Prediction, Chaos and Ecological Perspective.

As defined, the modeling procedure is quite broad. For example, the chosen compartments may contain a single organism, a population of organisms, or an ensemble of populations. A population compartment, in turn, could be homogeneous or possess structure in size or age. Likewise, the mathematical statements may be deterministic or probabilistic in nature, linear or nonlinear, autonomous or able to possess memory. Examples of all types appear in the literature. In practice, however, ecosystem modelers have focused upon particular types of model constructions. Most analyses seem to treat compartments which are nonsegregated (populations or trophic levels) and homogeneous. The accompanying mathematics is, for the most part, deterministic and autonomous. Despite the enormous effort which has gone into such ecosystem modeling, there remains a paucity of models which meets the rigorous &! validation criteria which might be applied to a model of a mechanical system. Most ecosystem models are short on prediction ability. Even some classical examples, such as the Lotka-Volterra predator-prey scheme, have not spawned validated examples.

Fish recolonization in temperate Australian rockpools: a quantitative experimental approach

Understanding recolonization processes of intertidal fish assemblages is integral for predicting the consequences of significant natural or anthropogenic impacts on the intertidal zone. Recolonization of experimentally defaunated intertidal rockpools by fishes at Bass Point, New South Wales (NSW), Australia, was assessed quantitatively by using one long-term and two short-term studies. Rockpools of similar size and position at four sites within the intertidal zone were repeatedly defaunated of their fish fauna after one week, one month, and three months during two shortterm studies in spring and autumn (5 months each), and every six months for the long-term study (12 months). Fish assemblages were highly resilient to experimental perturbations—recolonizing to initial fish assemblage structure within 1−3 months. This recolonization was primarily due to subadults (30−40 mm TL) and adults (>40 mm TL) moving in from adjacent rockpools and presumably to abundant species competing for access to vacant habitat. The main recolonizers were those species found in highest numbers in initial samples, such as Bathygobius cocosensis, Enneapterygius rufopileus, and Girella elevata. Defaunation did not affect the size composition of fishes, except during autumn and winter when juveniles (<30 mm TL) recruited to rockpools. It appears that Bass Point rockpool fish assemblages are largely controlled by postrecruitment density-dependent mechanisms that indicate that recolonization may be driven by deterministic mechanisms.

Modeling red sea urchin (Strongylocentrotus franciscanus) growth using six growth functions

The growth of red sea urchins (Strongylocentrotus franciscanus) was modeled by using tag-recapture data from northern California. Red sea urchins (n=211) ranging in test diameter from 7 to 131 mm were examined for changes in size over one year. We used the function Jt+1 = Jt + f(Jt) to model growth, in which Jt is the jaw size (mm) at tagging, and Jt+1 is the jaw size one year later. The function f(Jt), represents one of six deterministic models: logistic dose response, Gaussian, Tanaka, Ricker, Richards, and von Bertalanffy with 3, 3, 3, 2, 3, and 2 minimization parameters, respectively. We found that three measures of goodness of fi t ranked the models similarly, in the order given. The results from these six models indicate that red sea urchins are slow growing animals (mean of 7.2 ±1.3 years to enter the fishery). We show that poor model selection or data from a limited range of urchin sizes (or both) produces erroneous growth parameter estimates and years-to-fishery estimates. Individual variation in growth dominated spatial variation at shallow and deep sites (F=0.246, n=199, P=0.62). We summarize the six models using a composite growth curve of jaw size, J, as a function of time, t: J = A(B – e–Ct) + Dt, in which each model is distinguished by the constants A, B, C, and D. We suggest that this composite model has the flexibility of the other six models and could be broadly applied. Given the robustness of our results regarding the number of years to enter the fishery, this information could be incorporated into future fishery management plans for red sea urchins in northern California.

Stock-rebuilding time isopleths and constant-F stock-rebuilding plans for overfished stocks

Stock-rebuilding time isopleths relate constant levels of fishing mortality (F), stock biomass, and management goals to rebuilding times for overfished stocks. We used simulation models with uncertainty about FMSY and variability in annual intrinsic growth rates (ry) to calculate rebuilding time isopleths for Georges Bank yellowtail flounder, Limanda ferruginea, and cowcod rockfish, Sebastes levis, in the Southern California Bight. Stock-rebuilding time distributions from stochastic models were variable and right-skewed, indicating that rebuilding may take less or substantially more time than expected. The probability of long rebuilding times increased with lower biomass, higher F, uncertainty about FMSY, and autocorrelation in ry values. Uncertainty about FMSY had the greatest effect on rebuilding times. Median recovery times from simulations were insensitive to model assumptions about uncertainty and variability, suggesting that median recovery times should be considered in rebuilding plans. Isopleths calculated in previous studies by deterministic models approximate median, rather than mean, rebuilding times. Stochastic models allow managers to specify and evaluate the risk (measured as a probability) of not achieving a rebuilding goal according to schedule. Rebuilding time isopleths can be used for stocks with a range of life histories and can be based on any type of population dynamics model. They are directly applicable with constant F rebuilding plans but are also useful in other cases. We used new algorithms for simulating autocorrelated process errors from a gamma distribution and evaluated sensitivity to statistical distributions assumed for ry. Uncertainty about current biomass and fishing mortality rates can be considered with rebuilding time isopleths in evaluating and designing constant-F rebuilding plans.

Dynamical structure in paleoclimate data

Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. The theory of chaotic dynamical systems includes methods that can test whether any given set of time series data, such as paleoclimate proxy data, are consistent with a deterministic interpretation. Paleoclimate data with annual resolution and absolute dating provide multiple channels of concurrent time series; these multiple time series can be treated as potential phase space coordinates to test whether interannual climate variability is deterministic. Dynamical structure tests which take advantage of such multichannel data are proposed and illustrated by application to a simple synthetic model of chaos, and to two paleoclimate proxy data series.

Trend and growth analysis of marine fish production in Bangladesh

The study based on time series marine fish production data during the period of 1983-1984 to 2007-2008 in Bangladesh. For this growth analysis six deterministic time series models are considered. The estimated best fitting models are the cubic, quadratic and quadratic model is appropriate for industrial marine fish production, artisanal marine fish production and total marine fish production in Bangladesh respectively. The study attempts to provide forecasts of marine fish production in Bangladesh for the year of 2008-09 to 2012-13. The magnitude of instability in marine fish production was attempted by computing the coefficient of variation (CV) and the percentage deviation from three years moving average values. The study revealed that the total marine fish production was observed to be relatively stable (CV being 31.85%) compared to the artisanal marine fish production (CV being 32.04%) and industrial marine fish (CV being 47.20%). For the three components of marine fish production the growth rates were different over different time points. The variation of the growth rates in industrial marine fish production was -21.6% to 13.12%, in artisanal marine fish production was 2.39% to 5.29% and in total marine fish production was 11.23% to 24.85% during the study period.