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Mathematical Representations – Definition & Methods

Grade 10
Aug 23, 2022

Mathematical Representations 


Interdependent relations in the ecosystem 

Because of the interaction between creatures of the same or different species and non-living (physical) aspects of the environment, ecosystems are always changing.  

Organisms in an ecosystem interact with one another in complicated feeding hierarchies of producers, consumers, and decomposers, which together form a food web in search of matter and energy supplies to maintain life. 

Mathematical representation 

Mathematics and computation are essential tools for expressing physical variables and their interactions in both science and engineering.  

They may be used to build simulations, statistically evaluate data, and identify, express, and apply quantitative relationships, among other things. 

Finding the average population in the ecosystem 

Counting all of the individuals in the environment is the most accurate technique to measure population size. However, when examining broad environments, this strategy is sometimes neither logistically nor economically practical. 


A variety of approaches can be utilized to determine the number and density of populations. The quadrat and mark-recapture procedures are two of the most significant.  

Finding the average population in the ecosystem-Quadrats method 

Quadrats can be used to measure population size and density in static creatures like plants, as well as very small and slow-moving species. Within the habitat, each quadrat differentiates a region of the same size, typically a square area.  

A quadrat can be formed by taking off an area with sticks and rope or by laying down a wood, plastic, or metal square. After establishing quadrats, researchers tally how many people are within each one’s limits. 

Multiple quadrat samples are taken at various random sites across the habitat, ensuring that the numbers observed are indicative of the environment as a whole. Finally, the information may be utilized to estimate population size and density throughout the whole ecosystem.  

Mathematical Representations

Finding the average population in the ecosystem-Mark Recapture method 

The mark-recapture method is commonly used to measure population numbers for creatures that move about, such as mammals, birds, and fish. This approach entails catching a group of animals and marking them in some way, such as with tags, bands, paint, or other marks on their bodies.  


The marked animals are then released back into the wild, where they can blend in with the rest of the population. A fresh sample is obtained afterwards. Some of the individuals in this fresh sample will be marked (recaptures), while others will be unmarked. Scientists can determine the entire population size by looking at the ratio of marked to unmarked individuals.  

It is founded on the idea that if a segment of the population was marked in some way, then returned to the original population, and then a second sample was collected after full mixing, the proportion of marked people in the second sample would be the same as in the overall population. 

Trends in biodiversity 

Across a wide variety of biodiversity indicators, present rates of loss are many orders of magnitude higher than in the past and show no signs of diminishing. Land use change, climate change, invasive species, overexploitation, and pollution are all contributing to a fast decline in biodiversity.  

Demographic, economic, societal, cultural, technological, and other indirect variables all contribute to this. While the impact of these causes varies by ecosystem and area, current trends show that biodiversity is continuing to decline.  

Percentage Change 1950–90 in Land Area of Biogeographic Realms Remaining in Natural Condition or under Cultivation and Pasture. 

Oceania and Antarctica are two biogeographic areas that have been left out owing to a lack of data. Since 1950, the quantity of land under agriculture and pasture in the Nearctic has been stable, with no net change in cover. 


Relationship between native habitat loss prior to 1950 and subsequent losses between 1950 and 1990. 

native habitat

Graphical comparison 

A comparison of the prevalence of various biodiversity threats and the extent to which they are described: 

  1. Graph for all systems.  
  1. Graph for marine systems. 
Graphical comparison


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