COMPETITIVE POPULATION DYNAMICS AMONG

Congresso Brasileiro de Oceanografia – CBO´2012 13 a 16 de novembro de 2012 Rio de Janeiro – RJ

COMPETITIVE POPULATION DYNAMICS AMONG THREE DOMINANT SPECIES OF AMPHIPOD ASSOCIATED TO Bryocladia thrysigera, PERUÍBE, SÃO PAULO William Roberto Luiz Silva Pereira; Maria Teresa Valério-Berardo; Cleberson H. Moura; Máurea Nicoletti Flynn [email protected] (Instituto I2S)

ABSTRACT Ecology aims to study the fundamental relationship between organisms and their environment. Following Turchin (2001) any given population has the natural ability to grow (following the exponential law) and achieve stability (through resources limitation and resource-consumer oscillation laws). Population rates of the three dominant species (Hyale nigra, Caprella danileviskii and Caprella penantis) associated to Bryocladia thrysigera, Peruíbe, São Paulo were calculate and both three species revealed similar values in the intrinsic rate of growth. We suggested a three-species competition model in a discrete Ricker form that is capable to generate periodic cycles for the carrying capacity. To approximate model to data, a new method to find the coefficients competition emerged, in good agreement with ecological and behaviour particularities. Key words: Amphipoda, Three-species Competition Model, Competition Coeficient

INTRODUCTION Ecology aims to study the fundamental relationship between organisms and their environment. The partitioning of ecological phenomena in four hierarchical levels: individuals, populations, communities and ecosystems, favor ecological studies. For each of the four hierarchical levels there are specific rules and forms (Lawton, 1999) such as the allometric exponents and scaling laws (Marquet et al. 2004). At population level, Turchin (2001) proposed three laws (exponential growth, resources limitation and consumer-resource oscillations) with the potential to be used in modeling natural populations or experimental biological events and allowing the formulation of predictions based in rates and parameters of biological relevance. These laws have been explored by Flynn & Pereira (2011) for potential application in ecotoxicology. Furthermore, the predictability is increased at individual and population level (van Straalen, 2003). Any given population has the natural ability to grow (following the exponential law) and achieve stability (through resources limitation and resource-consumer oscillation laws). But there are other forces arising from intrinsically and extrinsically events that may affect a given population modifying its behavior. As postulated by Lawton (1999), organisms are limited by their environment. In controlled experiments and for a few natural populations, these laws are clearly observed, however for many natural populations they are not easily detected. Turchin (2001) discussed biological forces, with trophic origins, acting on exponential growth and resource limitation laws. In addition, contingency rules define the environmental key participation on species dynamics. Both may interfere in the natural population dynamics. The aim of this paper is to propose a model to describe the population dynamics of three dominant species of amphipods associated to the algal Bryocladia thrysigera, based on previously published field data by Valério-Berardo & Flynn (2002 and 2004) and Flynn et al. (2009). METHODOLOGY Based on data sampled by Valério-Berardo & Flynn (2002) and used to describe the composition and annual change in the community structure of amphipods associated to the Associação Brasileira de Oceanografia (AOCEANO)

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algae Bryocladia thrysigera from the intertidal region of Itanhaém beach in Peruíbe, population rates of the three dominant species (Hyale nigra, Caprella danileviskii and Caprella penantis) were calculated. The authors (Valério-Berardo & Flynn, 2002) concluded that environmental variables (salinity, temperature and dissolved oxygen) did not explain the variations in species abundance registered and suggested that dominance alternation among the three dominant species and predation force intensification during winter were responsible for the observed pattern. Valério-Berardo observed for C. danileviskii and C. penantis a sigmoid growth (unpublished data), adjusted here, for monthly data densities, to the Pearl-Verhulst equation. This adjustment provided the parameters r2, K2 for C. danileviskii and r3, K3 to C. penantis. For H. nigra, the population parameter r1 (intrinsic rate of natural growth, also called Malthusian or Darwinian fitness) was calculated by the construction of monthly life tables where a non density-dependent characteristic value was obtained (Flynn et al., 2009). The entire community can be simulated by an equation system in Ricker discrete form:

When reducing to three species,

where the coefficients , , , , , ( ) represent the competitive interference of species j on species i. Assuming that the carrying capacity (K) fluctuates cyclically (Gotelli, 2001), the cosine term does support the generation of periodic cycles of frequency . The term determines the cycle amplitude.

The cosine term for the first equation was replaced by the term sin as carrying capacity for H. nigra varies in opposite direction from that of the two other species (Valério-Berardo ) Flynn, 2002) (see Fig. 1). The parameters (cycle frequency) and (cycle amplitude) were considered based on the biennial cycle verified by Valério-Berardo & Flynn (2002), imposing a 180 days cycle adaptation with alternating dominance. Amplitudes were considered by the average density of each population (data from Valério-Berardo & Flynn, 2002). Population peaks were recorded and the ratio (mean population/population peak) calculated and then applied to the adjusted theoretical carrying capacity values. To calculate the competitive coefficients, growth rates (r1, r2, r3) and oscillating parameters (c1, c2, c 3 and k1, k2, k3) were previously stated. For the carrying capacities assessment (K1, K2 and K3) the population peaks values found by Valério-Berardo & Flynn (2002) were used. Modeling results, however, did not reflect the pattern presented by the actual data. To rectify this, an average curve was inserted for each theoretical population in order to adjust each curve to the field data . Whenever the theoretical population means coincided with the sampled one and the theoretical population peaks coincided (not equaled) with sampled population peaks, the resulting values of competition coefficients and carrying capacities were recorded.

RESULTS For H.nigra the average density was 2238 ind/50g algae, for C. danileviskii, 2136 ind/50g algae and for C. penantis, 1493 ind/50g algae. When applying correlation analysis to paired populations densities, there was a positive correlation for C penantis and C. danileviskii (+0.570), and negative correlation for H. nigra and C. danileviskii (-0.433) and H. nigra and C. penantis (-0.351),

Associação Brasileira de Oceanografia (AOCEANO)

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showing alternating dominance between Hyale and the two Caprella species, with coincidental oscillation, as pointed out by Valério-Berardo & Flynn (2002). Temporal series of each of the species considered is shown in Figure 1. Average density was higher for H. nigra, followed by C. danileviskii and C. penantis. The revealed population parameters r 1, K 1, r 2, K 2, r 3, K 3 can be checked in Figure 2. Growth rates for each of the three populations considered were very similar. The carrying capacity presented by C. danileviskii was below and by C. penantis well above those found by Valério-Berardo & Flynn (2002). The average intrinsic growth rate of H. nigra calculated by Flynn et al. (2009) is r1 = 0.138/generation but to feed the model we use r1 = 0.05/day and this can be explained in four different ways: in three species competition models, intrinsic increase rate is usually the same for all species considered (May & Leonard, 1975; Leach & Miritz, 2006); considering the scaling law (Fenchel, 1975) relating body size to rate of population increase (rmax  M -0,25), populations with similar body size presents similar increase rates; similar taxonomic species have similar life histories; and, finally, the adjustment to Pearl-Verhulst equation for H.nigra data resulted in the expected value r1 = 0.05/day (Figure 2). Competition interference of Caprella species on H. nigra was high: α12 = α13 = 1.20. And hence competition interference of H. nigra on each species of Caprella was lower: α21 = 0.26 and α31 = 0.21 (Table 1). The model showed that C. penantis exerts a strong competitive force on C. danileviskii (α23 = 0.90), and C. danileviskii affects less intensely C. penantis (α32 = 0.21). When starting the model simulation with initial population densities, each population quickly enters into an oscillatory pattern respecting the dominance alternation, and C. penantis never presenting numerical dominance over C. danileviskii. Population peaks, as well as average densities, remained close to those found in field populations (Figure 3).

DISCUSSION It would be highly desirable that ecological models were robust enough to predict the abundance of a given population in the future, helping the decision process by effectively signaling environmental stress (Van Straalen, 2003). In rare cases, simple models were effective making population based predictions (Flynn & Pereira, 2011). Different interference combinations in natural systems are endless and it can be considered, following Lawton (1999), that there are endless dynamics even with the basic laws supporting natural populations. Oscillatory fluctuations are not unique to models and experiments of trophic interactions. Models simulating three species competitive interactions also generate oscillatory behavior (May & Leonard, 1975; Leach & Miritz, 2006). The models however are simplified by the generalization of the competition coefficient to facilitate mathematical analysis, reducing, in this manner, its biological significance. Regarding the proposed model, some considerations must be made: the population parameters were found empirically, enhancing its representation; values generated for the intrinsic rate of increase for each species were close enough to permit the verification of other ecological laws; values for carrying capacity were above empirical population peaks allowing the model fit to empirical data. Theoretically the carrying capacity is known only if a population is kept isolated in the system. The model found K value of 9000 for H. nigra, and the maximum K value found empirically is 5000 (Flynn et al, 2009). There are several methods to calculate the competition coefficient. The most common is by MarArthur-Levins equation, transforming the use proportion by two species of a given resource in competitive coefficient. Despite the debate on the actual suitability and lack of symmetry of the coefficient (Pianka, 1974; Krebs, 1999), its applicability in the current context seems justified as the interference of species i on the species j is not the same as the inverse, which guarantees the asymmetry, and simultaneously allows the description of the resource distribution and niche overlap. The resources commonly considered are food or space (Krebs, 1999). In the present case, the limiting resource must be space, since food is not considered a limiting factor for epiphyte herbivorous species, such as H. nigra (Jacobucci, 2005). When comparing the morphological structures of


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Caprella and Hyale, it seems that the first would have a selective advantage to an algae substrate life. This would partially explain the high interference values of both Caprella on H. nigra.

ACKNOWLEDGEMENTS We are grateful to Maria Teresa Valério-Berardo in yield data. REFERENCES Fenchel, T. 1974. Intrinsic rate of natural Increase: the relationship with body size. Oecologia, 14: 317-326. Flynn, M.N.; Pereira, W.R.L.S.; Pires, R.C. & Valério-Berardo, M.T. 2009. Population dynamics of Hyale nigra (Haswell, 1879) (Amphipoda, Hyalidae) Associated to Bryocladia thrysigera (J. Agardh) at Peruíbe beach, Itanhaém (SP), southeastern Brazil. Nauplius, 17(1): 1-8. Flynn, M.N. & Pereira, W.R.L.S. 2011. Population-based approach in ecotoxicology. Revinter, 4: 7981. Gotelli, N.J. 2001. A Primer of Ecology. 3rd Edition. Sinauer Associates, Sunderland, Mass. 265pp. Jacobucci, G.B. 2005. Sargassum interactions epiphyte-grazing amphipods in Ubatuba, northern coast of São Paulo. PhD thesis. University Estadual de Campinas. Krebs, C.J. 1998. Ecological methodology. Addison Wesley Longman, Menlo Park, California, 620pp. Lawton, J.H 1999. Are there General Laws in ecology? Oikos, 84: 177-192. Leach P.G.L & Miritzis, J. 2006. Analytic behavior of competition among three species. Journal of Mathematical Nonlinear Physics, 3(4): 535-548. Marquet, P.A.; Quinones, R. A.; Abbots, S.; Labra, F.; Tognellim M.; Arim, M. & Rivadeneira, M. 2005. Scaling and power-laws in ecological systems. Journal of Experimental Biology, 208: 17491769 May, R.M. & Leonard, W.J. 1975. Nonlinear Aspects of competition between three species. SIAM Journal on Applied Mathematics, 29: 243-253. Pianka, E.R. 1974. Niche overlap and diffuse competition. Proceedings of the National Academy of Science of the U.S.A, 71: 2141-2145. Turchin, P. 2001. Does Population ecology have general Laws? Oikos. 94:17-26. Valério-Berardo, M.T. & Flynn, M.N. 2002. Composition and seasonality of an amphipod community to the Associated algae Bryocladia trysigera. Brazilian Journal of Biology, 62(4A): 735-742. Valério-Berardo, M.T. & Flynn, M.N. 2004. Population biology of Hyale nigra (Haswell, 1879) (Amphipoda, Hyalidae) Associated to Bryocladia thyrsigera (J. Agardh) at Peruibe, Itanhaém beach, southeastern Brazil. Nauplius. 12(1): 1-10. Van Straalen, N.M. 2003. Ecotoxicology Becomes stress ecology. Environmental Science and Technology. 37(17): 324A-330A


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Figure 1. H. nigra, C. danileviskii and C. penantis temporal fluctuations (March 1998). Horizontal lines represent the average density for each species considered.

1997

to

February

Figure 2. Sigmoid growth for C. danileviskii, C. penantis and H. nigra. The first two species were sampled from 30/03/1998 to 22/09/1998. The data for C penantis consist of three samples taken biweekly; deviations are represented on the chart by bars above and below. For C. danileviskii each point represents one sample. All individuals, male, female and young, were considered. The adjustment of the logistic curve revealed r2 = 0.050/day, K2 = 1500 and r3 = 0.040/day, K3 = 15000. The population parameters of H. nigra are for the period from October 1997 to February 1998. We found r1 = 0.050/day, K1 = 5000. Data from Valério-Berardo and Flynn (2002).


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Table 1. Parameters used on and disclosed by the competition model. Note that carrying capacities were higher than the population peaks assessed by Valério-Berardo and Flynn (2002).

Hyle nigra Parameters Model r1 0.500 K1 9000 α 12 α 13

1.20

Caprella danileviskii Parameters Model r2 0.500 K2 5400 0.26

1.20

α 21 α 23

c1

78% in K 1

k1

360/2

Caprella penantis Parameters Model r3 0.500 K3 3600 0.21

0.90

α 31 α 32

c2

77% in K 2

c3

83% in K 3

k2

360/2

k3

360/2

0.21

Figure 3. Values generated by modeling (theoretical) versus field (experimental) data. Despite the “noise” in field series and the asymmetrical biannual cycle, it is clear that the model retains the main features of the three species dynamics.


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