Tuesday, April 2, 2013

Aphid Math

Ahhh Spring. It’s that time of year when the greenhouse gardener’s thoughts and dreams turn to … aphids. 

Specifically, to how to make them go away. 

Based on my research, the spring aphids that are congregating on my radish leaves and broccoli seedlings are probably green peach aphids, even though they are not green. Whitney Cranshaw states in Garden Insects of North America that this aphid is “one of the most commonly damaging aphids of greenhouse crops.” I have questions about Cranshaw’s syntax (What do you think? Should “commonly” modify “damaging,” or should “common” modify “damaging insects”) but none at all regarding his entomological prowess. I will accept that my brown aphids are really green. If Whitney C. says so.

Note the ghosts of aphids past.
I got very excited seeing ghostly, leggy forms scattered among the plump marauders. The lacewing eggs I scattered two months ago must be hatching (!), I thought, and tiny lacewings are sucking the sweet life out of the plant suckers. But no. Between birth and adulthood, which takes all of 8 days, the aphids molt four times. The white forms are the skins they’ve shed along the way.

The thing about aphids is, if you miss them early on, your crop is doomed, your ship has sunk. Embryos start forming in their grandmother, making it possible for an adult female to give birth to as many as a dozen live nymphs a day. (1) Count it up: that’s 84 a week. From a single aphid. Meanwhile all those babies are shedding and maturing and, by the end of the week, having live babies of their own. I will leave it to the mathematician to calculate a sum total after a month of unchecked reproduction, should you miss that initial batch of a dozen or so aphids. 

Trust me: It is a big, big number.

And this is why, when the box of 4500 Asian ladybugs (Hippodamia convergens) arrived at my door late Friday afternoon, I rushed right over to the greenhouses to release them. No, these are not the same Asian ladybugs that enter your house in winter and crawl around on your windows and walls, in case you were wondering. Those are Harmonia axyridis. They look very similar, but they’re not the same. According to Whitney C. 

Prey is multitudinous. And conveniently slow!
I watered the greenhouses well, and tenderly situated my new allies in protected places. I nestled them among the carrot foliage and gave them shelter beneath broad leaves of chard, I gently shook a few out of the bag to populate the weeds along the greenhouse edges and rested others in the dried remains of last fall’s nasturtium vines. The next day, Easter Sunday, was cloudy and rainy—perfect for rest and recuperation after a 2-day journey from Arizona, cramped 281 (give or take a few) per cubic inch. 

On Monday (I am making an assumption here) they reveled in the bounty. What ladybug would not be thrilled to come upon a batch of tender, newly hatched, sap-sucking insects. What ladybug would not get right to work consuming their quota of about 22 aphids a day. After all—and this is a fact—unless she eats aphids, she will not lay sticky bunches of yellow eggs that, in a little over a month, will become hungry larvae. A built-in mechanism causes the developing eggs to be reabsorbed into her body unless there is a proper food supply about.(1) How civilized. 

But, assuming that aphids abound (which they do, in an April greenhouse that has been kept above freezing all winter), what happens next is a thrilling thought to one who wakes up to dreams of hoards of hungry sucking beasts destroying crops of baby bok choy: When the ladybug larva emerges from the yellow egg and encounters an aphid, it bites a hole in the body and sucks out the contents. Then it pumps the liquid back into the body and sucks it out several times to effectively mix the innards of their victim with digestive juices.(2) The mere thought makes my sleep more restful. 

Grey cabbage aphids like the cool weather of fall.
As a gardener, it’s difficult not to think in terms of the good, the bad, and the ugly. It’s easy to presume that one is winning the game, that ladybugs will solve the problem (and my, aren’t we clever). The truth, however, is far more intricate. The grey cabbage aphids of fall are still hanging about in small clumps here and there, waiting. Waiting for the tides to turn, waiting for the savoy cabbage to make an appearance, so that they can take instant advantage of its protective crinkles and give almost immediate birth to practically countless young who will keep the cycle alive. I will refrain from planting brassicas in certain problem areas in spring. I will put distance between the consumer and its favorite food. It may work. It may not.

As savvy as I think I am with my ladybugs and my strategic planting plan, my means are primitive in comparison to those of the tiny aphid, whose hollow stylus, thinner than a human hair, both pierces and sucks; who comes equipped with exudation tubes that drip sweet honeydew so rich in sugars that ants will protect the exuders so as to keep the tap flowing; whose generation time can be a mere 10 days, which allows them to adapt and evolve as circumstances change. Who does not give birth unless there is an adequate food supply. Who (unlike us, who must eat carrots and yams) can produce its own carotenoids! (3)

"Treating your adversary with respect is giving him an advantage to which he is not entitled," said poet, writer, and moralist  Samuel Johnson. I disagree. The mighty aphid is deserving of respect. 

Awe, even.

(1) http://online.sfsu.edu/bholzman/courses/Fall99Projects/ladybug.htm
(2) http://faculty.ucr.edu/~legneref/identify/ladybird.htm
(3) http://www.nsf.gov/news/news_summ.jsp?cntn_id=116842 


  1. Aphid Math, simplified...

    For simplicity's sake, we can assume an initial aphid population (Generation 0) of 10. We can assume that each aphid produces 10 nymphs per day, each nymph takes 7 days to be able to reproduce, and will then have a reproductive lifespan of 10 days.

    Assuming Gen0 is ready to reproduce on day 1 of the month, your 10 Gen0 aphids will yield 100 nymphs on day 1, 100 more on day 2, day 3, and so on up through day 10, when their reproductive lifespan is over. These nymphs are members of Gen1. Gen1 = 10 x 10 x 10, or 10^3

    The 100 Gen1 nymphs born on day 1 will each be ready to reproduce beginning on day 8, reach their height of reproduction on day 17 (when the Gen1 nymphs born on day 10 are ready to start reproducing), and fizzle out after day 26 (when the last-born Gen1 nymphs reach the end of their reproductive capabilities). All told, each of the 1,000 Gen1 aphids will make 10 nymphs per day over the course of her own 10-day reproductive cycle. So, Gen2 = 1,000 x 10 x 10, or 10^5.

    Gen2 will begin reproducing on day 15, and not fizzle until after day 42, so we can't count any aphid born after day 30. Gen3 begins reproducing on day 22, and Gen 4 on day 29.

    It gets a bit complicated (Wait, didn't I say simplified? Sorry.), but by day 30 you have Gen2 at the height of their reproduction, Gen3 getting into the swing of things, and Gen4 just starting out. With all these aphids reproducing, over 22 million nymphs would be born on day 30 alone.

    By now, of course, those Gen0 and Gen1 aphids will have begun dying off, but their numbers are so tiny in comparison that the loss is negligible.

    All told (and I have the spreadsheet to back it up), I find that the total aphid population after day 30 will be about 62 million.

    You might need a few more of those ladybugs.