas of reef decline in the Caribbean, where loss of corals and macroalgal domination has been due to hurricanes [START_REF] Woodley | Hurricane Allen's impact on Jamaican coral reefs[END_REF][START_REF] Crabbe | Lack of recruitment of nonbranching corals in Discovery Bay is linked to severe storms[END_REF], overfishing [START_REF] Jackson | Reefs since Columbus[END_REF][START_REF] Hawkins | Effects of artisanal fishing on Caribbean coral reefs[END_REF], die-off of the long-spined sea urchin Diadema antillarum in 1983-84 [START_REF] Hughes | Catastrophes, phase shifts and large-scale degradation of a Caribbean coral reef[END_REF], and coral disease [START_REF] Aronson | Evolutionary paleoecology of Caribbean coral reefs[END_REF]. Nutrient enrichment does not appear to have been a causal factor in the development of the reef macroalgal communities [START_REF] Greenaway | The effects of rainfall on the distribution of inorganic nitrogen and phosphorus in Discovery Bay, Jamaica[END_REF].

Maintaining coral reef populations in the face of large scale degradation and phase-shifts on reefs depends critically on recruitment [START_REF] Hughes | Recruitment failure, life histories and long-term decline of Caribbean corals[END_REF][START_REF] Coles | Twenty-five years of change in coral coverage on a hurricane impacted reef in Hawai'i: the importance of recruitment[END_REF], maintenance of grazing fish and urchin populations [START_REF] Mumby | Thresholds and the resilience of Caribbean coral reefs[END_REF], clade of symbiotic zooxanthellae [START_REF] Stat | Functional diversity in coral-dinoflagellate symbiosis[END_REF] and management of human activities related to agricultural land use and coastal development [START_REF] Mora | A clear human footprint in the coral reefs of the Caribbean[END_REF]. To manage coral reefs it is important to have an understanding of coral population demography -structure and dynamics [START_REF] Soong | Colony size as species character in massive reef corals[END_REF][START_REF] Meesters | Colony size-frequency distributions of scleractinian coral populations: spatial and interspecific variation[END_REF][START_REF] Smith | A demographic approach to monitoring the health of coral reefs[END_REF]. Ideally, this involves the quantification of numbers of individual colonies of different size classes -the population structure-through time, in addition to quantifying coral growth rates, recruitment and survival. The fringing reefs around Discovery Bay have seen a number of climate-related challenges in recent years, notably several hurricanes as well as a mass bleaching event in the Caribbean in 2005 [START_REF] Jones | Status of coral reefs in the northern Caribbean and western Atlantic node of GCRNM[END_REF]2008). Despite all these negative factors, there is evidence that prior to 2005 some Discovery Bay reefs were recovering (Idjadi et al., 2008), although a study subsequent to the 2005 bleaching event is not so positive [START_REF] Quinn | The recent collapse of a rapid phase-shift reversal on a Jamaican north coast reef after the 2005 bleaching event[END_REF]. Healthy reefs have a high proportion of small size-classes that include new recruits and juveniles [START_REF] Meesters | Colony size-frequency distributions of scleractinian coral populations: spatial and interspecific variation[END_REF], and the smallest size class of corals can be a good indicator of reef resilience [START_REF] Loya | Skeletal regeneration in a Red Sea scleractinian coral population[END_REF][START_REF] Connell | Diversity in tropical rain forests and coral reefs[END_REF]. This study set out to quantify the sizestructure of populations and the growth rates of a number of corals over time in order to test whether the Discovery Bay coral colonies were exhibiting resilience in the face of multiple acute stressors of hurricanes and bleaching. I take the definition of resilience as the ability of the system to recover from disturbance and change, while maintaining its function [START_REF] Carpenter | From metaphor to measurement: Resilience of what to what?[END_REF][START_REF] Grimsditch | Coral reef resilience and resistance to bleaching[END_REF]; for example a coral reef's ability to recover from a bleaching event. Resilience is a multifaceted concept [START_REF] Nyström | Capturing the cornerstones or coral reef resilience: linking theory to practice[END_REF], and factors that can improve coral reef resilience to a mass bleaching event include good species and functional diversity, good connectivity to larval sources, appropriate substrates for larval settlement and protection from other anthropogenic impacts.

Methods

Data on storms, hurricanes and bleaching events impacting Discovery

Bay

Data on storm severity as it impacted the Discovery Bay sites was obtained from UNISYS (http://weather.unisys.com/hurricane/atlantic/) and the NOAA hurricane site (http://www.nhc.noaa.gov/pastall.shtml).

Information on bleaching was obtained from the NOAA coral reef watch site:

(http://coralreefwatch.noaa.gov/satellite/current/sst_series_24reefs.html) and from [START_REF] Jones | The effects of coral bleaching in the northern Caribbean and western Atlantic[END_REF].

Sites and Sampling

Four haphazardly located transects, each 15 m long and separated by at least 5m, were laid at between 5-8.5 m depth at each of five sites [Rio Bueno (18° 28.805' N;77° 21.625' W),M1 (18° 28.337' N;77° 24.525' W),Dancing Ladies (18° 28.369' N;77° 24.802' W),Dairy Bull (18° 28.083' N;77° 23.302' W) and Pear Tree Bottom (18° 27.829' N;77° 21.403' W)] along the fringing reefs surrounding Discovery Bay, Jamaica (Fig. 1). GPS coordinates were determined using a hand-held GPS receiver (Garmin Ltd.). Corals 2m either side of the transect lines were photographed for archive information, and surface areas measured with flexible tape as described previously using SCUBA [START_REF] Crabbe | Lack of recruitment of nonbranching corals in Discovery Bay is linked to severe storms[END_REF][START_REF] Crabbe | Sediment impacts on growth rates of Acropora and Porites corals from fringing reefs of Sulawesi, Indonesia[END_REF][START_REF] Crabbe | Influence of Macroalgal Cover on Coral Colony Growth Rates on Fringing Reefs of Discovery Bay, Jamaica[END_REF]. For non-branching corals, this was done by measuring the widest diameter of the coral and the diameter at 90° to that. For branching corals (Acropora palmata and Acropora cervicornis), linear extension rates were measured using digital photography and image analysis, validated by measurements with flexible tape [START_REF] Crabbe | Lack of recruitment of nonbranching corals in Discovery Bay is linked to severe storms[END_REF][START_REF] Crabbe | Sediment impacts on growth rates of Acropora and Porites corals from fringing reefs of Sulawesi, Indonesia[END_REF]. Depth of samples was between 5-8.5 m, to minimise variation in growth rates due to depth [START_REF] Huston | Variation of coral growth rates with depth at Discovery Bay, Jamaica[END_REF]. To increase accuracy, surface areas rather than diameters of live non-branching corals were measured [START_REF] Crabbe | Lack of recruitment of nonbranching corals in Discovery Bay is linked to severe storms[END_REF][START_REF] Crabbe | Sediment impacts on growth rates of Acropora and Porites corals from fringing reefs of Sulawesi, Indonesia[END_REF]. Sampling was over as wide a range of sizes as possible. Colonies that were close together (<50 mm) or touching were avoided to minimise age discontinuities through fission and altered growth rates (Hughes and Jackson, 1980;Foster et al., 2007;Elahi and Edmunds, 2007).

In this study we ignored Montastrea annularis colonies, because their surface area does not reflect their age (Hughes and Jackson 1980), and because hurricanes can increase their asexual reproduction through physical damage (Foster et al., 2007).

Radial growth rates of non-branching corals and linear extension rates of branching corals were calculated for each year from 2000-2008 as described previously [START_REF] Crabbe | Lack of recruitment of nonbranching corals in Discovery Bay is linked to severe storms[END_REF][START_REF] Crabbe | Sediment impacts on growth rates of Acropora and Porites corals from fringing reefs of Sulawesi, Indonesia[END_REF]. Overall, over 8,000 measurements were made on over 1,500 coral colonies, equally distributed between the sites for species and numbers of colonies. Computer digital image analysis for coral linear extension rates was undertaken using the UTHSCSA (University of Texas Health Science Center, San Antonio, Texas, USA) Image Tool software [START_REF] Crabbe | Sediment impacts on growth rates of Acropora and Porites corals from fringing reefs of Sulawesi, Indonesia[END_REF]. One or twofactor ANOVA was used to compare coral data among sites; ± error values represent standard errors of the data. The skewness coefficient (sk) [START_REF] Zar | Biostatistical Analysis[END_REF] was used to quantify the relationship between the number of large and small corals within each population. The skewness for a normal distribution about the mean is zero, and any symmetric data should have a skewness near zero. Negative values for the skewness indicate data that are skewed left (more small colonies than in a normal distribution) and positive values for the skewness indicate data that are skewed right (more large colonies than in a normal distribution). Water quality measurements at the sites have been reported previously (D'Elia et al., 1981;[START_REF] Greenaway | The effects of rainfall on the distribution of inorganic nitrogen and phosphorus in Discovery Bay, Jamaica[END_REF].

RESULTS

Environmental climate stressors-tropical storms and bleaching events

Hurricanes that had the potential to impact the reef sites during the study period are shown in Fig. 2, with their paths of travel. Only one of these storms resulted in any significant damage on the reefs, Ivan in 2004, a category 4 hurricane as it passed south of the island. Visually, the damage was minimal as far as reef destruction was concerned, with some A. palmata colonies being fragmented and overturned, notably at Pear Tree Bottom (personal observation). Although hurricane Emily in 2005 was also a category 4 hurricane, the eye passed sufficiently south of the island so that the impact involved sediment transfer owing to the high winds and rain [START_REF] Crabbe | Industrial sedimentation lowers coral growth rates in a turbid lagoon environment, Discovery Bay, Jamaica[END_REF] The only bleaching event that significantly impacted the reef sites during the study period was the mass Caribbean bleaching event of 2005. Analysis of satellite data showed that there were 6 degree heating weeks (dhw) for sea surface temperatures in September and October 2005 near Discovery Bay, data which was mirrored by data loggers on the reefs [START_REF] Quinn | The recent collapse of a rapid phase-shift reversal on a Jamaican north coast reef after the 2005 bleaching event[END_REF]. Six dhw are equivalent to six weeks of sea surface temperatures (SSTs) one degree Celsius greater than the expected summer maximum. As the viability of small coral colonies over time can indicate reef resilience [START_REF] Loya | Skeletal regeneration in a Red Sea scleractinian coral population[END_REF][START_REF] Connell | Diversity in tropical rain forests and coral reefs[END_REF], the annual changes in the colony numbers of the smallest size class (0-250 mm 2 surface area) each year from 2002-2008 was plotted for all the non-branching species studied at the fringing reef sites, with examples shown in Fig. 5 for Sidastrea siderea, Diploria labyrinthiformis, Porites astreoides, and Colpophyllia natans. There was a reduction in the smallest size class for all the species at all the sites in 2006, with subsequent increases for all species at all sites in 2007 and 2008. Until 2006, there had been modest increases -or least no decreasesin the numbers of the smallest size classes, with the exception of D. labyrinthiformis at Rio Bueno, P. astreoides at Dancing Ladies, where the trends had decreased slightly. Interestingly, in 2005, the year after hurricane Ivan, the most severe storm to impact the reef sites over the study period, there was a slight reduction in the numbers of the smallest size classes, particularly notable at Dairy Bull.

Coral colony size-frequency distributions and growth rates

Dairy Bull reef was the site where studies resulted in the suggestion that there had been a rapid phase-shift reversal on Jamaican reefs [START_REF] Idjadi | Rapid phase-shift reversal on a Jamaican coral reef[END_REF], and which suffered a major loss of A. cervicornis in 2006 [START_REF] Quinn | The recent collapse of a rapid phase-shift reversal on a Jamaican north coast reef after the 2005 bleaching event[END_REF]. Table 1 shows mean percentage cover of live coral, macroalgae and live Acropora species Coral growth rates are part of a demographic approach to monitoring coral reef health [START_REF] Smith | A demographic approach to monitoring the health of coral reefs[END_REF], and Table 2 presents radial growth rates (mm yr -1 ) of non-branching corals and linear extension rates (mm yr -1 ) of branching corals 12 calculated on a annual basis and tabled from 2000-2003, 2003-2005, and 2005-2008 at all the sites studied. The growth rates are similar to those reported by [START_REF] Huston | Variation of coral growth rates with depth at Discovery Bay, Jamaica[END_REF]. There were few significant differences between the sites for each species studied, or across the time period of the study. Where growth rates were higher, they tended to be higher at Dairy Bull reef, but the differences were not significant. With the increase of D. antillarum at Rio Bueno in recent years, clearing the macroalgae, healthy A. palmata and A. cervicornis colonies have appeared at the Rio Bueno site from 2006. At Dancing Ladies, a site with much macroalgal cover, A. cervicornis colonies which were measurable from 2003-2005 had disappeared in 2006, possibly as a result of the mass bleaching event, while at M1, a site with even greater macroalgal cover, A. cervicornis colonies appeared which were measurable in 2008.

DISCUSSION

Surveys of size-frequency distribution of corals are important in evaluating the condition of and changes in coral populations [START_REF] Bak | Coral population structure: the hidden information of colony size-frequency distributions[END_REF][START_REF] Meesters | Colony size-frequency distributions of scleractinian coral populations: spatial and interspecific variation[END_REF][START_REF] Oigman-Pszczol | Size structure and spatial distribution of the corals Mussismilia hispida and Siderastrea stellata (Scleractinia) at Armação dos Búzios, Brazil[END_REF]). Here we have used a number of demographic tools to demonstrate the resilience of the fringing reefs around Discovery Bay, Jamaica, to a number of environmental stressors, in particular hurricanes and the mass bleaching event of 2005.

Hurricanes and tropical storms cause major damage and delayed mortality to corals [START_REF] Knowlton | Evidence for delayed mortality in hurricane-damaged Jamaican staghorn corals[END_REF]Done, 1999), as happened with hurricane Allen in 1980 to the fringing reefs in this study [START_REF] Woodley | Hurricane Allen's impact on Jamaican coral reefs[END_REF]. Alteration of substratum by storms reduces recruitment rates, as does the pre-emption of space by other corals or macroalgae [START_REF] Connell | Disturbance and recovery of coral assemblages[END_REF][START_REF] Connell | A 30-year study of coral abundance, recruitment, and disturbance at several scales in space and time[END_REF]. Storms have reduced the recruitment of non-branching corals both on these reefs [START_REF] Crabbe | Lack of recruitment of nonbranching corals in Discovery Bay is linked to severe storms[END_REF] and on the Meso-American Barrier Reef off the coast of Belize [START_REF] Crabbe | Influence of Macroalgal Cover on Coral Colony Growth Rates on Fringing Reefs of Discovery Bay, Jamaica[END_REF], and it is interesting that in this study the numbers of colonies in the smallest size class of corals was lower after hurricane Ivan in 2004, although the reduction was insignificant relative to the reduction after the bleaching event of 2005. Bleaching of Acropora colonies generally led to mortality, with predation by the coral snail Coralliophilia abbreviata and the bearded fire worm Hermodice carunculata [START_REF] Quinn | The recent collapse of a rapid phase-shift reversal on a Jamaican north coast reef after the 2005 bleaching event[END_REF]; this was often followed by invasion of filamentous algae.

It is the synergistic effect of multiple stressors that is damaging to reefs [START_REF] Hughes | Multiple stressors on coral reefs:a long term perspective[END_REF][START_REF] Mumby | Bleaching and hurricane disturbances to populations of coral recruits in Belize[END_REF]Gardner et al., 2003). The Jamaican reefs are subject to a number of both acute and chronic stressors, the last including overfishing and continuing coastal development, including the much-publicised development on land adjacent to Pear Tree Bottom reef and the resurfacing of the North Jamaican coastal highway [START_REF] Westfield | Identification of sediment sources using geochemical fingerprinting at Pear tree Bottom Reef, Runaway Bay, Jamaica[END_REF]. On top of these came tropical storms and the mass bleaching event during the study period. Fortunately, there was little damage after the tropical storms, although in the year following hurricane Ivan, which produced the highest winds in the area of the reef sites during the study period, there was a reduction in the smallest size classes of the majority of the non-branching corals studied, suggesting that the hurricane might have influenced coral recruitment. Storms and hurricanes can influence sedimentation and turbidity, which themselves have significant effects on coral growth [START_REF] Gimour | Experimental investigation into the effects of suspended sediment on fertilisation, larval survival and settlement in scleractinian coral[END_REF][START_REF] Crabbe | Industrial sedimentation lowers coral growth rates in a turbid lagoon environment, Discovery Bay, Jamaica[END_REF]. While occasional storms can increase the survivorship of A. palmata colonies [START_REF] Lirman | A simulation model of the population dynamics of the branching coral Acropora palmata -effects of storm intensity and frequency[END_REF], increased freshwater inputs from storms reduces salinity, and influences nutrient concentrations [START_REF] Greenaway | The effects of rainfall on the distribution of inorganic nitrogen and phosphorus in Discovery Bay, Jamaica[END_REF][START_REF] Mallela | Calcium carbonate budgets for two coral reefs affected by different terrestrial runoff regimes, Rio Bueno, Jamaica[END_REF] which in turn increase pre-and post-settlement mortality, changed larval behaviour and substrate choice upon settlement [START_REF] Vermeij | Pelagic conditions affect larval behavior, survival, and settlement patterns in the Caribbean coral Montastrea faveolata[END_REF].

Despite the multiple influences on the reef sites over the study period, the size classes of the corals studied showed resilience to change. Interestingly, there were differences between the sites, and between the species of corals. Dairy Bull, Rio Bueno and Pear Tree Bottom showed a decrease in the numbers of smaller colonies relative to a normal distribution for most species from 2002 to 2008. The reef sites which had the most macroalgal cover, Dancing Ladies and M1, showed fewer changes in size class distribution through the study period, possibly because these sites show large macroalgal cover [START_REF] Crabbe | Influence of Macroalgal Cover on Coral Colony Growth Rates on Fringing Reefs of Discovery Bay, Jamaica[END_REF]. There were no significant differences in fishing pressure between the sites. This study concentrates on sizeclasses and growth rates; coral recruitment or survival [START_REF] Smith | A demographic approach to monitoring the health of coral reefs[END_REF] has not been measured, although we have modelled coral recruitment at these sites [START_REF] Crabbe | Lack of recruitment of nonbranching corals in Discovery Bay is linked to severe storms[END_REF] and it has been measured in other studies [START_REF] Quinn | The recent collapse of a rapid phase-shift reversal on a Jamaican north coast reef after the 2005 bleaching event[END_REF]. In this study we have not considered reef connectivities, relative colonisation rates or socioeconomic variables in reef resilience [START_REF] Nyström | Capturing the cornerstones or coral reef resilience: linking theory to practice[END_REF].

By far the major acute influence on the reef sites was the mass bleaching event Interestingly, growth rates of both branching and non-branching corals showed similar values throughout the study period, with trends, not significant, for slightly higher values at Dairy Bull reef.

Diary Bull reef has for several years been the fringing reef with the most coral cover, with a benthic community similar to that of the 1970s [START_REF] Huston | Variation of coral growth rates with depth at Discovery Bay, Jamaica[END_REF], and it was the subject of the study which suggested a rapid phase-shift reversal [START_REF] Idjadi | Rapid phase-shift reversal on a Jamaican coral reef[END_REF]. After the 2005 bleaching event there was a major loss of live coral cover, particularly of A. cervicornis [START_REF] Quinn | The recent collapse of a rapid phase-shift reversal on a Jamaican north coast reef after the 2005 bleaching event[END_REF] this study), and it is encouraging that both coral cover and the rapidly growing A. cervicornis colonies have returned to the reef at levels approaching pre-bleaching values. The influence of M. annularis colonies on the reef, acting as structural refugia [START_REF] Idjadi | Rapid phase-shift reversal on a Jamaican coral reef[END_REF], may have facilitated this recovery. Interestingly, we found a variety of clades of zooxanthellae, including clade C, in corals at Dairy Bull reef [START_REF] Crabbe | Industrial sedimentation lowers coral growth rates in a turbid lagoon environment, Discovery Bay, Jamaica[END_REF], and that may be a factor in their recovery [START_REF] Stat | Functional diversity in coral-dinoflagellate symbiosis[END_REF].

Dairy Bull reef behaves somewhat like a successional niche [START_REF] Pacala | Models suggesting field experiments to test two hypotheses explaining successional diversity[END_REF][START_REF] Kinzig | Successional biodiversity and ecosystem functioning[END_REF], as late successional species are not the strongest competitors, and the high population of D. antillarum at the site keep the macroalgae in check. Despite continued overfishing [START_REF] Hawkins | Effects of artisanal fishing on Caribbean coral reefs[END_REF], there is a good diversity of fish species, including herbivores such as Scaridae and Acanthuridae, although fish sizes are small (usually <100 mm) (personal observation). Even at M1, with one of the highest covers of macroalgae and no D. antillarum, we have seen that A. cervicornis can form colonies after the major disturbance of the mass bleaching event in 2005. Most reefs are open non-equilibium systems, (Connel, 1978) with diversity maintained by disturbance and recruitment. While that may be true at the macro-or landscape level, Dairy Bull reef, after the mass bleaching event, is exhibiting some properties of niche diversification [START_REF] Jackson | Adaptation and diversity of reef corals[END_REF][START_REF] Pacala | Models suggesting field experiments to test two hypotheses explaining successional diversity[END_REF][START_REF] Kinzig | Successional biodiversity and ecosystem functioning[END_REF].

What is apparent from this study is that despite the chronic and acute disturbances between 2002 and 2008, demographic studies indicate good levels of coral resilience on the fringing reefs around Discovery Bay in Jamaica. The bleaching event of 2005 resulted in mass bleaching but relatively low levels of mortality [START_REF] Quinn | The recent collapse of a rapid phase-shift reversal on a Jamaican north coast reef after the 2005 bleaching event[END_REF], unlike corals in the US Virgin islands where there was extensive mortality [START_REF] Vermeij | Pelagic conditions affect larval behavior, survival, and settlement patterns in the Caribbean coral Montastrea faveolata[END_REF]Whelen et al. 2007), possibly because of their greater degree heating week values. The Jamaican reefs have suffered from long term human-induced chronic stressors, such as overfishing and land development [START_REF] Adger | Socialecological resilience to coastal disasters[END_REF][START_REF] Jdalumbi | Ecosystems in action: Lessons from marine ecology about recovery, resistance and reversibility[END_REF][START_REF] Mora | A clear human footprint in the coral reefs of the Caribbean[END_REF]Mumby and Hasting, 2008).

Unfortunately, previously successful efforts to engage the local fisherman in controlling catches around Discovery Bay [START_REF] Sary | Effects of an increase in trap mesh size on an over-exploited coral reef fishery at Discovery Bay, Jamaica[END_REF] have not been maintained, and it may be that the development of a Discovery Bay Marine Park is the only solution. 2 5 1 -5 0 0 5 0 1 -7 5 0 7 5 1 -1 0 0 0 1 0 0 1 -1 2 5 0 1 2 5 1 -1 5 0 0 1 5 0 1 -1 7 5 0 1 7 5 1 -2 0 0 0 2 0 0 1 -2 2 5 0 2 2 5 1 -2 5 0 0 2 5 0 1 -2 7 5 0 2 7 5 0 -3 0 0 0 3 0 0 1 -3 2 5 0 3 2 5 1 -3 5 0 0 3 5 0 1 -3 7 5 0 3 7 5 1 -4 0 0 0 Size class surface area (mm 2 5 1 -5 0 0 5 0 1 -7 5 0 7 5 1 -1 0 0 0 1 0 0 1 -1 2 5 0 1 2 5 1 -1 5 0 0 1 5 0 1 -1 7 5 0 1 7 5 1 -2 0 0 0 2 0 0 1 -2 2 5 0 2 2 5 1 -2 5 0 0 2 5 0 1 -2 7 5 0 2 7 5 0 -3 0 0 0 3 0 0 1 -3 2 5 0 3 2 5 1 -3 5 0 0 3 5 0 1 -3 7 5 0 3 7 5 1 -4 0 0 0 Size class surface area (mm

Legends to Figures

Porites astreoides 2002

-2 5 0 2 5 1 -5 0 0 5 0 1 -7 5 0 7 5 1 -1 0 0 0 1 0 0 1 -1 2 5 0 1 2 5 1 -1 5 0 0 1 5 0 1 -1 7 5 0 1 7 5 1 -2 0 0 0 2 0 0 1 -2 2 5 0 2 2 5 1 -2 5 0 0 2 5 0 1 -2 7 5 0 2 7 5 0 -3 0 0 0 3 0 0 1 -3 2 5 0 3 2 5 1 -3 5 0 0 3 5 0 1 -3 7 5 0 2 5 1 -5 0 0 5 0 1 -7 5 0 7 5 1 -1 0 0 0 1 0 0 1 -1 2 5 0 1 2 5 1 -1 5 0 0 1 5 0 1 -1 7 5 0 1 7 5 1 -2 0 0 0 2 0 0 1 -2 2 5 0 2 2 5 1 -2 5 0 0 2 5 0 1 -2 7 5 0 2 7 5 0 -3 0 0 0 3 0 0 1 -3 2 5 0 3 2 5 1 -3 5 0 0 3 5 0 1 -3 7 5 0

  This work was conducted at Discovery Bay during July 15-31 and December 19-30 in 2000, March 26 -April 19 in 2002, March 18 -April 10 in 2003, July 23 -August 21 in 2004, July 18 -August 13 in 2005, April 11-18 in 2006, December 30 in 2006 -January 6 in 2007, and July 30 -August 16 in 2008. Surveys were made at the same locations at the same sites each year.

  . Tropical storms Iris (category 1 hurricane, 2001), Lili (tropical storm, 2002), Bonnie (tropical wave, 2004), Charley (category 1 hurricane, 2004), Dennis (category 3 hurricane, 2005), Olga (tropical storm, 2007) and Dean (hurricane category 4, 2007) did not result in significant damage to the reef sites.

Fig 3 a

 3 Fig 3 a-h compares the size-frequency distribution of the corals Sidastrea

  along transects at Dairy Bull reef in 2005 (pre-bleaching), 2006, 2007 and 2008. Cover of live coral, macroalgae and cover and live Acropora for 2005 and 2006 are similar to figures reported by Quinn and Kojis (2008). While macroalgal cover remained essentially unchanged in 2007 and 2008, there were increases in live coral cover and live Acropora species in both 2007 and 2008. The majority of the increase in coral is represented by increases in live A. cervicornis. This is illustrated in Fig. 6, which shows complete bleaching of an A. cervicornis colony typical of Dairy Bull reef after the mass bleaching event of 2005 and a large live colony of A. cervicornis typical of Dairy Bull reef in 2008.

  of late 2005. Mean size classes of most of the corals studied at the reef sites were reduced in 2006, and while there was considerable recovery by 2008 in mean size class of some species studied, there was no significant recovery to 2002 levels in mean size class for C. natans, D. labyrinthiformis, or D. strigosa colonies at most sites between 2006 and 2008, and in general mean size class was lower for these corals than in 2002. While there was a considerable drop in the smallest size class of all corals at all sites after the 2005 bleaching event, by 2008 numbers of colonies at all the sites had recovered considerably. In the coming years, if there are no major new catastrophic disturbances, these smaller colonies may result in increases in the mean size class to pre-2006 levels.

Fig. 1 .

 1 Fig. 1. Satellite image showing the location of fringing reef sites in this study (Rio

Fig. 2 .

 2 Fig. 2.Hurricane tracks impacting the Jamaican fringing reefs around Discovery Bay

Fig. 4 .

 4 Fig. 4. Mean size classes in 2002, in 2006 and in 2008 of: Sidastrea siderea (a);

Fig. 5 .

 5 Fig. 5. Graphs of annual changes in the colony numbers of the smallest size class (0-250 mm 2 surface area) from 2000-2008 for: Sidastrea siderea (a); Diploria

  Fig.3

  Fig. 3a.

  Fig 3b.

  Fig. 3e. 3

  Fig. 3f. 7

Table 1 .

 1 Mean percentage cover of live coral, macroalgae and live Acropora species along transects at Dairy Bull, in 2005 (pre-bleaching), 2006, 2007 and 2008. Values are ± standard errors.

	Year	Live coral (%)	Macroalgae (%)	Acropora species (%)
	2005	46 ± 8	8 ± 3	33 ± 5
	2006	13 ± 5	6 ± 3	2 ± 2
	2007	20 ± 9	6 ± 3	10 ± 4
	2008	31 ± 7	5 ± 2	22 ± 7

Fig.1

Fig.2

Acknowledgements

I thank the Royal Society and the Earthwatch Institute for funding, Mr. Anthony Downes, Mr. Peter Gayle, Dr. George Warner, Dr. Norman Quinn and the staff of the Discovery Bay Marine Laboratory for their invaluable help and assistance, Dr. Debbie Lloyd for expert assistance in 2002, to many volunteers for their considerable help underwater during this project, and the anonymous referees for their helpful comments on the manuscript. This is publication number 765 from the Discovery Bay Marine Laboratory.

2 5 1 -5 0 0 5 0 1 -7 5 0 7 5 1 -1 0 0 0 1 0 0 1 -1 2 5 0 1 2 5 1 -1 5 0 0 1 5 0 1 -1 7 5 0 1 7 5 1 -2 0 0 0 2 0 0 1 -2 2 5 0 2 2 5 1 -2 5 0 0 2 5 0 1 -2 7 5 0 2 7 5 0 -3 0 0 0 3 0 0 1 -3 2 5 0 3 2 5 1 -3 5 0 0 -2 5 0 2 5 1 -5 0 0 5 0 1 -7 5 0 7 5 1 -1 0 0 0 1 0 0 1 -1 2 5 0 1 2 5 1 -1 5 0 0 1 5 0 1 -1 7 5 0 1 7 5 1 -2 0 0 0 2 0 0 1 -2 2 5 0 2 2 5 1 -2 5 0 0 2 5 0 1 -2 7 5 0 2 7 5 0 -3 0 0 0 3 0 0 1 -3 2 5 0 3 2 5 1 -3 5 0 0 3 5 0 1 -3 7 5 0

Colpophyllia natans 2002

-2 5 0 2 5 1 -5 0 0 5 0 1 -7 5 0 7 5 1 -1 0 0 0 1 0 0 1 -1 2 5 0 1 2 5 1 -1 5 0 0 1 5 0 1 -1 7 5 0 1 7 5 1 -2 0 0 0 2 0 0 1 -2 2 5 0 2 2 5 1 -2 5 0 0 2 5 0 1 -2 7 5 0 2 7 5 0 -3 0 0 0 3 0 0 1 -3 2 5 0 3 2 5 1 -3 5 0 0 3 5 0 1 -3 7 5 0 2 5 1 -5 0 0 5 0 1 -7 5 0 7 5 1 -1 0 0 0 1 0 0 1 -1 2 5 0 1 2 5 1 -1 5 0 0 1 5 0 1 -1 7 5 0 1 7 5 1 -2 0 0 0 2 0 0 1 -2 2 5 0 2 2 5 1 -2 5 0 0 2 5 0 1 -2 7 5 0 2 7 5 0 -3 0 0 0 3 0 0 1 -3 2 5 0 3 2 5 1 -3 5 0 0 3 5 0 1 -3 7 5 0 3 7 5 1 -4 0 0 0 Size class surface area (mm