In what specific ways are economy and ecology linked? What are the outcomes of this linkage? What is/are the associated larger social significance(s)?

Economy and ecology are two disparate ideas that are intrinsically linked. To help with your understanding, I'll go through some key examples of how each impacts the other—but first, we'll look at them separately.
The economy is the sum total of industry, business, and financial actions with a country or group (this can be thought of as the global economy, national economy, or even a smaller subdivision). Ecology is the organization of the natural world in a region—the wildlife, flora, fauna, and environment such as climate. While these seem like separate concepts, they are intimately linked.
The economy impacts businesses and organizations, and these organizations make decisions that will ultimately impact the environment at large. For instance, let's use Duke Energy in North and South Carolina as an example. In the energy industry, Duke was attempting to cut corners and reduce costs, and instead of properly disposing of coal ash, the company decided to dump it in local lakes, rivers, ponds, and estuaries. This caused major contamination and has caused generational impacts on the ecology in those regions. A similar example would be BP and the oil spill they caused in the early 2000s.
Essentially, the economy will dictate an industry's actions by forcing them to decide on the most profitable actions. In many cases, it costs less money for a company to take detrimental action towards the environment and pay the associated fines than it costs to take the appropriate action in the first place.
A much more overarching example is carbon capture additions to smoke stacks and exhaust pipes on industrial facilities. Industrial facilities are encouraged to implement carbon-capturing devices onto their exhaust structures so as not to contribute excess pollution and increase the level of greenhouse gases in the atmosphere. However, for that company, it is prohibitively expensive to implement these devices (for instance, it is not uncommon for it to cost upwards of $500,000 to install all of the necessary devices at a large facility). If the associated fine for having emissions above acceptable levels is low enough in comparison (for instance, $100,000 every year the facility is above the acceptable level), the company may deem it worth it to pay the fine annually because they can afford to in the short run comparatively.
There are many ways the economy affects ecology, and its impact is far-reaching. It is imperative, therefore, that it becomes economically beneficial to take care of the environment, because only then will the economy encourage companies to care for the planet.