1 Australian Institute of Marine Science, PMB - Science Direct

Ecological Modelling, 49 (1990) 153-177

153

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

A CANTHA STER PLANCI A STARFISH-CORAL

OUTBREAK SITE MODEL

INITIATION:

R.E. REICHELT i W. GREVE 2, R.H. BRADBURY i and P.J. MORAN 1

1Australian Institute of Marine Science, PMB 3, Townsville MC, Qld. 4810 (Australia) 2 Biologische Anstalt Helgoland, Notkestr. 31, 2000 Hamburg 52 (Federal Republic of Germany) (Accepted 21 July 1989)

ABSTRACT Reichelt, R.E., Greve, W., Bradbury, R.H. and Moran, P.J., 1990. Acanthaster planci outbreak initiation: a starfish-coral site model. Ecol. Modelling, 49: 153-177. A lumped parameter model of the dynamics of the crown of thorns starfish (predator) and hard corals (prey) based on simple recruitment, growth and feeding equations was used to simulate the conditions that would lead to a starfish outbreak. The logical consistency of hypotheses concerning the onset of starfish outbreaks were tested by simulation. Results showed that adult starfish populations could change from extremely low to outbreak density within I year under the ' runoff' hypothesis and the ' predation of larvae' hypothesis. All other hypotheses showed that exponential increase of starfish populations could lead to outbreaks within a few years. Therefore, the testing of several of the hypotheses depends on whether outbreaks are the result of single massive recruitment to an otherwise small population or whether the outbreaks build over several years at an exponential rate and future field data collection should concentrate on low density starfish populations in the pre-outbreak phase. The model demonstrates not only the intuitively obvious result that processes influencing larval mortality can have a radical effect on the size of adult populations, but also the less obvious result that small changes in adult mortality and possibly juvenile mortality, can also cause the starfish to outbreak owing to density-dependent effects. The predation hypotheses are logically sound if the rate of predation on the starfish varies markedly with starfish population size. This density-dependent predation result is similar to that found for other outbreaking species such as the spruce budworm.

INTRODUCTION T h e A c a n t h a s t e r p h e n o m e n o n is a p r e d a t o r - p r e y s y s t e m o n I n d o - P a c i f i c c o r a l r e e f s i n w h i c h t h e p r e d a t o r , A. planci u n d e r g o e s l a r g e p o p u l a t i o n fluctuations and causes similar fluctuations in its prey, the hard corals ( M o r a n , 1986). O u r p r i m e c o n c e r n i n t h i s p a p e r is w i t h t h e p h e n o m e n o n a s seen in the central section of the Great Barrier Reef (GBR), Australia. 0304-3800/90/$03.50

© 1990 Elsevier Science Publishers B.V.

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A number of previous modelling studies of the population dynamics of A. planci have been mainly theoretical (Antonelli and Kazarinoff, 1984; Bradbury et al., 1985a; McCallum, 1987), although Antonelli et al. (1989) used field data to verify their model of large-scale waves of outbreaks progressing along the GBR. Done (1987) also used field observations of coral populations to test a transition matrix model of the effects of starfish outbreaks but in this case the emphasis was on the coral populations rather than on the dynamics of the starfish populations. The present state of knowledge of the Acanthaster phenomenon is such that modelling studies cannot be quantitatively predictive because there is still no agreement about which parameters are critical; and for those that are considered critical there are often no empirical observations. Here we develop a 'site model' (sensu Holling, 1978) of the starfish-coral interaction to provide a framework within which the main hypotheses regarding the causes of outbreaks can be examined. In doing so the aim is to improve our understanding of the starfish-coral system and to highlight gaps in that knowledge. At the outset the lack of field data for many parameters is acknowledged and one role of this paper is to emphasize the parameters that need to be measured in future field studies. This work is at the stage of model development rather than the stage of generating quantitative predictions, so model validation must be restricted mainly to an assessment of the assumptions of the model rather than testing model predictions against field observations. TYPE OF OUTBREAKS

There have been two periods of increased numbers of starfish outbreaks on the GBR in the last 25 years (Kenchington and Pearson, 1982; Moran, 1986). A primary outbreak is an increase in starfish population size derived entirely from the parent population at the same site as the outbreak; secondary outbreaks are derived from outside the site, that is, another reef or reefs - in this case the outbreak could be composed of migratory adults (Endean, 1973) or an immigrant patch of larvae. In attempting to understand the causes of outbreaks, a secondary outbreak is of slightly less interest because it has been propagated from a pre-existing outbreak elsewhere. To complicate matters, however, it is not known whether factors regulating the two different types of outbreak are the same in some or even most respects. One school of thought suggests that most of the outbreaks on the GBR are secondary. If this is true the original triggers are absent in many of the outbreaks observed on the GBR. This must be accounted for in the design of field experiments to test the various hypotheses.

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A SITE MODEL

Starfish life history In summary, the starfish is thought to have the following life cycle (after Lucas, 1975, 1984): females have large numbers (1 million or more) of planktonic eggs; an unknown proportion of eggs are fertilized externally in the seawater; planktonic larval development lasts about 2 weeks; benthic life follows settlement and metamorphosis; diet switches from algae to coral about 6 months after settlement; growth rate increases at the time of the diet switch; gonochoristic; sexual maturity at diameter about 15 cm; spawning season thought to be December-January on the GBR. Aspects of A. planci life history remain uncertain, particularly the juvenile stages, but the above outline has gained wide acceptance (Moran, 1986).

Parameter selection The selection of parameters for a model of outbreak initiation depends on the hypotheses to be assessed using the model. Although a variety of hypotheses has been formulated to explain primary outbreaks (Potts, 1981; Moran, 1986), we have selected two main ones which have received most attention in the literature. They can be termed: the terrestrial runoff hypothesis (Birkeland, 1982), and the predator removal hypothesis (Endean, 1977). The terrestrial runoff hypothesis as proposed by Birkeland (1982) contains two important elements which should be distinguished. One element is the direct or indirect positive effect on larval survival caused by runoff material (rainwater and nutrients). The other element is the concentration effect of local current patterns in keeping the food and the starfish larvae from dispersing very widely. These two elements are treated here as two separate hypotheses, the (1) runoff and (2) advection hypotheses, because the importance of both elements was emphasized in the original description of the hypothesis (Birkeland, 1982). This dissection of causal processes is important because the effects of the individual hypotheses, when taken together, may not necessarily accumulate linearly. In addition, there may be combinations of mechanisms operating in the GBR system other than the runoff/advection scenario considered by Birkeland (1982). A variant of the runoff hypothesis described above, but qualitatively different in the operation of the causal process, is one we have termed (3) the productivity threshold hypothesis. This hypothesis states that a small increase in productivity, caused by a chronic increase in nutrients rather than a very large bloom, gradually increases the survivorship of starfish

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TABLE 1 Description of variables used in the site model Variable Definition Driving variables (set before each simulation run) t Fback Yflood Calg Cmin Crnax Rg Pla

ej. Pad Pd

time-step phytoplankton abundance (background level) a year of flood coralline algae abundance a m i n i m u m possible coral cover (%) maximum possible coral cover (%) coral growth rate (see Fig. 1) predation on larvae; proportion of larvae killed by predators a predation on juveniles (settlement to 10 cm diameter); proportion killed a predation on adults (sexually mature starfish); proportion killed a density-dependent predation on adults (adults eaten); numbers of individuals killed relationship between coral cover and 'starvation' state of coral-eating starfish number of larvae per female (sex ratio = 0.5) proportion of larvae retained within the site minimum n u m b e r of adult starfish at the site starfish feeding rate (m 2 of coral per starfish per time-step)

Pstarve L Nar Snfin Rsf State variables dependent on outcome of simulation

F~o.c amount of phytoplankton (depends on floods) a c coral cover Abundance of starfish age classes b total number of larvae actually spawned Ls number of larvae surviving until settlement Lset Lset Jan-Feb Sla juvenile (algae feeder, < 1 cm) Mar-Apr Sj,1 juvenile (algae feeder, < 1 cm) May-Jun Sj,2 juvenile (algae feeder, 1 cm) Jul-Aug Sjum (Can delay diet switch for up to 6 months) juvenile (coral feeder, 1.6 cm) Sep-Oct Sjcl juvenile (coral feeder, 2.5 cm) Nov-Dec Sjc2 juvenile (coral feeder, 3.9 cm) Jan-Feb Sic3 juvenile (coral feeder, 6.2 cm) Mar-Apr s~4 juvenile (coral feeder, 9.7 cm) May-Jun Sj~5 adult (coral feeder, 4.8 cm) Jul-Aug Sad6 adult (coral feeder, 21.6 cm) Sep-Oct Sad7 adult (coral feeder, > 28 cm) Nov-Dec Sad (This class can survive up to 2 more years) sum of reproductive adult classes Sr~

-

Year Year Year Year

1 1 1 1

-

Year Year Year Year Year Year Year Year

1 1 2 2 2 2 2 2

a These variables are represented as a proportion b The sizes of these age classes, in conjunction with feeding rate, were used to determine the amount of coral consumed by starfish (see site model methods for derivation of sizes).

A C A N T H A S T E R PLANCI O U T B R E A K INITIATION

] 57

larvae to some threshold level beyond which the starfish-coral system develops into an outbreak. This hypothesis relies on non-linear threshold behaviour of the system to produce the outbreaks rather than a single catastrophic event such as the floods in the runoff hypothesis. As with the first main hypothesis, the predation hypothesis can be treated separately as (4) the predation on larvae hypothesis, (5) the predation on juveniles hypothesis and (6) the predation on adults hypothesis. These hypotheses include a change in adult starfish population size induced by a change in the predator pressure on the three respective stages of the starfish life cycle. The mechanism for the change in predator pressure is not explicitly stated. Predator populations may vary for a range of reasons, including the collection of the predators, for example fish or molluscs, by humans.

Model definition and initial conditions A consideration of the six hypotheses described above, and the known life history parameters of the starfish (Lucas, 1975, 1982, 1984) led to the design of a site model that included the parameters shown in Table 1 with a flow of events following those shown in Table 2. The model is expressed as a Fortran subroutine that runs within the modelling analysis package, BAHSIM, developed at the Biologische Anstalt Helgoland, Hamburg. The model time-step, t, is 2 months, this being the shortest age class of starfish that was used. The site is considered to be 100 ha of coral reef in an area of relatively high coral growth. With no starfish predation the coral cover grew 3% to 35% in 12 years. This matches field data on coral recovery from Pearson (1981) and Moran et al. (1985). The 2-monthly increment in coral cover, G, is a function of coral cover (c), coral growth rate (Rg) and maximum coral cover ( Cmax ) :

G=

c R g ( C m a x -- C)

Cma

where Rg = 0.05, Cm~x= 0.5 (i.e. 50%, after Moran et al., 1985). The minimum possible cover, Cmi~= 3%, matched observed values for John Brewer Reef (Moran et al., 1985). The shape of the coral recovery curve, when there is no starfish predation, is therefore the logistic curve shown in Fig 1A. Compared with Pearson's (1981) data for coral community regeneration, the parameters used here produce a more rapid recovery. A. planci feeding rate is set to 1 m 2 coral cover consumed per 2-month period per adult starfish of 28 cm or greater (this represents a median value of estimates of feeding rates reviewed by Moran, 1986). For coral-feeding starfish less than full size, this rate was reduced in proportion to the size of

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TABLE 2 Sequence of events in the site model The following five steps occur in every 2 month time-step (1) (2) (3)

(4)

(5)

coral grows, coral is consumed (equations in text) Determine Qst. . . . the starvation state of the starfish, a non-linear function of coral cover (see Fig. 1B) Calculate abundances of the coral-eating age classes, Sad to Sic1, e.g. Sad6 = Sjc5 - ( S j c s a s t a r v e ) - (Sic5 P a d ) - Pd Adult starfish have a lifespan of a further 2 years after reaching Sad stage. The proportion of algae eaters that become coral eaters is the complement of the starvation state of starfish: Sjel = Sjum(1 -- Qstarve) Calculate abundances of the algae-eating age classes, Sjum to Sju1, e.g. = ( sjuac.,,) - ( sj., % ) Sj~m (algae eaters) can survive for 6 months without switching to coral. Newly settled starfish: Sjul = L~tCaz~ Calculate the number of larvae that reach metamorphosis. Is there a flood? NO: set F~o,¢ to background (low) level. YES: set F~o,c to maximum (1.0). Is it spawning season? NO: no larvae are produced. YES: reproductive adults spawn. The number of larvae spawned: L~ = (( S , ~ w / 2 ) N a r L ( 1 - Qstarve)) and the number reaching settlement after losses caused by food limitation and then by predation: Lset = LsFconc - LsPla

A

B

1.0 i

minimumcoral cover ( very high starvationeffect )

40

8

~0'5

~"

0

2o

.~/

0

Jo Time steps

/

o

starvationthreshodl no starvation effect , to maximum possible coral cover

2'0 % Coral cover

Fig. 1. (A) Coral growth curve used in site model showing increase in percent coral cover over 120 time steps (20 model years). (B) Relationship between the starvation state of starfish, Qstarve, and the percent cover of coral.

ACANTHASTER PLANCI O U T B R E A K I N I T I A T I O N

159

the starfish in each age class. Starfish size was approximated by the area of a circle with diameter equal to the starfish diameter (arm tip to arm tip). The area of a starfish at each age class, At+l, is derived from a Verhulst type growth model: (Amax- At) At+ 1 = A t + A t R s

Amax

With starfish growth rate, R s = 1.5 and Amax equal to the area of a 30 cm diameter circle, the areas, and from them the diameters that are shown in Table 1, were calculated for each age class. Actual sizes at particular ages are not known for starfish from the GBR mainly because of the practical difficulty of tagging individuals, although reared starfish show a very slightly slower growth rate (Lucas, 1975) than that used here. The three size classes of starfish with diameters of about 15 cm or greater were considered to be sexually mature and capable of spawning at the appropriate time each year (after Lucas, 1975) and the largest size class was allowed to live only for 2 years after reaching this class. This represents the senility discussed by Lucas (1975) even though good evidence for this phenomenon from field observations is not available. A single variable, Qstarve, is used to represent the 'starvation' state or food availability for the starfish. This variable is dependent on percent coral cover (Fig. 1B) and is used in three ways: (1) It is the proportion of starfish that die or leave the site owing to lack of food. (2) The complement (1 - Q s t a r v e ) is the proportion of starfish that have not died or moved out of the site because of food availability. In this sense it represents the nutritional state of adult starfish and is multiplied by individual starfish fecundity (1 million) when calculating the number of larvae produced by a starfish. It is not intended here to represent directly a physiological index of health. (3) ( 1 - Qstarve) is also the proportion of algae-feeding juveniles that become coral-feeders. It is apparent that points (2) and (3) above are obviously very simplifying assumptions and further field studies such as Kettle and Lucas (1987) are needed to refine these points. The value of Ostarve is a step function of coral cover, and for sensitivity analysis the shape of the curve was controlled by fixing the ends of the curve and then varying the position of the starvation threshold point shown in Fig. lB. The values shown in Fig. 1B were used for all simulation runs. These values were chosen to reflect in the model the fact that the starfish are mobile and that corals are usually patchily distributed, so that starfish can avoid starvation until coral cover is quite low. This step function was added to simulate the rapid, almost catastrophic, drop in

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R.E. R E I C H E L T E T AL.

starfish numbers which is observed in the field (Moran et al., 1985) b u t not yet explained properly. In any case, the process of starvation is neither well known nor simple in asteroid echinoderms because of their ability to switch diet, to utilize nutrients stored in the pyloric caecae, to lower respiration rate and to lower metabolic rate in order to overcome prolonged periods without food (Lawrence, 1985; Watts and Lawrence, 1985). The spawning season occurred every sixth time-step (each model year) and lasted for one time-step (Moran, 1986). The fecundity of an adult starfish was set so that 1 million larvae were produced from the eggs of each female adult in each spawning season, and a sex ratio of 0.5 is assumed. There are published estimates as high as 60 million eggs per female (Conand, 1983), but there are no field data on fertilization success comparable to the echinoid work of Pennington (1985). The estimate of I million larvae per female used here represents an assumption of gamete dilution reducing fertilization rate to between 1% and 10% success. Fecundity and fertilization success must be considered along with the joint effects of larval survivorship and loss of larvae from the site. These parameters all influence recruitment success directly and one of the first results of the site model was to highlight how little is known about these factors. Although a proportion of larvae m a y be lost from the model system, no larvae can be imported from outside and so the system is partially closed. The minimum number of adult starfish on the model site is 10. This is more than was considered 'normal' b y Endean (1974) but less than that cited by Dana et al. (1972) or Ormond et al. (1973). In all cases, simulation runs were started with maximum coral cover (50%) and minimum starfish abundance (10). Although many model runs were done to explore the behaviour of the model system, the scenarios intended to simulate each of the six hypothesized mechanisms for triggering outbreaks were set up with critical parameters set as shown in Table 3. SIMULATION RESULTS The results are presented in the form of three-dimensional graphs representing sensitivity analysis model runs with a duration of 100 time-steps (200 model months) and in all cases, one of the model parameters has been varied linearly over a range of ten values. The results shown here were selected to illustrate the model's behaviour pertaining to the outbreak trigger hypotheses. Actual values of some of the critical parameters that could influence starfish outbreaks are unknown. Therefore in the runs presented here, the initial conditions were set to produce starfish outbreaks where the

ACANTHASTERPLANCIOUTBREAKINITIATION

161

TABLE 3 Values of critical parameters in model runs to simulate outbreaks triggered under the conditions specified for each of the six hypotheses

Hypothesis Runoff Advection

Figure Fback 2 3

Productivity 4 threshold Predation on 5, 6 larvae 7 Predation on 8 juveniles 9 Predation on 10 adults 11

Nar

[0.8-1.0] 0.95

Pla

0.50 0.90 [0.00001- 0.90 0.00501] [0.90-0.95] 0.001 0.90 0.90

0.1

0.95

0.1

0.95

0.001

Pju

Pad

0.3 0.3

0 0

ed 0 0

0.3

0

0

[0.8, 0.0-1.0] 0.3 0 0 [0.7-1.0] 0.9 [0.0-1.0] 0 0 [0.9-0.6] 0.9 0.2 [0.4-0.0] 0 0 [15-5]

Values in square brackets indicate the range used in the sensitivity analysis; Figure indicates the figure number displaying the results of each run. maximum number of starfish was in the tens to hundreds of thousands. This is typical of the numbers observed in the central G B R (Moran, 1986). The six hypotheses about outbreak triggers are dealt with in turn and a summary of model parameters is given in Table 3.

Runoff hypothesis.

In this run the mortality of starfish larvae by starvation was allowed to fall to zero for a single spawning period. This was done by setting Fconc, level of phytoplankton, to 1 in the spawning period of the first year (time-step 6), and to a background level, Fbaok of for the rest of the run. This background level was varied from 0.8 to 1.0 in the 10 model runs shown in the sensitivity analysis (Fig. 2). The loss of larvae by advection was relatively low (Nat = 0.5) in keeping with the scenario of Birkeland (1982). Predation of larvae and juveniles was set to arbitrary levels (P~a = 0.9, Pj, = 0.3), noting that there are no empirical data for these predation values. The 'flood' caused an outbreak of about 30000 starfish within 2 - 3 years which is consistent with Birkeland's hypothesis (1982). This outbreak lasted for several years by which time the coral cover had declined to very low levels. The change in the background level of p h y t o p l a n k t o n from zero up to a value of 0.9 made no difference in the outbreak pattern until a critical level was reached where sufficient larvae were surviving in non-flood spawning periods to allow the starfish population to increase in those non-flood conditions. This increase invariably produced a p r e d a t o r - p r e y cycle controlled by the rate of increase of starfish and the rate of coral recovery. A second outbreak occurred (Fig. 2) when the value of Fback is greater than

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R.E. R E I C H E L T

E T AL.

l 15480 adult starfish

t 1.0-

,

~

Fb~

~k-,.\\\\\\\\\\\\\\\-~ O.

I

0

Time steps

1 O0

Fig. 2. Abundance of starfish adults (on a linear vertical axis) after a single flood in response to variation in Fbaek,the backgroundlevel of phytoplankton (runoff hypothesis); 1 time step is 2 months; time axis shows 200 months. 0.9. The size of the outbreak was sensitive to changes in the number of larvae lost from the system by advection away from the site, as suggested by Birkeland (1982).

Advection hypothesis.

In order to examine an outbreak induced by larval retention, the mortality of larvae by starvation was kept low (phytoplankton, Fbacg -----0.95). The proportion of larvae retained, Nat, was varied from 0.00001 to 0.00501 in equal steps of 0.0005 (Fig. 3). These parameter values were chosen such that, given the other initial conditions, an outbreak of several hundred thousand starfish would occur at the high end of the range of values. Since food availability for larvae (Fback) and losses by advection (Nat), are both represented as proportions of larvae surviving, any change in one parameter is counteracted by varying the other parameter inversely. When Nat was at its minimum value of 0.000 01 (Fig. 3), the result of each spawning would lead to only a few adults entering the population some 18 months later, and no starfish outbreaks occur. The gradual increase in Nar from this point initiated an outbreak cycle with a decreasing period between outbreaks. A change in retention of larvae from 1 in 10000 to 30 in 10000 (two orders of magnitude) caused the starfish population to change from a non-outbreak state to an outbreak cycle pattern.

163

ACANTHASTER PLANCI OUTBREAK INITIATION

201050adult starfish

o.oo5olN

!

oo

o

o

~

~''~

I

Timesteps

100

Fig. 3. Abundance of starfish adults with varying values of N a r , the proportion of larvae retained at the site by water circulation effects (advection hypothesis).

79061 adultstarfish

Fback o

Time steps

Fig. 4. Abundance of starfish adults with varying values of levels, but no floods (productivity threshold hypothesis).

1O0 Fback ,

background phytoplankton

164

R.E REICHELT

E T AL.

93023 adult starfish

0.8 ~

.

~

~

~. Time steps

Fig. 5. A b u n d a n c e of starfish adults with hypothesis).

Pla

-100

varying between 0.8 a n d 1 ( p r e d a t i o n on larvae

Productivity threshold hypothesis.

The larval food supply (Fback) was allowed to vary from 0.90 to 0.95 (Fig. 4). This represents a 5% change in larval mortality caused by starvation. The results in Fig. 4 are not greatly different from those obtained for the advection hypothesis by varying Nat, except that the time to onset of the outbreak is less in Fig 3.

Predation of larvae hypothesis.

The mortality caused by predation of larvae allowed to vary from 0 to 1 and mortality of larvae by starvation set to 10% (Fbacg = 0.9) which is relatively high in order to remove the effect of food limitation on the larvae. Figure 5 shows the effect of varying P~a on the abundance of adult starfish. The corresponding graph illustrating the effects of varying P~a on live coral cover during the simulation runs are shown in Fig. 6, indicating the sensitivity of coral cover to the rapidly changing starfish population as predation on larvae (Pla) changes from about 0.8 to 1. In another set of runs made to examine the behaviour of the system near the point of onset of outbreaks, between P~a = 0.7 and P~a = 1, an exceptional peak of about 850000 starfish adults was observed (Fig. 7). This peak is a generation of starfish that become adults just as the coral is depleted but before the starfish 'starve'. The peak was not present in Fig. 5 because the critical values of P1, that produce the peak fall between two of the (P]a) was

ACANTHASTER PLANCI OUTBREAK INITIATION 0

165 Time steps

1 O0

coral cover

Fig. 6. Live coral cover with P~ varying between 0 and 1 (predation on larvae hypothesis).


1"0 ~'~'~'~\~-~"~'~'\~"~"~'~-\\\\\~ I ~'~'~'~'~'~'~'~'~"~'~"~'~"~\~-~'~'~\~\~\~\~

0

Fig. 7. Abundance of starfish adults with hypothesis).

Time steps

I O0

Pla varying between 0.7 and 1 (predation on larvae

166


ET AL.


v'/u

~

~

,~.\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\. . . . . . . . . s ~ % . \ \ \ \ . ~

0

Time steps

1O0

Fig. 8. Abundance of starfish adults with Pju varying between 0 and 1 (predation on juverfiles hypothesis).

incremental values used in the earlier set of runs. The results show that a change in larval mortality (mediated by predators of larvae in this case) as small as 3% (one of the incremental steps in Fig. 8) can shift the system from no outbreaks to an outbreak of several hundred thousand starfish in 3 - 4 years. Most importantly, the results demonstrate that the abundance of adults in the outbreaks is not a linear function of the level of predation of larvae.

Predation of juveniles hypothesis. The sensitivity graph of adult starfish abundance obtained by varying predation on juveniles (Pju) from 0 to 1 is shown Fig. 8. Although Fig. 8 is superficially similar to Fig. 7, there is a difference between the two results in the region where outbreaks begin to occur. This difference is made clear in Fig. 9 where the model is run with values of Pju in varying from 0.9 down to 0.6. The onset of the outbreaks is relatively more gradual in Fig. 9 than in Fig. 7 where Pla w a s varied.

Predation of adults hypothesis.

In the case of the adults, in contrast with the larvae and juveniles for which predators are unknown, there are a few predators on adult A. planci (Potts, 1981). The starfish is large, covered with rigid, shaw spines and contains toxic substances in its body. The main species known to be predators of adult starfish include three fish and two molluscs whilst several other predators have been reported from elsewhere in the Indo-Pacific region (Moran, 1986). Because of the likelihood of there

ACANTHASTER

167

PLANCI OUTBREAK INITIATION


t o6

x-x\~ 0.9

\\~\\\

o

"~\" " """\\\\\\\\\~

,x-x.\\'~,,\\\\\\\\\\\\\\\\x.

.x\--x

I

Time steps

lOO

Fig. 9. Abundance of starfish adults with Pju varying between 0.9 and 0.6 to show onset of outbreaks (predation on juveniles hypothesis).

U

Time steps

1 O0

Fig. 10. Abundance of starfish adults with Pad varying between 0.4 and 0 (predation on adults hypothesis).

168


o

Time steps

E T AL.

1 O0

Fig. 11. Abundance of starfish adults with Pd varying between 15 and 5 (predation on adults hypothesis).

being relatively few predators of the adult starfish, the hypothesis was examined using the model in two ways. First, sensitivity runs were made by varying the proportion of adults eaten per time-step (Pad) between 0.4 and 0 (Fig. 10). Secondly, the absolute number of adults killed (density-dependent predation, Pa) was varied between 15 and 5 per time-step (Fig. 11). Figure 10 shows that as predation is relaxed from 0.4 there is a slow increase in the starfish populations until Pad = 0 where the starfish numbers increase gradually over 6 or 7 years. In contrast, Fig. 11 shows no outbreak when Pd = 14 killed/time-step, but when Pd = 13 there is an outbreak of about 70000 starfish. Figure 11 also indicates that as Pd becomes less, the time to reach the maximum numbers of starfish is not greatly reduced but the numbers of starfish in the outbreak is substantially increased. DISCUSSION

Outbreak trigger hypotheses Runoff hypothesis. When an outbreak is caused solely by a flood-induced rise in food supply for larvae, then an outbreak would be expected shortly after the flood (up to 3 years after). Birkeland (1982) suggested that changes in food supply effects of several orders of magnitude could be involved in

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generating a starfish outbreak. In our model, changes of this magnitude would create an outbreak only when the other sources of mortality, such as predation of larvae and losses by advection, were low. With other sources of mortality increased, a change in larval food supply of only 10-20% induced an outbreak (Fig. 2). This begs the question of just how 'far' from outbreaking are the reefs of the GBR normally? Is a three order of magnitude change in phytoplankton really a necessary condition for an outbreak? Do larvae normally suffer extremely adverse effects in non-flood conditions? Olson (1985, 1987) has demonstrated that larvae can survive to settlement on natural levels of food suggesting that bloom conditions are not required for enhancing larval survivorship. In the runoff hypothesis, the rapidity with which outbreaks occur is a critical issue (Birkeland, 1982). The results of the model run shown here fit the scenario described by Birkeland. The starfish population increases within one starfish generation to an outbreak level. Depending on the background level of phytoplankton, a second settlement of starfish may occur before the food (coral) is depleted (Fig. 2), as Observed on John Brewer Reef in 1985 (personal observation). For reefs on the GBR, however, there are no data on the speed of development of primary outbreaks because starfish populations are difficult to monitor. Regular monitoring usually begins after a substantial number of starfish have already reached adulthood because this is the only life stage that is readily observable in the field. A further problem is that the source of recruits for any population is unknown, making it impossible to distinguish primary from secondary outbreaks. The evidence both for and against the operation of this hypothesis on the GBR is still equivocal (Moran, 1986). Olson (1987) suggests that food limitation effects on starfish larvae in the GBR region are small but Birkeland's (1982) hypothesis includes factors other than direct larval starvation as being potentially important for regulation of starfish populations. In addition, it has been suggested (Cameron, 1977; Cameron and Endean, 1982) that this hypothesis does not clearly distinguish A. planci from the herbivorous, planktonic larvae of the many other coral reef species which do not undergo outbreaks. This same criticism may be leveled at the predation of larvae and juveniles hypotheses unless it is established that the predators of A. planci are specialized feeders on this species of starfish alone.

Adoection hypothesis.

The results of the sensitivity analysis of the parameter controlling rate of loss of larvae by advection, Nar (see Fig. 3) showed that, like larval food supply, this is a relatively sensitive parameter. Although a relatively small increase in Na~ could cause an outbreak, the period of the predator-prey cycle would be long, meaning that the outbreak would build

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very slowly. While there is very little field data to indicate slow build up of populations, this could be due to the difficulty of detecting starfish when their density is low. The reef substrata are often topographically very complex which impedes searching by divers, and the young starfish may be settling in depths beyond the usual operating limit for non-decompression scuba which is approximately 30 m. The results show that a change in Nat of several orders of magnitude is required to produce an outbreak 3 within years. The question remains whether a change in starfish population from ten starfish to tens or hundreds of thousands of starfish over about 3 years is realistic. As mentioned in the discussion of the runoff hypothesis, this is a critical point in understanding the triggering of primary outbreaks. Without intensive sampling for small individuals before a major outbreak occurs, the rate of increase of the starfish population cannot be determined. It is unlikely that casual observation even by experienced divers will be sufficient, nor will the rapid survey techniques used for detecting large outbreaks, such as manta tow survey (Kenchington and Morton, 1976), be sufficient to detect the small changes in population size that this hypothesis predicts for an incipient outbreak. Establishing the source of the larvae in order to determine whether the outbreak is either primary or secondary presents further difficulties. If this hypothesis alone were a significant factor in causing outbreaks then one would expect numerous other coral reef species to show extremely large population fluctuations. Data are scarce for the GBR, but many coral reef species are patchily distributed with fluctuating population sizes and there have been some reports of outbreaks of coral-eating species in other coral reef systems. For example, significant coral mortality caused by Drupella comus (Moyer et al., 1982), Jennaria (Glynn et al., 1972) and Culcita (Goreau et al., 1972) has been reported. The advection hypothesis remains a plausible mechanism for enhancing an outbreak triggered by some other cause. Wolanski and Hamner (1988) have demonstrated the concentrating effects of topographically controlled fronts within coral reefs which is a necessary, and perhaps sufficient, condition for this hypothesis to operate.

Productiuity threshold hypothesis. The result shown in Fig. 4 is similar to Fig. 3 because in both cases the critical parameters act in a similar way on larval survivorship. The interesting features of the result obtained for this set of runs are the same as for the advection hypothesis. Firstly, are invertebrate populations such as A. planci in the real coral reef system of the G B R so sensitive to variation in larval survivorship that a 5% change in larval survivorship could induce outbreaks? Secondly, do the primary outbreaks build up over several years in a steeply exponential way or are they really a


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discontinuous j u m p as occurs on a catastrophe manifold surface (Poston and Stewart, 1978). As with the runoff hypothesis, there is a pressing need to investigate both seasonal and interannual variation in productivity of phytoplankton. In particular, the effect of nutrient pulses observed after cyclonic storms on the GBR (M. Furnas, Australian Institute of Marine Science, personal communication) needs to be determined. The question of the larval diet is critical in both hypotheses because estimates of chlorophyll levels in the ecosystem may be inadequate indicators of the larval food supply (Olson, 1987) and other factors influencing larval survivorship.

Predation of larvae hypothesis. The simulation results in Figs. 5, 6, and 7 illustrate a number of points. As with the other parameters that influence larval survivorship (Nat and Fback) the effect of changing predation levels on starfish larvae (Pla) shows a sharp boundary between the presence and absence of outbreaks. The outbreaks are not instantaneous as in the runoff hypothesis but still develop rapidly. The effect of changing predation on starfish larvae is even sharper on the coral community than on the starfish populations. Parenthetically, the hypothesis that variation in predation on larvae can cause outbreaks is of special interest because one of the potential predators of starfish larvae is the corals themselves (Yamaguchi, 1974). If the corals were significant predators of larvae then the possibility exists that there is trophic inversion as the older juveniles begin to eat coral. In a pelagic, ctenophore-copepod system where the effect is strong it has been shown that such an inversion creates a region of instability in the predator-prey relationship so that the system tends to be dominated by one species or the other (Greve et al., 1980). The likelihood of this p h e n o m e n o n being of major importance in the starfish-coral system is lessened by the fact that there are many areas of coral reef substrata that have relatively low cover of live coral where a starfish larva could settle without being eaten by a coral. The extraordinary peak of adults in Fig. 8 showed that the response of the starfish population to changing predation levels on starfish larvae is very sensitive to the timing of starfish recruitment relative to the state of the declining coral community.

Predation of juveniles hypothesis.

When the mortality by predation is represented as a proportion of the individuals, that is density-dependent, it is expected that the relative sensitivity of the three parameters Pla, Pju and Pad should be progressively less because the absolute numbers of larvae, juveniles and adults are progressively fewer. While small variations in Pla caused large

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fluctuations in adult numbers, the variation of Pjo caused a more gradual increase in adult starfish. Figures 8 and 9 show that, as expected, there are values of Pj, that can produce large outbreaks, but that a very small change in Pj, does not tend to make the system j u m p from non-outbreak to large, rapidly developing outbreaks. There are no data on juvenile mortality caused by predation. In a population of starfish in Fiji, Zann et al. (1987) found that juvenile mortality was high (ca. 99%) for starfish between 2.2 cm and 14 cm in diameter and the source of mortality was thought to be disease, rough seas and predation. More field observations of juvenile starfish populations are needed to test this hypothesis further.

Predation of adults hypothesis. Figures 10 and 11 indicate that depending on the type of predation, the effect on the adult population is very different. In the case of the density-dependent predation (Pa) it is clear that there is an intensely non-linear effect when a fixed number of adults are killed each time-step rather than a fixed proportion of adults. This non-linear effect creates a threshold in the same way that the external driving variable Ynood in the runoff hypothesis pushes the system beyond an outbreak threshold. This threshold effect is shown in Fig. 11 by the different trajectories when Pd = 14 (no outbreak) and when Pd = 13 (large, rapidly building outbreak). The exponential build-up of starfish in the density-dependent case (Fig. 11) illustrates a mechanism for predation on adults to cause the fast-increasing populations that have been observed in the field. The type of predation modelled in Fig. 10, in contrast, does not produce the fast-increasing outbreaks. This result agrees with the well known properties of density independent effects versus density dependent effects on populations. With regard to the rate of increase of the starfish population in Fig. 11 it is important to note that although the last stages of the outbreaks are visible as occurring over about 3 years, the predators were absent from the start of the run, some 6 model years earlier. The model results highlight the fact that the predation of adults hypothesis involves a very small change in the predator populations many years before the outbreak becomes obvious. The proposed mechanism for triggering a primary outbreak is also consistent with the propagation of secondary outbreaks in the system if it is assumed that the population of predators on starfish is unable to control a massive influx of starfish larvae from another reef. So, unlike the hypotheses relating to larval nutrition, there is no logical clash between the proposed trigger for primary outbreaks and the propagation of secondary outbreaks elsewhere in the system. The location of primary versus secondary outbreaks on the G B R remains a debatable point. Some argue that the series of outbreaks seen in the GBR system are multiple primary outbreaks while others suggest that

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certain parts of the GBR contain primary outbreaks which act as a source for secondary outbreaks. The critical problems for research into predation on adult starfish predation is to identify the predators of starfish in the central GBR region where most outbreaks have occurred, to determine the variability in natural densities of the predators and their rates of feeding, and finally, to determine whether there is any evidence that the populations of these predators have fluctuated significantly before or since the series of outbreaks observed at and near Green Island in the early 1960's.

Model assumptions and validation It is important to reiterate that actual (observed in the field) values are unknown for many of the parameters that were very sensitive in the model. Available field evidence has been discussed earlier. The effects of some of the simplifying assumptions made in the present model can be predicted in some cases. For instance, a likely effect of adding a spatial component at the within reef scale would be to influence the duration of outbreaks because of variations in spatial distributions of corals and starfish. The spatial structure, that is geomorphology, of individual reefs is also likely to affect aggregation patterns of large starfish populations (Reichelt et al., 1988). If predators on starfish are influential then a spatial component may be even more important. The lack of field data on the life span of A. planci makes it difficult to assess the assumption made here of a 4-year life span. This assumption has little effect on the model behaviour in the initial stages of an outbreak. When outbreaks occurred in the simulation runs described here, most starfish disappeared because of starvation effects caused by low coral cover before they died of old age. If the focus had been on the aftermath of outbreaks and the pattern of coral recovery then this assumption would be more important. In fact, large outbreaks do seem to 'disappear' very quickly (Moran et al., 1985) with little indication of the cause of disappearance (or death). Another difficult area to model realistically is the starfish population at extremely low densities (McCallum,1987). Cameron (1977) has suggested that a full understanding of the biology of A. planci and its propensity to outbreak depends on an appreciation of the evolutionarily specialized features of its biology. It may be that the very features that enable the starfish to persist at low densities in the coral reef system also cause the species to outbreak when the system is perturbed. For instance, the fact that the starfish has specialized defenses against predation could lead to the presence of a few relatively specialized predators that are then a sensitive part of the

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system when disturbed. In the simulation presented here, the model is able to describe the large range of response in the starfish population that results when only two or three adult starfish survive that in a non-outbreak system would have otherwise been eaten by predators. The model is relatively crude, however, in dealing with the low density starfish population. There is a minimum value of 10 adults set and nothing is allowed to drive the population below this level.This may be an unrealistic figure given the findings of other workers (Endean, 1977) and use of this arbitrary lower boundary in the model precludes its use in simulating the system when starfish abundance is extremely low. CONCLUSION The results presented here for any single hypothesis do not rule out absolutely any other hypothesis. There is, at present, no reason to think that only one or two hypotheses may be operating in the G B R system. In other words, there may be no single trigger of starfish outbreaks. Some processes may have a dominating influence in some regions of the G B R but not in others and even if many outbreaks are secondary then some hypotheses may be necessary but not sufficient to explain the outbreaks observed on the GBR over the last 27 years. For example, a likely scenario is that advection effects may be a necessary precondition for the predation hypotheses to operate. In most of the simulated outbreaks, except in those triggered by floods when background phytoplankton levels were very low, the system was in an oscillating state. The graphical results illustrate this in a number of cases. When coral cover had recovered, the starfish population bloomed. It is incorrect to label the oscillations observed in the field as limit cycles because endogenously driven cycling in the real system has not been conclusively demonstrated but merely hypothesized (Bradbury et al., 1985a, b) to exist as qualitatively stable cycles. If the real starfish-coral system is behaving in a cyclical way on the G B R at present, and historical distribution data are now being analysed to test the 'repeated cycle' hypothesis, then several points must be considered. First, the system may not always have behaved this way. Second, the system may continue to behave in this way until it is altered in some manner. Third, repeated occurrences of the triggers of primary outbreaks may not have a great effect on the system, rather they could act to entrain the oscillation and do nothing more than alter the frequency of starfish outbreaks rather than their amplitude. This has been suggested by others also (Potts, 1981). There are two large gaps in knowledge of the starfish population biology. One is the lack of understanding of the dynamics of low density popula-


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tions, particularly with respect to spawning, aggregation, and predation effects, and the other is the dynamics of post-settlement starfish juveniles. Parameters in the model relating to these areas were very sensitive in affecting adult starfish population size. In particular, density-dependent factors, such as predation, were very important as potential outbreak triggers. It is clear that, in addition to studies of specific processes such as recruitment and predation, a detailed monitoring program is essential for an increased understanding of the Acanthaster p h e n o m e n o n on the GBR. This is an important recommendation because, although the value of detailed experimental studies is universally acknowledged, monitoring programs are not always considered essential. Unfortunately, monitoring A. planci populations when densities are low poses great logistic difficulties. ACKNOWLEDGMENTS Thanks to Frank Reiner for assistance with the B A H S I M modelling package in Germany; Rosalie Buck for computing assistance; A. Dartnall and L. DeVantier for critical comments on the paper. The G e r m a n y Australia Bilateral Science Agreement (Canberra) and the Biologische Anstalt H a m b u r g (Hamburg) supported this work. This is AIMS contribution number 476. REFERENCES Antonelli, P.L. and Kazarinoff, N.D., 1984. Starfish predation of a growing coral reef community. J. Theor. Biol., 107: 667-684. Antonelli, P.L., Kazarinoff, N.D., Reichelt, R.E., Bradbury, R.H. and Moran P.J., 1989. A reaction-diffusion-transport model for large-scale waves in crown-of-thorns starfish outbreaks on the Great Barrier Reef. J. Math. Appl. Med. Biol. Birkeland, C., 1982. Terrestrial runoff as a cause of outbreaks of Acanthaster planci (Echinodermata: Asteroidea). Mar. Biol. Berlin, 69: 175-185. Bradbury, R.H., Hammond, L.S., Moran, P.J. and Reichelt, R.E., 1985a. Coral reef communities and crown-of-thorns starfish: evidence for qualitatively stable cycles. J. Theor. Biol., 113: 69-80. Bradbury, R.H., Hammond, L.S., Moran, P.J. and Reichelt, R.E., 1985b. The stable points, stable cycles and chaos of the Acanthaster phenomenon: a fugue in three voices. In: Proc. 5th Int. Coral Reef Cong., Tahiti, 27 May-1 June 1985, Vol. 5. Antenne Museum-EPHE, Moorea, pp. 303-308. Cameron, A.M., 1977. Acanthaster and coral reefs: population outbreaks of a rare and specialized carnivore in a complex high-diversity system. In: Proc. 3rd Int. Coral Reef Symp., Vol. 1. Rosenstiel School of Marine and Atmospheric Sciences, University of Miami, Miami, FL, pp. 193-199.

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