Restoration Ecology: Two-Sex Dynamics and Cost Minimization

We model a spatially detailed, two-sex population dynamics, to study the cost of ecological restoration. We assume that cost is proportional to the number of individuals introduced into a large habitat. We treat dispersal as homogeneous diffusion. The local population dynamics depends on sex ratio at birth, and allows mortality rates to differ between sexes. Furthermore, local density dependence induces a strong Allee effect, implying that the initial population must be sufficiently large to avert rapid extinction. We address three different initial spatial distributions for the introduced individuals; for each we minimize the associated cost, constrained by the requirement that the species must be restored throughout the habitat. First, we consider spatially inhomogeneous, unstable stationary solutions of the model's equations as plausible candidates for small restoration cost. Second, we use numerical simulations to find the smallest cluster size, enclosing a spatially homogeneous population density, that minimizes the cost of assured restoration. Finally, by employing simulated annealing, we minimize restoration cost among all possible initial spatial distributions of females and males. For biased sex ratios, or for a significant between-sex difference in mortality, we find that sex-specific spatial distributions minimize the cost. But as long as the sex ratio maximizes the local equilibrium density for given mortality rates, a common homogeneous distribution for both sexes that spans a critical distance yields a similarly low cost

Fisher Waves and Front Roughening in a Two-Species Invasion Model with Preemptive Competition

We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits power-law dependence on the difference between the two species' clonal propagation rates (key ecological parameters). The mean-field approximation behaves similarly, but the power law's exponent slightly differs from the individual-based model's result. We also study roughening of the front, using the framework of non-equilibrium interface growth. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, this finding implies, and is also confirmed by simulations, that the temporal correction to the asymptotic front velocity is of ${\cal O}(t^{-2/3})$.Comment: 8 pages, 5 figures; Papers on related work can be found at http://www.rpi.edu/~korniss/Researc

Metabolic state alters economic decision making under risk in humans

Background: Animals' attitudes to risk are profoundly influenced by metabolic state (hunger and baseline energy stores). Specifically, animals often express a preference for risky (more variable) food sources when below a metabolic reference point (hungry), and safe (less variable) food sources when sated. Circulating hormones report the status of energy reserves and acute nutrient intake to widespread targets in the central nervous system that regulate feeding behaviour, including brain regions strongly implicated in risk and reward based decision-making in humans. Despite this, physiological influences per se have not been considered previously to influence economic decisions in humans. We hypothesised that baseline metabolic reserves and alterations in metabolic state would systematically modulate decision-making and financial risk-taking in humans. Methodology/Principal Findings: We used a controlled feeding manipulation and assayed decision-making preferences across different metabolic states following a meal. To elicit risk-preference, we presented a sequence of 200 paired lotteries, subjects' task being to select their preferred option from each pair. We also measured prandial suppression of circulating acyl-ghrelin (a centrally-acting orexigenic hormone signalling acute nutrient intake), and circulating leptin levels (providing an assay of energy reserves). We show both immediate and delayed effects on risky decision-making following a meal, and that these changes correlate with an individual's baseline leptin and changes in acyl-ghrelin levels respectively. Conclusions/Significance: We show that human risk preferences are exquisitely sensitive to current metabolic state, in a direction consistent with ecological models of feeding behaviour but not predicted by normative economic theory. These substantive effects of state changes on economic decisions perhaps reflect shared evolutionarily conserved neurobiological mechanisms. We suggest that this sensitivity in human risk-preference to current metabolic state has significant implications for both real-world economic transactions and for aberrant decision-making in eating disorders and obesity

Elevated arousal at time of decision-making is not the arbiter of risk avoidance in chickens

The somatic marker hypothesis proposes that humans recall previously experienced physiological responses to aid decision-making under uncertainty. However, little is known about the mechanisms used by non-human animals to integrate risk perception with predicted gains and losses. We monitored the behaviour and physiology of chickens when the choice between a high-gain (large food quantity), high-risk (1 in 4 probability of receiving an air-puff) option (HGRAP) or a low-gain (small food quantity), no-risk (of an air-puff) (LGNAP) option. We assessed when arousal increased by considering different stages of the decision-making process (baseline, viewing, anticipation, reward periods) and investigated whether autonomic responses influenced choice outcome both immediately and in the subsequent trial. Chickens were faster to choose and their heart-rate significantly increased between the viewing and anticipation (post-decision, pre-outcome) periods when selecting the HGRAP option. This suggests that they responded physiologically to the impending risk. Additionally, arousal was greater following a HGRAP choice that resulted in an air-puff, but this did not deter chickens from subsequently choosing HGRAP. In contrast to human studies, we did not find evidence that somatic markers were activated during the viewing period, suggesting that arousal is not a good measure of avoidance in non-human animals

Control of primary productivity and the significance of photosynthetic bacteria in a meromictic kettle lake.

During 1986 planktonic primary production and controlling factors were investigated in a small (A0 = 11.8 · 103 m2, Zmax = 11.5 m) meromictic kettle lake (Mittlerer Buchensee). Annual phytoplankton productivity was estimated to ca 120 gC · m–2 · a–1 (1,42 tC · lake–1 · a–1). The marked thermal stratification of the lake led to irregular vertical distributions of chlorophylla concentrations (Chla) and, to a minor extent, of photosynthesis (Az). Between the depths of 0 to 6 m low Chla concentrations (< 7 mg · m–3) and comparatively high background light attenuation (kw = 0,525 m–1, 77% of total attenuation due to gelbstoff and abioseston) was found. As a consequence, light absorption by algae was low (mean value 17,4%) and self-shading was absent. Because of the small seasonal variation of Chla concentrations, no significant correlation between Chla and areal photosynthesis (A) was observed. Only in early summer (June–July) biomass appears to influence the vertical distribution of photosynthesis on a bigger scale. Around 8 m depth, low-light adapted algae and phototrophic bacteria formed dense layers. Due to low ambient irradiances, the contribution of these organisms to total primary productivity was small. Primary production and incident irradiance were significantly correlated with each other (r2 = 0.68). Although the maximum assimilation number (Popt) showed a clear dependence upon water temperature (Q10 = 2.31), the latter was of minor importance to areal photosynthesis

Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a "roughened" front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner's relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front's mean position. We find that a class of models with different assumptions about neighborhood interactions exhibit universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.Comment: The original publication is available at www.springerlink.com/content/8528v8563r7u2742

The effect of fight cost structure on fighting behaviour

A common feature of animal populations is the stealing by animals of resources such as food from other animals. This has previously been the subject of a range of modelling approaches, one of which is the so called "producer-scrounger" model. In this model a producer finds a resource that takes some time to be consumed, and some time later a (generally) conspecific scrounger discovers the producer with its resource and potentially attempts to steal it. In this paper we consider a variant of this scenario where each individual can choose to invest an amount of energy into this contest, and the level of investment of each individual determines the probability of it winning the contest, but also the additional cost it has to bear. We analyse the model for a specific set of cost functions and maximum investment levels and show how the evolutionarily stable behaviour depends upon them. In particular we see that for high levels of maximum investment, the producer keeps the resource without a fight for concave cost functions, but for convex functions the scrounger obtains the resource (albeit at some cost)