Socio-Spatial Dynamics and Discrete Non-Linear Probabilistic Chains

Author(s):  
Michael Sonis ◽  
Dimitrios S. Dendrinos
Keyword(s):  
2021 ◽  
Author(s):  
Stephen C. L. Watson ◽  
Adrian C. Newton ◽  
Lucy E. Ridding ◽  
Paul M. Evans ◽  
Steven Brand ◽  
...  

Abstract Context Agricultural intensification is being widely pursued as a policy option to improve food security and human development. Yet, there is a need to understand the impact of agricultural intensification on the provision of multiple ecosystem services, and to evaluate the possible occurrence of tipping points. Objectives To quantify and assess the long-term spatial dynamics of ecosystem service (ES) provision in a landscape undergoing agricultural intensification at four time points 1930, 1950, 1980 and 2015. Determine if thresholds or tipping points in ES provision may have occurred and if there are any detectable impacts on economic development and employment. Methods We used the InVEST suite of software models together with a time series of historical land cover maps and an Input–Output model to evaluate these dynamics over an 85-year period in the county of Dorset, southern England. Results Results indicated that trends in ES were often non-linear, highlighting the potential for abrupt changes in ES provision to occur in response to slight changes in underlying drivers. Despite the fluctuations in provision of different ES, overall economic activity increased almost linearly during the study interval, in line with the increase in agricultural productivity. Conclusions Such non-linear thresholds in ES will need to be avoided in the future by approaches aiming to deliver sustainable agricultural intensification. A number of positive feedback mechanisms are identified that suggest these thresholds could be considered as tipping points. However, further research into these feedbacks is required to fully determine the occurrence of tipping points in agricultural systems.


2019 ◽  
Author(s):  
Chaitanya S. Gokhale ◽  
Hye Jin Park

AbstractSpatial dynamics can promote the evolution of cooperation. While dispersal processes have been studied in simple evolutionary games, real-world social dilemmas are much more complicated. The public good, in many cases, does not increase linearly as per the investment in it. When the investment is low, for example, every additional unit of the investment may help a lot to increase the public good, but the effect vanishes as the number of investments increase. Such non-linear behaviour is the norm rather than an exception in a variety of social as well as biological systems. We take into account the non-linearity in the payoffs of the public goods game as well as the natural demographic effects of population densities. Population density has also been shown to impact the evolution of co-operation. Coupling these non-linear games and population size effect together with an explicitly defined spatial structure brings us one step closer to the complexity of real eco-evolutionary spatial systems. We show how the non-linearity in payoffs, resulting in synergy or discounting of public goods can alter the effective rate of return on the cooperative investment. Synergy or discounting in public goods accumulation affects the resulting spatial structure, not just quantitatively but in some cases, drastically changing the outcomes. In cases where a linear payoff structure would lead to extinction, synergy can support the coexistence of cooperators and defectors. The combined eco-evolutionary trajectory can thus be qualitatively different in cases on non-linear social dilemmas.


1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)


Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér

1979 ◽  
Author(s):  
George W. Howe ◽  
James H. Dalton ◽  
Maurice J. Elias
Keyword(s):  

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