Donald Ludwig

LIKELIHOOD OF ANCESTOR STATES IN ADAPTIVE RADIATION

Theories of ecological diversification make predictions about the timing and ordering of character state changes through history. These theories are testable by “reconstructing” ancestor states using phylogenetic trees and measurements of contemporary species. Here we use maximum likelihood to estimate and evaluate the accuracy of ancestor reconstructions. We present likelihoods of discrete ancestor states and derive probability distributions for continuous ancestral traits. The methods are applied to several examples: diets of ancestral Darwins finches; origin of inquilinism in gall wasps; microhabitat partitioning and body size evolution in scrubwrens; digestive enzyme evolution in artiodactyl mammals; origin of a sexually selected male trait, the sword, in platies and swordtails; and evolution of specialization in Anolis lizards. When changes between discrete character states are rare, the maximum‐likelihood results are similar to parsimony estimates. In this case the accuracy of estimates is often high, with the exception of some nodes deep in the tree. If change is frequent then reconstructions are highly uncertain, especially of distant ancestors. Ancestor states for continuous traits are typically highly uncertain. We conclude that measures of uncertainty are useful and should always be provided, despite simplistic assumptions about the probabilistic models that underlie them. If uncertainty is too high, reconstruction should be abandoned in favor of approaches that fit different models of trait evolution to species data and phylogenetic trees, taking into account the range of ancestor states permitted by the data.

MANAGEMENT OF EUTROPHICATION FOR LAKES SUBJECT TO POTENTIALLY IRREVERSIBLE CHANGE

We analyzed management policies for ecosystems subject to alternate states, thresholds, and irreversible changes. We focused on the problem of lake eutrophication by excessive phosphorus (P) input. Eutrophic lakes may be classified, with respect to their response to reduced P input alone, as reversible (recovery is immediate and proportional to the reduction in P input), hysteretic (recovery requires extreme reductions in P input for a period of time), or irreversible (recovery cannot be accomplished by reducing P input alone). A model with one state variable and one control variable describes the responses of lake trophic state to changes in P input and other management interventions. Activities that generate P input to the lake are assumed to create profits, while the value of ecosystem services provided by the lake declines at high P levels. We then calculated P input policies that maximize the discounted net benefits from polluting activities and ecosystem services. If “optimality” is defined as maxim...

Size and Timing of Metamorphosis in Complex Life Cycles: Time Constraints and Variation

Complex life cycles are characterized by niche shifts at the time of metamorphosis. Current models predict optimal sizes for metamorphosis based on maximizing growth, minimizing mortality, or some balance of these goals. These models predict optimal sizes that are independent of the time of metamorphosis. Reproduction and other major events in the life history of organisms are often constrained to seasons, and the state (e.g., mass) of the organism at that time is related to fitness. Therefore, an organisms state as well as the time that that state is achieved are central variables in these time—constrained life histories. We extend earlier theory to include explicit time constraints in three, hypothetical, complex life cycles. Dynamic optimization models are constructed to determine optimal time and mass trajectories for niche shifts. First, we consider the habitat shift at emergence in mayflies, where reproduction terminates a growth period in the first habitat and is constrained to a season. Second, we consider the habitat shift at metamorphosis in amphibians, where reproduction terminates a growth phase in the second habitat and reproduction is constrained to a single point in time. Third, we combine the first two effects to allow an extended period of reproduction in amphibians. Here optimal time and mass trajectories are determined for two niche shifts–the shift from aquatic to terrestrial habitat and the shift from a growth phase to a reproductive phase. We present analytical theory that allows both quantitative and qualitative predictions. Problem constructions and solutions are presented graphically to aid intuition in interpreting our results and extending the framework to other parameter values and other life—history examples. The general conclusion is that time constraints on complex life histories lead to optimal sizes for niche shifts that vary with time. In time—constrained life histories, any variation in the state of individuals at some time prior to reproduction will be preserved to some degree at reproduction. Therefore, in time—constrained life histories, we expect optimal switches in habitat use or life history stage to depend not only on state but also on the time that state is achieved.

The Era of Management Is Over

The management paradigm fails when confronted with complex problems where there are no clearly defined objectives and a plethora of mutually contradictory approaches, each of which is plausible in a particular frame of reference. The notion of the disinterested expert cannot withstand scrutiny, and putative experts must earn public trust. Scientists must be prepared to share their advisory and decision-making roles with a variety of interested parties and participate with them on an equal footing.

IS IT MEANINGFUL TO ESTIMATE A PROBABILITY OF EXTINCTION

I calculate probabilities of quasi-extinction of natural populations from time series of census data or estimated abundance. The results depend sensitively upon estimated parameters. Short time series or poor fits of the model to data lead to wide confidence intervals for the probability of quasi-extinction. In many cases there are substantial errors in estimated abundance. These errors further increase the size of the confidence interval, to the point where the estimates may become meaningless. A further complication is that natural populations are subject to occasional catastrophes, and these increase the probability of extinction. Unfortunately, evidence concerning the frequency of occurrence of catastrophes and the distribution of their sizes is generally lacking. Assessments that fail to compute confidence intervals or that disregard observation errors or possible catastrophes may be unduly optimistic about the viability of natural populations.

Life-History Strategies for Energy Gain and Predator Avoidance Under Time Constraints

Short-term foraging behavior is typically influenced by the needs to obtain food at a high rate and to avoid predation. There is increasing evidence that the need to balance these conflicting demands plays a role in ontogenetic habitat shifts, including the spectacular shifts characteristic of complex life cycles. Previous theory has led to rules that are independent of time to predict the size at which habitat shifts take place. We develop a model that incorporates time constraints, by assuming that reproduction or some other major event, such as diapause or metamorphosis, must occur by a specified time or date. We incorporate recent formulations of dynamic programming that allow strategies to balance conflicting behaviors by expressing them in the common currency of future reproductive output. The resulting theory predicts optimal strategies for pre-reproductive habitat shifts that depend on both time and body weight. Our theory, although derived from a single set of assumptions, leads to a synthesis of insights gained from a diversity of previous dynamic optimization problems.

Time, condition, and the seasonal decline of avian clutch size

A seasonal decline in clutch size is typical of bird populations. This phenomenon may result from a conflict between the advantages of early breeding (greater offspring value) and the advantages of delay (greater accumulated condition and hence clutch size). We construct a dynamic model for adaptive seasonal decline in clutch size on the basis of these premises. The model requires a small number of well-supported assumptions; it is formulated and analyzed in both analytical and graphical forms. We outline some novel predictions and suggest tests of our conclusions. Initial comparisons of our predictions with results available from wild birds in the field are favorable. We briefly extend the model to consider the evolution of multiple clutches within a season and the effects of between-season costs of reproduction. Although this work focuses on avian clutch size, the analysis provides a general framework for studies of conditiondependent transitions in life histories. Such transitions between stages (e.g., maturation, metamorpbosis, or reproduction) characterize the ontogeny of organisms. We expect that such conflicts between the advantages of early and late transitions are common to life-history decisions

Stability, regulation, and the determination of abundance in an insular song sparrow population

The population dynamics of the Song Sparrow, Melospiza melodia, were studied for 15 yr on Mandarte Island, in southwestern British Columbia, Canada. This population exhibited a high median density (7.8 females/ha) and fluctuated strongly (10—fold or more) from year to year. The population received few successful immigrants, even at low densities, and its dynamics were thus driven by local events. Two strong density—dependent regulating mechanisms were detected. First, reproductive output was strongly depressed at high densities because of an increased rate of nest failure and a decline in mean clutch size. Greater nest failure at high density was due to increased predation on eggs and nestlings. Nest failure increased with the rate of nest parasitism by Brown—headed Cowbirds (Molothrus ater) and was lowest when cowbirds were absent from Mandarte, suggesting that cowbirds either cause or facilitate nest failure. Second, the rate of juvenile recruitment was inversely related to the density of adults, becaus...

Uncertainty and the Assessment of Extinction Probabilities

A proper assessment of the probability of early collapse or extinction of a population requires consideration of our uncertainty about crucial parameters and processes. Simple simulation approaches to assessment consider only a single set of parameter values, but what is required is consideration of all more or less plausible combinations of parameters. Bayesian decision theory is an appropriate tool for such assessment. I contrast standard (frequentist) and Bayesian approaches to a simple regression problem. I use these results to calculate the probability of early population collapse for three data sets relating to the Palila, Laysan Finch, and Snow Goose. The Bayesian results imply much higher risk of early collapse than maximum likelihood methods. This difference is due to large probabilities of early collapse for certain parameter values that are plausible in light of the data. Because of simplifying assumptions, these results are not directly applicable to assessment. Nevertheless they imply that maximum likelihood and similar methods based upon point parameter estimates will grossly underestimate the risk of early collapse.

Limitations of Economic Valuation of Ecosystems

Valuation methods have been prominent in recent discussions because they are being used in legal efforts to protect and restore ecosystems (Portney1994). Such methods also seem to be a promising way to include ecological values when various public policies and projects are under consideration. Economic valuations may have quite perverse and pernicious effects unless they are applied with a careful regard for their limitations. I believe that, in fact, the proper domain of application of such methods is quite limited. Such methods work well for small projects of minor importance, or possibly for fine-tuning of larger projects. But these methods-and economic methods in general-are inappropriate and harmful when used to determine important public policies. There is a large literature on economics and the environment. The following are some of my favorite works. They offer some discussion of the underlying issues rather than attempting to offer a theory or methods that must be accepted holus-bolus. Goulder and Kennedy (1997) examine some of the philosophical issues that underlie application of economic methods. A deeper and more devastating critique was given by Gunnar Myrdal (1953). I urge everyone to read these works. Some of the ideology that underlies much economic thought is discussed by Bromley (1990) and Galbraith (1992). Comprehensive expositions of the issues involved in environmental economics are provided by Cooper (1981) and Common (1995). Both of these authors go to great pains to explain economic assumptions and discuss their validity. More polemical works are Sagoff (1988) and Brown (1991). Portney(1994) is an economist writing for other economists about the significance of the issue of economic valuation. This work is quite accessible. My main objections to valuation are: