THE MINNESOTA FARM REAL ESTATE MARKET IN 1961

Land Economics/Use,

THE MINNESOTA FARM REAL ESTATE MARKET IN 1958

Land Economics/Use,

THE MINNESOTA FARM REAL ESTATE MARKET IN 1957

Land Economics/Use,

A soluble model of evolution and extinction dynamics in a rugged fitness landscape

We consider a continuum version of a previously introduced and numerically studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve by an optimization process in a rugged fitness landscape and die due to their competitive interactions. We first formulate dynamical equations for the fitness distribution and the survival probability. Secondly we analytically derive the $t^{-2}$ law which characterizes the life time distribution of biological genera. Thirdly we discuss other dynamical properties of the model such as the rate of extinction and conclude with a brief discussion.Comment: 6 pages LaTeX source with 2 figures. Submitted to PRL (Jan. 97

Mechanical basis of morphogenesis and convergent evolution of spiny seashells

Convergent evolution is a phenomenon whereby similar traits evolved independently in not closely related species, and is often interpreted in functional terms. Spines in mollusk seashells are classically interpreted as having repeatedly evolved as a defense in response to shell-crushing predators. Here we consider the morphogenetic process that shapes these structures and underlies their repeated emergence. We develop a mathematical model for spine morphogenesis based on the mechanical interaction between the secreting mantle edge and the calcified shell edge to which the mantle adheres during shell growth. It is demonstrated that a large diversity of spine structures can be accounted for through small variations in control parameters of this natural mechanical process. This physical mechanism suggests that convergent evolution of spines can be understood through a generic morphogenetic process, and provides unique perspectives in understanding the phenotypic evolution of this second largest phylum in the animal kingdom.\ud \ud Homoplasy, the appearance of similar traits in separate evolutionary lineages as a result of convergence, parallelism, or evolutionary reversals, is a major concern in phylogenetic analysis for which it is viewed as noise. However, over the past two decades, homoplasy has also become a subject of increasing interest, stimulated by the rise of evolutionary developmental biology (evo devo) and the wish to uncover the developmental basis of this phenomenon (1⇓–3). Spines constitute the most prominent ornamentation of mollusk shells and have evolved in many distantly related fossil and current mollusk species (at least 55 genera and 21 families of current gastropods; 10 genera and 8 families of current bivalves; 11 genera and 8 families of ammonoids; and 6 fossil nautiloid genera; see Fig. 1 for examples). Convergent evolution of spines in mollusks has been addressed in functional terms, these structures being interpreted as having evolved as a defense in response to shell-crushing predators (4⇓–6). This hypothesis is itself the basis of the widely cited “escalation hypothesis,” according to which long-term trends in the fossil record were caused by the evolutionary response of prey to predation pressure (7). The idea that convergent evolution of similar mollusk ornamentations might be fully explained in functional terms is based on the premise that similar characters, perceived as well designed for a presumed function, cannot conceivably have independently evolved fortuitously. Therefore, natural selection is thought to have repeatedly shaped similar functional traits out of random variations

Extremal dynamics on complex networks: Analytic solutions

The Bak-Sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks. By using the rate equation and the random walk approaches, we obtain the analytic solution of the fitness threshold $x_c$ to be 1/(_f+1), where _f=/ (=) in the quenched (annealed) updating case, where is the n-th moment of the degree distribution. Thus, the threshold is zero (finite) for the degree exponent \gamma 3) for the quenched case in the thermodynamic limit. The theoretical value x_c fits well to the numerical simulation data in the annealed case only. Avalanche size, defined as the duration of successive mutations below the threshold, exhibits a critical behavior as its distribution follows a power law, P_a(s) ~ s^{-3/2}.Comment: 6 pages, 2 figure

Survival and selection biases in early animal evolution and a source of systematic overestimation in molecular clocks

Important evolutionary events such as the Cambrian Explosion have inspired many attempts at explanation: why do they happen when they do? What shapes them, and why do they eventually come to an end? However, much less attention has been paid to the idea of a ‘null hypothesis’—that certain features of such diversifications arise simply through their statistical structure. Such statistical features also appear to influence our perception of the timing of these events. Here, we show in particular that study of unusually large clades leads to systematic overestimates of clade ages from some types of molecular clocks, and that the size of this effect may be enough to account for the puzzling mismatches seen between these molecular clocks and the fossil record. Our analysis of the fossil record of the late Ediacaran to Cambrian suggests that it is likely to be recording a true evolutionary radiation of the bilaterians at this time, and that explanations involving various sorts of cryptic origins for the bilaterians do not seem to be necessary

The fossil record of early tetrapods: worker effort and the end-Permian mass extinction

It is important to understand the quality of the fossil record of early tetrapods (Tetrapoda, minus Lissamphibia and Amniota) because of their key role in the transition of vertebrates from water to land, their dominance of terrestrial faunas for over 100 million years of the late Palaeozoic and earlyMesozoic, and their variable fates during the end−Permian mass extinction. The first description of an early tetrapod dates back to 1824, and since then discoveries have occurred at a rather irregular pace, with peaks and troughs corresponding to some of the vicissitudes of human history through the past two centuries. As expected, the record is dominated by the well−sampled sedimentary basins of Europe and North America, but finds from other continents are increasing rapidly. Comparisons of snapshots of knowledge in 1900, 1950, and 2000 show that discovery of new species has changed the shape of the species−level diversification curve, contrary to earlier studies of family−level taxa. There is, however, little evidence that taxon counts relate to research effort (as counted by numbers of publications), and there are no biasing effects associated with differential study of different time intervals through the late Palaeozoic and Mesozoic. In fact, levels of effort are apparently not related to geological time, with no evidence that workers have spent more time on more recent parts of the record. In particular, the end−Permian mass extinction was investigated to determine whether diversity changes through that interval might reflect worker effort: it turns out that most records of early tetrapod taxa (when corrected for duration of geological series) occur in the Lower Triassic

Branching Processes and Evolution at the Ends of a Food Chain

In a critically self--organized model of punctuated equilibrium, boundaries determine peculiar scaling of the size distribution of evolutionary avalanches. This is derived by an inhomogeneous generalization of standard branching processes, extending previous mean field descriptions and yielding $\nu=1/2$ together with $\tau'=7/4$, as distribution exponent of avalanches starting from species at the ends of a food chain. For the nearest neighbor chain one obtains numerically $\tau'=1.25 \pm 0.01$, and $\tau'_{first}=1.35 \pm 0.01$ for the first return times of activity, again distinct from bulk exponents.Comment: REVTex file, 12 pages, 2 figures in eps-files uuencoded, psfig.st

Schumpeterian economic dynamics as a quantifiable minimum model of evolution

We propose a simple quantitative model of Schumpeterian economic dynamics. New goods and services are endogenously produced through combinations of existing goods. As soon as new goods enter the market they may compete against already existing goods, in other words new products can have destructive effects on existing goods. As a result of this competition mechanism existing goods may be driven out from the market - often causing cascades of secondary defects (Schumpeterian gales of destruction). The model leads to a generic dynamics characterized by phases of relative economic stability followed by phases of massive restructuring of markets - which could be interpreted as Schumpeterian business `cycles'. Model timeseries of product diversity and productivity reproduce several stylized facts of economics timeseries on long timescales such as GDP or business failures, including non-Gaussian fat tailed distributions, volatility clustering etc. The model is phrased in an open, non-equilibrium setup which can be understood as a self organized critical system. Its diversity dynamics can be understood by the time-varying topology of the active production networks.Comment: 21 pages, 11 figure