Spread betting hedging plants
- 02.03.2022
- Milkis
- 0.00001441 btc
- 0
Therefore, in the limit of small switching rates of the environment, the bet-hedging region is wider in the spatially varying case than in the temporally varying case. In the opposite limit of high rates of environmental switch, the function to be optimized is linear, and the optimal strategy is a pure strategy, i.
This conclusion holds both for temporally and spatially varying environments. Discussion Understanding the precise mechanisms of population expansions is of utmost importance, not only for understanding species diversity, but also to cope with invasive species in new habitats [ 20 — 23 ], bacterial infections [ 24 — 26 , 73 ], and cell migration, such as those occurring during tissue renewal or cancer metastasis [ 5 ].
Phenotypic diversity is a convenient strategy for the success of population expansions in a broad range of contexts [ 20 — 26 ]. Although precise experimental measures are not easy to obtain, a recent study shows that populations with increased variability in individual risk-taking can colonize wider ranges of territories [ 74 ].
In this work, we proposed a general mathematical and computational framework to analyze such scenarios. In particular, we introduced a population model with diverse phenotypes that perform differently depending on the type of environment.
We found that, contrarily to the well-mixed case, bet-hedging can be convenient in expanding populations. This result complements the study in [ 53 ] for a fixed habitat and supports the view that diversification is of broad importance for spatially-structured populations. For environments varying slowly in time, the expansion is relatively slow, and diverse communities can be optimal depending on the parameters.
On the contrary, for fast environmental changes, the optimal population always adopts a unique strategy. A remarkable outcome of our analysis is that spatial fluctuations create more opportunities for bet-hedging than temporal fluctuations, in that the region of parameter space where the optimal population is diverse, is always larger in the former case. One intuitive explanation is that in the case of spatial fluctuations, the population spends less time traversing favorable patches than adverse ones.
This means that the beneficial effect of favorable patches is reduced with respect to the case of temporal fluctuations. Therefore, a pure risky strategy is less efficient in the case of spatial variability and can be more easily outcompeted by a diversified bet-hedging strategy.
The framework presented here can be extended to accommodate other scenarios. We have assumed that the fraction of individuals adopting each phenotype is fixed by the phenotypic switching rates. Another potentially relevant extension would be to consider two-dimensional habitats.
Although the classic theory for Fisher waves [ 7 , 8 ] is unaffected in higher dimensions, in the presence of spatial heterogeneity the front shape can become anisotropic, potentially affecting the results.
Similarly, it would be interesting to analyze the combined effect of spatial and temporal variability. We also limited ourselves to the case where the different environments affect individual growth rates, whereas in general, one could also expect them to have an effect on motility [ 14 , 15 , 75 — 77 ], opening the way for different forms of bet-hedging. Finally, the present study was limited to pulled waves. It would be interesting to study the effect of bet-hedging on pushed waves, for example to describe population expansion in the presence of an Allee effect [ 78 , 79 ].
It would be also interesting to experimentally test our results. Experiments of expanding bacterial colonies in non-homogeneous environments have already been performed and shed light, for example, on the evolution of antibiotic resistance in spatially-structured populations [ 80 ]. In reality, the varying weather presents a risk, primarily from precipitation and temperatures that deviates from the average.
So, the first thing to consider is just how variable is the precip and temperature at your location for your cover crop growing window? This variability can be evaluated using a statistical calculation called the standard deviation 1. Those locations that are more likely to have rainfall close to average will have a low standard deviation gray curve below. Where rainfall is more variable, the standard deviation will be higher orange and blue curves.
Probability curves for locations with different average precipitation totals and variance standard deviations, SD The standard deviation SD not only tells us how far rainfall can be expected to vary from the average, but also shows the probability of such a variance. The other thing to consider is the amount of rainfall you can expect.
So, we need to consider the variability and compare it to the average. This is called the coefficient of variation, CV, and is also used as an indicator of stability. For the example above, this would be 1. If I had great programming and data skills, I could make a cool animated map of the US showing long-term rainfall CVs for a moving 3 week fall cover crop planting window. Watch what happens to rainfall over the High Plains in the late summer and fall, a common cover crop planting window.
From Brian Brettschneider, Climatologist49, on Twitter. Used with permission. Ask your local climate expert for the precipitation coefficient of variation for your critical cover crop growth period. The same can be done with temperature if that is your critical weather factor. Finally, consider that for more extreme deviations from normal rainfall, crop adaptations are less and less relevant because all crops need a certain amount of water and only thrive in a certain range of temperatures.
In these situations, mixtures and monocultures would most likely fare equally badly. To make bet-hedging work with cover crop mixtures, we need the unpredictable factor; here it is precip and temperature. We also need to place our bets on several different outcomes to account for that unpredictability. The different outcomes are the different species in the mixture. Here are some species adaptations that would be beneficial in a bet-hedging mixture: Ability to germinate in lower moisture soil Quick germination and establishment after a rainfall Ability to survive a short-term drought after establishment Crop species differ in these adaptations e.
Broadleaf or grass, legume, or Brassica, it does not matter as long as they expand the range of conditions such that at least one species in the mixture will handle what comes better than the others, i. Whether the mixture is better than a monoculture depends on if the range of conditions the mixture can handle is wider than that of any one crop species. There will be years where a monoculture will do better than the mixture.
In a review of cover crop mixture research Florence and McGuire, , cereal rye was nearly always the best producing species for the researched growing windows. It is the favored cover crop because it is easy to establish, fast growing, and surpasses all other species in growing in low temperatures. Since our most available cover crop windows are in the cool season, there are few cases where using cereal rye in a monoculture or a large share of a mixture would not make sense.
I will not analyze all the situations for bet-hedging mixtures, but here is where I think the strategy may or may not work. Where to use bet-hedging mixture and where not to? Given the factors we have discussed, bet-hedging mixtures should have higher odds of success in these scenarios: Generally, in locations where the critical weather rainfall, temperature, or both is highly variable.
Specifically, in regions that are normally dry and with variable rainfall, assuming you can find a mixture to handle the variability. Where variability is higher, the probability of picking the best species for monoculture decreases, but only so far. If the swings in rainfall are too drastic, then there may be no crops that grow well.
Longer growing windows that span two seasons. This is where bet-hedging mixtures have their best chance of success as the conditions across the growing window are going to vary much more than those within a single season.
For example, a mid-summer cover crop that grows into fall and winter. Where bet-hedging mixtures have lower odds of success: Irrigated cropping systems. Irrigation removes the uncertain rainfall factor. Late fall planting windows. Cool-season grasses will be the only species that can produce significant biomass, with cereal rye or winter triticale being the best. Where weather variability is small from year-to-year, or in wetter regions, it will be less difficult to pick the best species to grow as a monoculture or a bi-culture mix of a grass with a legume to take advantage of the proven nitrogen benefits.
If rainfall has filled the soil profile before planting, then a large amount of the weather availability has been eliminated and the risk is much reduced. Shorter growing windows. The shorter the window, the less variable weather the cover crop will face, and the less bet-hedging makes sense.
The inevitable tradeoffs Note that bet-hedging is not the beneficial interaction of different plant species symbiosis. It is solely a strategy to reduce the risk of a cover crop failure based on probability. And we know that because it is allowed in Las Vegas, it will never be a win-win in the long-term; you know who pays for all those lights. Bet hedging always incurs some loss.
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