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Ye et al.(1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.'s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future.With the term "equation-free" in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka-Volterratype models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing "clarity and precision into conjecture" (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.However, mathematics has not had the "unreasonable effectiveness" in ecology that it has had in physics. Critics point out that models in ecology have not passed the criterion of predictive ability (3, 4). There are many reasons for this, one being the highly nonlinear nature of ecological interactions. This has led to arguments over whether the "right" models are being used, but also to broad opinion that, unlike in physics, there are no right models to describe the dynamics of ecological systems, and that the best that can be done is to find models that are at least good approximations for the phenomena they are trying to describe. It is common in introductions of ecological modeling to find descriptions of the "modeling cycle," in which a question is formulated, hypotheses are made, a model structure is chosen in the form of variables and equations, the equations are parameterized according to best information, and the model is analyzed and compared with patterns in nature. The cycle can be repeated again and again to obtain the best fit or validation by data. Although this methodology may work for some case...

Climate change and urban growth impact habitats, species, and ecosystem services. To buffer against global change, an established adaptation strategy is designing protected areas to increase representation and complementarity of biodiversity features. Uncertainty regarding the scale and magnitude of landscape change complicates reserve planning and exposes decision makers to the risk of failing to meet conservation goals. Conservation planning tends to treat risk as an absolute measure, ignoring the context of the management problem and risk preferences of stakeholders. Application of risk management theory to conservation emphasizes the diversification of a portfolio of assets, with the goal of reducing the impact of system volatility on investment return. We use principles of Modern Portfolio Theory (MPT), which quantifies risk as the variance and correlation among assets, to formalize diversification as an explicit strategy for managing risk in climate‐driven reserve design. We extend MPT to specify a framework that evaluates multiple conservation objectives, allows decision makers to balance management benefits and risk when preferences are contested or unknown, and includes additional decision options such as parcel divestment when evaluating candidate reserve designs. We apply an efficient search algorithm that optimizes portfolio design for large conservation problems and a game theoretic approach to evaluate portfolio trade‐offs that satisfy decision makers with divergent benefit and risk tolerances, or when a single decision maker cannot resolve their own preferences. Evaluating several risk profiles for a case study in South Carolina, our results suggest that a reserve design may be somewhat robust to differences in risk attitude but that budgets will likely be important determinants of conservation planning strategies, particularly when divestment is considered a viable alternative. We identify a possible fiscal threshold where adequate resources allow protecting a sufficiently diverse portfolio of habitats such that the risk of failing to achieve conservation objectives is considerably lower. For a range of sea‐level rise projections, conversion of habitat to open water (14–180%) and wetland loss (1–7%) are unable to be compensated under the current protected network. In contrast, optimal reserve design outcomes are predicted to ameliorate expected losses relative to current and future habitat protected under the existing conservation estate.

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Within the Big Bend region of the northeastern Gulf of Mexico, one of the least developed coastlines in the continental USA, intertidal and subtidal populations of eastern oyster Crassostrea virginica (hereafter referred to as "oyster") are a critical ecosystem and important economic constituent. We assessed trends in intertidal oyster populations, river discharge, and commercial fishing activity in the Suwannee River estuary within the Big Bend region using fisheries-independent data from irregular monitoring efforts and publicly available environmental data. We used generalized linear models to evaluate counts of oysters from line-transect surveys over time and space. We assessed model performance using simulation to understand potential bias and then evaluated whether these counts were related to freshwater inputs from the Suwannee River and commercial oyster fishing effort and landings at different time lags. We found that intertidal oyster counts have declined over time and that most of these declines are found in inshore intertidal oyster bars, which are becoming degraded. We also found a significant relationship between oyster counts and a 1-year lag on mean daily Suwannee River discharge, but including commercial fishery trips or landings did not improve model fit. It is unclear whether declines in intertidal oyster bars are offset by formation of new oyster reefs elsewhere. These results quantify rapid declines in intertidal oyster reefs in a region of coastline with high conservation value that can be used to inform ongoing and proposed restoration projects in the region.