Curves

I teach biology. Which means that in an average workday I can be counted on to discuss properties of living things, ask students whether something we're talking about is alive, expound, as I frequently do, on why and how life requires energy input from outside the system, and generally utilize words rooted in the word "life" roughly bazillion times. I am good at this thing. And most of the time, I am good at staying with the immediate subject matter, even in my head. While I am talking of these things, my mind doesn't replay scenes or talk to me of how quickly alive can turn to not. Not that things like that don't happen to me anymore. They do, just not usually at work. Not, usually, triggered by work.

Except. Except every time I teach Intro, there is this one day, the Population Ecology day. The day I talk about survivorship curves. And the funny thing is, given that I just told you these things bring my life right into the classroom, funny thing is that I love survivorship curve day, and I love survivorship curves.

Even the whole tossed salad of personal and professional aside, I am sure such strong attachment to things inanimate is ever-so-slightly weird. It's ok, you can say it-- I can take it and I know you love me anyway. Yes, I fly my nerd flag at all times, but even I can appreciate that one might maybe, possibly, however unlikely that would be find it a bit out there to gush like that about a curve. You know, infinite number of points on a plane. But hear me out and see if you don't come to share my feelings, or at least appreciate them. So, without further ado, here they are, survivorship curves of Types I, II, and III.

They are also known as Late Loss, Constant Loss and Early Loss survivorship curves, respectively. Yes, ladies and gentlemen, the word loss, right there in the title. Imagine that, in a science classroom. And sure-- it's not there for the emotional meaning of the word, but for the very cut and dried actuarial one, but still-- it's there.

So what do these actually depict? Glad you asked, 'cause I am bursting to tell you. First of all, these are three different curves, superimposed for easy comparison. So each curve tells a story of what tends to happen to the young of a group of species. On the graph, the horizontal, x axis is essentially passing of time, usually in increments of age heading towards the highest possible for a species. The vertical axis simply marks numbers of individuals surviving. In each case, the curve starts in the top left corner with a number of individuals, all born at approximately the same time. We call that bunch of individuals a cohort.

So we can think about these curves as stories of what happens to a cohort. Starting from that highest point, and moving to the right, the curve shows the number of individuals from that starting cohort decreasing as time goes by. In other words, dying. We call these graphs survivorship curves because for any time point, its corresponding point on the curve shows how many from the cohort are still alive. 

So why, you might ask, are there three kinds of curves? Because, see, different species reproduce in different ways, and their young have different likelihood of surviving. Type III curve, for example, the Early Loss curve, that one describes species like fish, and frogs, and bugs, and plants. Finding Nemo notwithstanding, all of these species produce a lot of young, but do not tend to invest heavily in raising these young. If you've ever seen fish runs and results thereof (and here I mean fertilized fish eggs covering all sorts of underwater surfaces, and not layers of leftover fish sperm on the surface of the water), you know what I am talking about. Type II, Constant Loss curve, is usually the province of birds-- the kind of species where whether a predator gets you or not doesn't seem to depend too much on how old you are, just that you were in a wrong place at a wrong time.

Which brings us to the curve of type I, the Late Loss curve, the one about us. Us as a species, not us an individuals. Mammals tend to be described by that curve, as the kinds of species that have relatively few offspring at a time, but invest heavily in the care of those few offspring. So we feed our young, and provide them shelter, and, in at least one species of mammal, electronic devices as well. And toys, and clothes, and books, and playdates. The curve is called Late Loss because see, most individuals die in old or at least older age. Fish eggs are food for whoever cares to scoop some up, and grown fishes do much better, being mobile and all. Our curve is the opposite of that-- our young, in general, are fairly well protected, and it is individuals past their prime who tend to go. But that's in general, not for every individual, and the gentle incline of the first part of our curve testifies to that.

So do you see it yet? The reason why I love this curve? It is because when relatives and friends and the whole damned world have forgotten, the curve remembers. The curve, unlike people, doesn't pretend our children were never here. They are there, right there, in the curve itself, in the bend of it, in the gentle slope. They are all there-- those who died before labor ever started, those who didn't make it through birth, those whose parents had to make that awful choice in the NICU, and those whose parents where spared the choice, but not the outcome. SIDS babies are there too, and heart babies, and cancer babies. And just to the right-- older babies and toddlers, the two year olds who died in freak accidents; and farther yet teenagers who were killed by a drunk driver or a stray bullet, and those who tragically made the choices that resulted in their own deaths-- the drunk drivers who met trees head on and kids who squeezed the triggers one day, and ended up on the wrong end of a gun another. They are still and forever part of their respective cohorts, and so, in the bend of the curve that reflects their being no longer alive, they are there.

I don't say any of this to my students. I talk to them about science, not about grief. But that is what I see in survivorship curve of Type I-- oceans of human grief behind every itty-bitty fraction of a degree of incline of the curve. But I also see commonality. I see understanding. I see fellowship. We, who remain to love and to grieve, we recognize and support each other. Because while the world prefers to forget, we know how sadly many of us are there, and how, sadly, more join our ranks every day. And the curve, it knows too.

Do you have a curve of your own-- something in your professional or personal life that doesn't mean much to many others, but speaks to you about your experience? Do you feel fellowship with bereaved parents whose children died when they were older? What about people grieving other losses?