OCEANOLOGICA ACTA- VOL. 19- W3-4 ~ -----~- Life-cycle The consequences of broadcasting, Demography Asteroidea brooding, and asexual reproduction Transition matrix Cycle de vie Démographie in echinoderm metapopulations Asteroidea Matrices de transition Thomas A. EBERT Department of Biology, San Diego State University, San Diego, CA 92182-4614 USA. Received 17/01/95, in revised form 22/01/96, accepted 23/01/96. ABSTRACT Different modes of reproduction were examined in the context of entire life cycles for seven starfish species so that adult survival could be compared with reproductive output and first year survival. Data were assembled from the litera­ ture and included two asexual species, Linckia multifora and Nepanthia belcheri; two brooders, Asterina phylactica and Leptasterias hexactis; one species with benthic eggs that does not brood, Asterina gibbosa; one species with lecithotro­ phic development in the plankton, Patiriella pseudoexigua; and one planktotro­ phic species, Pisaster ochraceus. A negative correlation was found between first­ year survival and adult survival rates which also correlated with mode of reproduction: highest adult survival and lowest first-year survival was found for P. ochraceus, the planktotrophic species, and lowest adult survival was coupled with highest first-year survival in asexual species. A matrix model was developed to explore the metapopulation consequences of different modes of reproduction. Asexual species are similar to species with planktonic larvae that also have long-lived adults in that both are weil insulated from the vagaries of planktonic life, one by avoiding the plankton ali together and the other by having very low transition probabilities for the first year of life but high transition probabilities for retention of adults in the population. Species with short-lived adults and planktonic development of larvae are more closely tied to changes in first-year survival rates with respect to over-all dynamics of metapopulations. RÉSUMÉ Les conséquences de divers modes de reproduction, production de larves pélagiques, incubation et reproduction asexuée chez les métapopulations d'échinodermes. Différents modes de reproduction sont examinés à travers les cycles vitaux de sept espèces d'étoiles de mer; le taux de survie des adultes est comparé à la pro­ duction gonadique et au taux de survie durant la première année. Les données, extraites de la littérature, se rapportent à 1) deux espèces asexuées, Linckia multi­ fora et Nepanthia belcheri, 2) deux espèces incubantes, Asterina phylactica et Leptasterias hexactis, 3) une espèce à développement benthique qui ne protège pas ses œufs, Asterina gibbosa, 4) une espèce à développement planctonique lécithotrophique, Patiriella pseudoexigua, et 5) une espèce planctotrophique, Pisaster ochraceus. Une corrélation négative est observée entre le taux de survie durant la première année et le taux de survie des adultes, lui-même corrélé au mode de reproduc­ tion. Le plus fort taux de survie des adultes et le plus faible taux de survie durant la première année sont observés chez P. ochraceus, l'espèce planctotrophique, 217 T.A. EBERT tandis que le plus faible taux de survie des adultes est associé au plus fort taux de survie durant la première année chez les espèces asexuées. Un modèle matriciel a été développé pour analyser les conséquences des diffé­ rents modes de reproduction chez les métapopulations. Les espèces asexuées sont similaires aux espèces à larves planctoniques et longue durée de vie, dans la mesure où toutes deux échappent aux caprices de la vie pélagique, les unes ne dépendant pas du plancton en général, les autres ayant peu de chances de survie au-delà de la première année mais une forte probabilité de maintien des adultes dans la population. Les espèces à courte durée de vie et à développement larvaire planctonique ont un taux de survie nettement plus variable durant leur première année, en rapport avec la dynamique des métapopulations. OceanologicaActa, 1996,19,3-4,217-226. INTRODUCTION with transition probabilities, and there are none that supply such information so spatial and temporal variability can be evaluated. Y et it is clear that such information is needed Life cycles of organisms represent a long history of selec­ not only to understand the evolution of life histories but tive tinkering and, in general, the !ife cycle that is observed also for applied purposes such as management of natural is expected to show adjustments in ali parts of the cycle in resources and the design of marine reserve systems. response to changes in one part. Schedules of survival and reproduction are at the core of ali theoretical discussions of This paper examines data on echinoderms, and in particu­ life cycles dating back to Fisher (1930), Birch (1948), and lar starfishes, to evaluate the effects of different reproducti­ Cole (1954) and implicit or explicit in ali life-history dis­ ve modes on transitions in the life cycle, specifically first­ cussions is that trade-offs exist such that if resources are year and adult survival rates. Also, after making estimates used for one activity they can not be used for something of these transitions for a selection of echinoderm species, 1 else. Analysis of tradeoffs bas focused on relationships will present a mode! for combining populations into meta­ among numbers and sizes of offspring, adult size and populations that provides sorne insights into the importan­ growth, and survival (e.g, Stearns, 1992). ce of dispersal with respect to fitness and probable stability characteristics of metapopulations of species with different Population growth rate or fitness is determined by mean modes of reproduction. values for schedules of survival and fecundity as weil as variability of these traits (e.g. Tuljapurkar, 1982 a, b; Orzack, 1985; Caswell, 1989) and so changes in morpholo­ gy, physiology, or behavior that change means and METHODS variances of life-cycle transitions will change fitness. Changes in mean values for offspring number are correla­ ted with mode of reproduction in marine invertebrates, as Life-cycle information in the form of age- or size-specific weil as other groups of organisms, and these changes in rates of survival and reproduction was obtained from a mode of reproduction are perceived as changes that should number of published studies. To reanalyze data, 1 bad to modify early survivorship (e.g. Menge, 1975). make a number of assumptions. The two most important assumptions are: 1) populations have seasonally stable There is general agreement concerning the ranking of structure; that is, at the same time each year they have the reproductive modes that should improve the chances of same proportions in ages or sizes; and, 2) populations are first year survival: the form of reproduction with the lowest seasonally stationary, which means that from year to year first-year survival is planktotrophy, followed by planktonic the population growth rate, Â, is equal to 1.0. lecithotrophy, attached benthic lecithotrophic eggs with no planktonic stage, brooding, and, finally, asexual reproduc­ Two different, though related, forms of the life cycle were tion, such as autotomy of body parts that regenerate, and used for analysis (Figs. 1, 2). In the first (Fig. 1), an age­ fission of a body into two or more pieces of approximately structured matrix was created with a terminal age, ro, and equal size. Asexual reproduction should have the highest with the possibility of age-specifie changes in reproduction first year survival rate. and survival for adults. This is the standard Leslie matrix. Data that were used included ali information but one tran­ Changes that increase the mean and reduce variation in sition; namely, first year survival Po. The characteristic survival from spawning or asexual reproduction to an age equation for Figure 1 was obtained by following the outli­ of one year should improve fitness and as a consequence ne provided by Casweli (1985, 1989). A Z-transformation free resources that bad been used for maintenance to was performed, which is just multiplying ali transitions by increase fitness in other ways, such as more offspring. This Â-l. Ali possible loops through node 1 were determined scenario bas been presented by Stearns (1976) and conti­ and then ali transitions in a loop were multiplied together. nues to be an attractive explanation (e.g. Grant, 1990). Products from ali individual loops were then added toge­ Few studies on life-history traits of echinoderm species ther and set equal to 1.0. A bit of additional algebra was ali with different modes of reproduction have been conducted that was needed to form the characteristic equation of the in sufficient detail that complete !ife-cycles can be drawn graph: 218 ECHINODERM METAPOPULATIONS St =Soo(1- e-Z) :~:e-Zi (1- b.e-K(t+i) )-n (5) i=O With the Richards function for modeling growth and constant adult survival the parameters in Eq. 5 are: 1 2 Â. ro- b1 PoÂ.ro- - b2PoÂ. ro- ... bwPo = 0 Soo = asymptotic size 1 K = the growth-rate constant with units of ti me-1 n =a shape parameter; e.g. n =-1 for the Brody-Bertalanf­ fy equation and + 1 for logistic growth Figure 1 s-IIn -S-1/n Life-cycle with age-structure that is the equivalent of the Leslie b= oo R (6) s-lln matrix; Po = first year survival; Px = age-specifie survival for age 00 classes from 1 to oo; mx = age-specifie fecundity; formula for estima­ ting Pois for population growth rate Â. set equal to 1. t = time since recruitment of animais that are size SR; t generally is set equal to O. SR = size of new recruits, generally set as equal to the mode of the smallest component of a size-frequency distri­ (1) bution or series of size-frequency distributions. where b1 is m~o bz is P1m2, b3 is P1P2m3, etc. After setting Z =the instantaneous rate of mortality when Nx = Noe-Zx Â.