I am taking a course in Geography and often It seems to blame 'an exponential growth in the human population' for pretty much every environmental problem in the world. Some of the problems it associates with a growing population are that it:
Places pressure on natural resources
Leads to land degradation and destruction of the environment
Leads to greater production of waste, pollution and greenhouse gases
Accounts for the vast appropriation of surface water and groundwater
Leads to the intensification of farming thus soil erosion and pollution from chemical fertilisers and pesticides
Impacts on climate change and loss of biodiversity
Led to greater industrialisation due to higher demand and consumption
Intensifies inequalities in the world, between rich 'developed' countries and poorer 'developing' countries
Creates a problem for how to manage resources, deal with waste and provide food water and energy to the world population
We have talked about how capitalism is harmful to the environment - but at the same time annoyingly how it 'incentivises' people, creates 'innovation', 'efficiency' and new technologies 
- and we have also looked at inequalities in the 'developed and 'developing' world and the differences in population growth between them, but still 'overpopulation' is mostly blamed for all the problems.
I don't disagree with any of the above points and the course so far has made me much more aware of how we have drastically altered the entire planet. There is actually a theory that climate change began not with the industrial revolution, but with the development of agriculture and that if we had not cut down the forests and domesticated livestock the planet would have actually headed into another ice age a few thousand years ago.
http://en.wikipedia.org/wiki/Early_anthropocene
I still don't like though that the problem is often put down to there being 'too many humans on the planet' as its misanthropic and could result in reactionary policies or ideas about killing or allowing people to die because they are a burden, non-productive, inefficient and a strain on resources, and I have seen people (who ironically call themselves 'libertarians') argue that the poor should be left to die for those reasons and justifying poverty and famine as natures way of getting rid of all the non-productive people.
So I am just looking then for the libertarian communist perspective on population growth and the causes of the environmental crisis.
It's virtually always taught this way, substituting racialised population control politics for a critique of political economy...
On the early anthropocene hypothesis, my understanding is it's an interesting but unproven conjecture at this point. Apparently a lot of it comes down to a technical question of how best to align climatalogical datasets (see here).
On overpopulation, this has been a reactionary trope for over 200 years. Danny Dorling's Population 10 Billion is a good recent, fairly mainstream account that critiques Malthusian over-population theories along the way.
With climate and population specifically, population growth serves as a convenient fig leaf to obscure the imperative for capital to grow. For example, the IPCC reports talk about 'economic and population growth' (at least in the Summaries for Policy Makers, which is all anyone except a handful of specialists reads!). The problem with this conflation is that there's very different mechanisms driving population and economic growth: the exponential phase of a sigmoid demographic transition and the dynamics of capital accumulation, respectively. This conflation is often presented via the Kaya Identity:
The component 'population x GDP/person' includes economic activity as a mean per person. But as any stats 101 class will tell you, the arithmetic mean is a poor way to represent a highly skewed sample like economic income. Specifically, the places where population growth is highest usually have amongst the lowest GDPs per capita, greenhouse gas emissions, and so on. Whereas the states where population growth is lowest also tend to have the highest greenhouse gas emissions and GDPs per capita.
And if you zoom in within those countries and look at income distribution (as opposed to the mean of GDP/capita), then it's the activities of the rich and commercial activity etc contributing most to climate change. That said, focussing on consumption patterns, even of the rich, occludes the imperatives to economic growth and the structural imperatives to treating the environment as a disposable 'externality'.
So behind the rather innocuous looking arithmetic of the Kaya Identity, the imperative for capitalist growth is occluded by a misleading focus on (anyhow decelerating) population growth. It's a convenient way for the predominantly rich white dudes on the boards of major multinationals to pin responsibility for climate change, environmental destruction etc on supposedly prolifically pregnant impoverished black and brown women in the former colonies, the housing projects, and the prisons.
Out of the Woods' blogs have touched on this. See the section 'population is not the problem' here, and the section on 'absolute scarcity' here.
Edit: I haven't read it myself, but ecosocialist Ian Angus has co-authored a book called 'Too many people?' which is meant to be a socialist critique of overpopulation theories.